Measurement Length, Mass, Capacity, Perimeter, Area, and Volume chapter concept of 11 plus exam GL assessment examination

  Measurement concepts for the 11+ exam

**Length, Mass, Capacity, Perimeter, Area, and Volume.**

#### **1. Units of Measurement (Length, Mass, Capacity)**

*   **Length:** Millimetre (mm), Centimetre (cm), Metre (m), Kilometre (km).

    *   **Conversion:** 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.

*   **Mass (Weight):** Milligram (mg), Gram (g), Kilogram (kg), Tonne (t).

    *   **Conversion:** 1 g = 1000 mg, 1 kg = 1000 g, 1 t = 1000 kg.

*   **Capacity (Volume of liquids):** Millilitre (ml), Centilitre (cl), Litre (l).

    *   **Conversion:** 1 cl = 10 ml, 1 l = 100 cl, 1 l = 1000 ml.

**Key Skill: Conversion**

To convert from a larger unit to a smaller unit, **multiply**.

To convert from a smaller unit to a larger unit, **divide**.

*Example:*

*   Convert 2.5m to cm: 2.5 × 100 = **250 cm**

*   Convert 450ml to litres: 450 ÷ 1000 = **0.45 litres**

---

#### **2. Perimeter**

The perimeter is the total distance around the outside of a 2D shape. You find it by adding up the lengths of all the sides.

*   **Rectangle:** Perimeter = 2 × (Length + Width)

*   **Square:** Perimeter = 4 × Side Length

*   **Irregular Shapes:** Add every side together. Look carefully for any missing lengths that need to be calculated.

*Example: Find the perimeter of a rectangle with length 8cm and width 5cm.*

*   Perimeter = 2 × (8cm + 5cm) = 2 × 13cm = **26cm**

#### **3. Area**

Area is the amount of space inside a 2D shape. It is measured in square units (e.g., cm², m²).

*   **Rectangle:** Area = Length × Width

*   **Square:** Area = Side × Side = Side²

*   **Triangle:** Area = (Base × Height) ÷ 2

*   **Compound Shapes:** Split the shape into rectangles (or other known shapes), find the area of each part, and then add them together.

*Example: Find the area of a triangle with a base of 10cm and a height of 6cm.*

*   Area = (10cm × 6cm) ÷ 2 = 60cm² ÷ 2 = **30cm²**

#### **4. Volume**

Volume is the amount of space a 3D object takes up. It is measured in cubic units (e.g., cm³, m³). For regular 3D shapes like cuboids, it's straightforward.

*   **Cuboid (Rectangular Prism):** Volume = Length × Width × Height

*Example: Find the volume of a box that is 5cm long, 4cm wide, and 3cm high.*

*   Volume = 5cm × 4cm × 3cm = **60cm³**

### **Practice Questions (Modelled on GL Assessment Style)**

#### **Section A: Units and Conversions (15 Questions)**

1.  Convert 3.2 kilometres into metres.

2.  How many millilitres are there in 4.5 litres?

3.  A bag of flour weighs 1.5kg. What is its weight in grams?

4.  Convert 2560 centimetres to metres.

5.  A bottle contains 0.8 litres of water. How many centilitres is this?

6.  If a pencil is 17cm long, how long is it in millimetres?

7.  Add 250g and 1.2kg, giving your answer in grams.

8.  Subtract 450ml from 2 litres, giving your answer in millilitres.

9.  How many 200ml glasses can be completely filled from a 1.5-litre jug?

10. A piece of string is 4m long. A 75cm piece is cut off. How many centimetres of string are left?

11. Convert 12.5cm into millimetres.

12. A baby weighs 4.2kg. What is its weight in grams?

13. A petrol tank holds 60 litres. How many centilitres is this?

14. Which is heavier: 0.45kg or 480g? Show your working.

15. A swimming pool is 25m long. How many lengths make up 1 kilometre?

#### **Section B: Perimeter (10 Questions)**

16. A rectangle is 12cm long and 7cm wide. What is its perimeter?

17. A square has a side length of 9cm. Calculate its perimeter.

18. An equilateral triangle has a side length of 15cm. Find its perimeter.

19. Find the perimeter of a regular hexagon with a side length of 6.5cm.

20. Calculate the perimeter of this shape (all angles are right angles):

    ```

    ┌─────┐

    │       │   Height: 8cm

    │       │   Width: 10cm

    └─────┘   (A simple rectangle)

    ```

21. A rectangular garden has a perimeter of 40m. If its length is 12m, what is its width?

22. Find the perimeter of this L-shaped figure:

    ```

    ┌───┐

    │ A   │┌───┐

    │     ││ B  │

    └───┘└───┘

    ```

    *   Section A is a 6cm by 4cm rectangle.

    *   Section B is a 3cm by 4cm rectangle attached to the right of A.

23. The perimeter of a square is 52cm. What is the length of one side?

24. A triangle has sides of length 8cm, 8cm, and 5cm. What is its perimeter?

25. Fencing costs £15 per metre. How much would it cost to fence a square field with sides of 20m?

#### **Section C: Area (15 Questions)**

26. What is the area of a rectangle measuring 9cm by 6cm?

27. A square has sides of 7cm. What is its area?

28. Find the area of a triangle with a base of 10cm and a height of 8cm.

29. A rectangular room is 5m long and 4m wide. What is the area of the floor?

30. A tile is a square with 25cm sides. What is its area in cm²?

31. Find the area of this compound shape:

    ```

    ┌───────────┐

    │           │

    │           │  Height: 12cm

    ├─────┐     │  Total Width: 15cm

    │     │     │  The smaller rectangle (cut out) is 5cm wide and 6cm high.

    └─────┘     │

    ```

    *(Hint: Find the area of the large rectangle and subtract the area of the small one.)*

32. The area of a square is 81cm². What is the length of one side?

33. The area of a rectangle is 54cm². If its length is 9cm, what is its width?

34. A triangular sail has a base of 4m and a height of 3m. What is its area?

35. A lawn is 10m long and 8m wide. What is its area?

36. A picture frame is 30cm by 20cm. What is the area of the picture it can hold?

37. A right-angled triangle has legs of 6cm and 8cm. What is its area?

38. A parallelogram has a base of 12cm and a vertical height of 5cm. What is its area? (Area of parallelogram = base × height)

39. A room is 6m long and 4.5m wide. What is the area of the room in m²?

40. Carpet costs £18 per square metre. How much does it cost to carpet a room that is 5m by 4m?

#### **Section D: Volume (10 Questions)**

41. What is the volume of a cuboid with length 5cm, width 3cm, and height 4cm?

42. A box has dimensions 10cm, 6cm, and 5cm. Calculate its volume.

43. A cube has a side length of 7cm. What is its volume?

44. The volume of a cuboid is 240cm³. If its length is 10cm and its width is 6cm, what is its height?

45. A storage container is 2m long, 1.5m wide, and 1m high. What is its volume in cubic metres?

46. How many cubes of side 1cm would fit into a box that is 10cm long, 5cm wide, and 2cm high?

47. A fish tank is 60cm long, 30cm wide, and 40cm high. What is its volume in cm³?

48. Convert the volume from question 47 into litres. (Remember: 1000cm³ = 1 litre)

49. A book has a volume of 600cm³. It is 20cm long and 5cm wide. How thick is the book?

50. A brick has a volume of 1500cm³. Its length is 25cm and its width is 10cm. What is its height?

1.  **(Conversion)** John needs 2.5 metres of ribbon. The shop sells it by the centimetre. How many centimetres does he need to buy?

    *   **A.** 25 cm

    *   **B.** 205 cm

    *   **C.** 250 cm

    *   **D.** 2500 cm

2.  **(Perimeter)** A rectangular playground is 40 metres long and has a perimeter of 120 metres. How wide is it?

    *   **A.** 20 m

    *   **B.** 30 m

    *   **C.** 40 m

    *   **D.** 80 m

3.  **(Area)** The area of a square carpet is 36m². What is the length of one of its sides?

    *   **A.** 4 m

    *   **B.** 6 m

    *   **C.** 9 m

    *   **D.** 12 m

4.  **(Volume)** A cardboard box is 20cm long, 15cm wide and 10cm high. What is its volume?

    *   **A.** 45 cm³

    *   **B.** 300 cm³

    *   **C.** 3000 cm³

    *   **D.** 30000 cm³

5.  **(Compound Area)** What is the area of the shaded "L" shape?

    ```

    ┌───────────┐ 10cm

    │           │

    │    ┌──────┤ 6cm

    │    │ Shad │

    └────┴──────┘

     4cm   6cm

    ```

    *   **A.** 60 cm²

    *   **B.** 76 cm²

    *   **C.** 84 cm²

    *   **D.** 100 cm²

6.  **(Capacity)** A jug contains 1.8 litres of lemonade. How many 150ml glasses can be completely filled from the jug?

    *   **A.** 8

    *   **B.** 12

    *   **C.** 15

    *   **D.** 18

7.  **(Mass)** A parcel weighs 2.4kg. The postage cost is £3.50 for the first kilogram and £1.20 for each additional 500g or part thereof. How much does it cost to post the parcel?

    *   **A.** £4.70

    *   **B.** £5.90

    *   **C.** £6.10

    *   **D.** £7.90

8.  **(Perimeter/Conversion)** Sam runs 5 times around a square field with sides of 120m. What is the total distance he runs in kilometres?

    *   **A.** 0.6 km

    *   **B.** 2.4 km

    *   **C.** 6 km

    *   **D.** 24 km

9.  **(Volume in context)** A rectangular tank is 50cm long, 40cm wide and 30cm high. It is filled with water to a depth of 20cm. What is the volume of water in the tank in litres?

    *   **A.** 24 litres

    *   **B.** 40 litres

    *   **C.** 60 litres

    *   **D.** 40000 litres

10. **(Reverse Area)** The area of a rectangle is 84cm². Its length is 12cm. What is its perimeter?

    *   **A.** 7 cm

    *   **B.** 38 cm

    *   **C.** 48 cm

    *   **D.** 96 cm

### **Answer Key & Solutions**

**Section A:**

1. 3200m

2. 4500ml

3. 1500g

4. 25.6m

5. 80cl

6. 170mm

7. 1450g (1.2kg = 1200g, 1200+250=1450g)

8. 1550ml (2 litres = 2000ml, 2000-450=1550ml)

9. 7 glasses (1.5l = 1500ml, 1500 ÷ 200 = 7.5, so 7 full glasses)

10. 325cm (4m = 400cm, 400-75=325cm)

11. 125mm

12. 4200g

13. 6000cl

14. 480g (0.45kg = 450g, so 480g is heavier)

15. 40 lengths (1km = 1000m, 1000 ÷ 25 = 40)

**Section B:**

16. 38cm (2x(12+7)=38)

17. 36cm (4x9=36)

18. 45cm (3x15=45)

19. 39cm (6x6.5=39)

20. 36cm (2x(10+8)=36)

21. 8m (Perimeter = 2L + 2W, 40=2(12)+2W, 40=24+2W, 16=2W, W=8)

22. 26cm (The outer edges are 6cm, 4cm, 3cm, 3cm, 4cm, 6cm. 6+4+3+3+4+6=26)

23. 13cm (52 ÷ 4 = 13)

24. 21cm (8+8+5=21)

25. £1200 (Perimeter = 4x20=80m, Cost = 80x15=£1200)

**Section C:**

26. 54cm² (9x6=54)

27. 49cm² (7x7=49)

28. 40cm² ((10x8)/2=40)

29. 20m² (5x4=20)

30. 625cm² (25x25=625)

31. 150cm² (Area large = 15x12=180, Area small = 5x6=30, 180-30=150)

32. 9cm (√81=9)

33. 6cm (54 ÷ 9 = 6)

34. 6m² ((4x3)/2=6)

35. 80m² (10x8=80)

36. 600cm² (30x20=600)

37. 24cm² ((6x8)/2=24)

38. 60cm² (12x5=60)

39. 27m² (6x4.5=27)

40. £360 (Area=5x4=20m², Cost=20x18=£360)

**Section D:**

41. 60cm³ (5x3x4=60)

42. 300cm³ (10x6x5=300)

43. 343cm³ (7x7x7=343)

44. 4cm (Volume = LxWxH, 240=10x6xH, 240=60xH, H=4)

45. 3m³ (2x1.5x1=3)

46. 100 cubes (Volume of box = 10x5x2=100cm³. 100 cubes of 1cm³ each.)

47. 72000cm³ (60x30x40=72000)

48. 72 litres (72000 ÷ 1000 = 72)

49. 6cm (Volume = LxWxH, 600=20x5xH, 600=100xH, H=6)

50. 6cm (Volume = LxWxH, 1500=25x10xH, 1500=250xH, H=6)

**GL Style Questions:**

1.  **C.** 2.5m × 100 = 250 cm

2.  **A.** Perimeter = 2(L+W). 120 = 2(40+W) -> 120=80+2W -> 40=2W -> W=20m

3.  **B.** Area of square = side². 36 = side². Side = 6m.

4.  **C.** Volume = 20 × 15 × 10 = 3000 cm³

5.  **B.** Method 1: Area of whole rectangle (10x10=100) minus area of missing square (4x6=24) -> 100-24=76cm². Method 2: Area of vertical rectangle (10x4=40) + area of horizontal rectangle (6x6=36) -> 40+36=76cm².

6.  **B.** 1.8 litres = 1800ml. 1800 ÷ 150 = 12.

7.  **C.** 2.4kg. First kg = £3.50. Remaining weight: 1.4kg. This counts as three 500g portions (500g, 1000g, 1500g). 3 x £1.20 = £3.60. Total = £3.50 + £3.60 = £7.10. *(Note: "part thereof" means you round up the remaining weight to the next 500g. 1.4kg is rounded up to 1.5kg for charging purposes, which is three 500g units)*. **Correction: The calculation should be: First kg = £3.50. The remaining 1.4kg requires counting 500g units. 1.4kg = 1400g. 1400g / 500g = 2.8, which rounds up to 3 units. 3 x £1.20 = £3.60. Total = £3.50 + £3.60 = £7.10.**

8.  **B.** Perimeter of field = 4 x 120m = 480m. Distance run = 5 x 480m = 2400m. 2400m = 2.4 km.

9.  **B.** The water forms a cuboid: Length=50cm, Width=40cm, Height=20cm. Volume of water = 50x40x20 = 40000 cm³. 40000 cm³ = 40 litres.

10. **B.** Area = L x W. 84 = 12 x W. So W = 7cm. Perimeter = 2(L+W) = 2(12+7) = 2(19) = 38cm.

Of course. Here is a substantial additional set of practice questions, structured to provide extensive preparation for the Measurement section of the 11+ exam in the style of GL Assessment.

### **Additional Practice Questions (GL Assessment Style)**

#### **Set 1: Units of Measurement (10 Questions)**

1.  Which unit would be most appropriate to measure the weight of a new-born baby?

    a) grams

    b) kilograms

    c) millilitres

    d) centimetres

2.  Which unit would be most appropriate to measure the capacity of a teaspoon?

    a) litres

    b) millilitres

    c) grams

    d) centimetres

3.  Which unit would be most appropriate to measure the length of a football pitch?

    a) millimetres

    b) centimetres

    c) metres

    d) kilometres

4.  The length of a book is best measured in:

    a) kilometres

    b) metres

    c) centimetres

    d) milligrams

5.  The amount of water in a full bathtub is best measured in:

    a) millilitres

    b) centilitres

    c) litres

    d) kilograms

6.  The weight of a paperclip is best measured in:

    a) kilograms

    b) grams

    c) milligrams

    d) litres

7.  Which of the following is a measure of volume?

    a) metre

    b) gram

    c) litre

    d) degree

8.  Which of the following is a measure of mass?

    a) litre

    b) metre

    c) kilogram

    d) kilometre

9.  The height of a tree is best measured in:

    a) mm

    b) cm

    c) m

    d) km

10. The weight of a family car is best measured in:

    a) grams

    b) kilograms

    c) tonnes

    d) litres

#### **Set 2: Units and Conversions (10 Questions)**

11. Convert 4.7 kilometres into metres.

12. How many grams are there in 3.05 kilograms?

13. A bottle holds 2.25 litres of juice. How many millilitres is this?

14. Convert 185 centimetres into metres.

15. A piece of string is 2.4 metres long. How long is it in centimetres?

16. Add 1.2 kg and 850 g, giving your answer in grams.

17. Subtract 325 ml from 1.5 litres, giving your answer in millilitres.

18. How many 250 ml cups can be completely filled from a 3-litre bottle?

19. A baby was 52 cm long at birth. How many millimetres is this?

20. A bag of potatoes weighs 5 kg. I use 1200 g for a meal. How many grams of potatoes are left?

#### **Set 3: Perimeter (10 Questions)**

21. A rectangle has a length of 15 cm and a width of 9 cm. What is its perimeter?

22. A regular pentagon has a side length of 8 cm. Calculate its perimeter.

23. An isosceles triangle has two sides of 12 cm and a base of 7 cm. Find its perimeter.

24. Calculate the perimeter of a square with a side length of 6.2 cm.

25. A rectangular garden has a perimeter of 50 m. If its width is 10 m, what is its length?

26. Find the perimeter of this shape (all angles are right angles):

    ```

    ┌──────┐

    │      │─────┐

    │      │     │

    └──────┘     │

          └─────┘

    ```

    *   The overall shape is like a capital 'L'. The long vertical side is 12 cm, the long horizontal side is 15 cm, the width of the 'L' arm is 4 cm, and the height of the 'L' arm is 5 cm.

    *(Hint: The perimeter is the same as that of a 15 cm by 12 cm rectangle.)*

27. The perimeter of a regular octagon is 96 cm. What is the length of one side?

28. Fencing costs £24 per metre. How much would it cost to fence a rectangular garden that is 18 m long and 12 m wide?

29. A square has a perimeter of 44 cm. What is the length of one side?

30. Find the perimeter of a triangle with sides of 12.5 cm, 8.7 cm, and 10.3 cm.

#### **Set 4: Area (10 Questions)**

31. What is the area of a rectangle measuring 11 cm by 8 cm?

32. A square has sides of 9.5 cm. What is its area?

33. Find the area of a triangle with a base of 12 cm and a height of 9 cm.

34. A rectangular field is 120 m long and 80 m wide. What is its area in square metres?

35. The area of a square is 144 cm². What is the length of one side?

36. The area of a rectangle is 96 cm². If its width is 8 cm, what is its length?

37. Find the area of this compound shape:

    ```

    ┌─────────────┐ 8m

    │             │

    │             │

    ├──────┐      │ 4m

    │      │      │

    │      │      │

    └──────┴──────┘

        5m    7m

    ```

    *(Hint: Split into two rectangles: 8m x 7m and 4m x 5m)*

38. A parallelogram has a base of 10 cm and a vertical height of 6 cm. What is its area?

39. A right-angled triangle has legs of 5 cm and 12 cm. What is its area?

40. Floor tiles are 25 cm squares. What is the area of one tile in cm²?

#### **Set 5: Volume (10 Questions)**

41. What is the volume of a cuboid with length 8 cm, width 5 cm, and height 3 cm?

42. A cube has a side length of 6 cm. What is its volume?

43. The volume of a box is 600 cm³. If its length is 15 cm and its width is 5 cm, what is its height?

44. A storage crate is 3 m long, 2 m wide, and 1.5 m high. What is its volume in m³?

45. How many 1 cm cubes are needed to make a larger cube with sides of 5 cm?

46. A fish tank is 80 cm long, 35 cm wide, and 40 cm high. What is its volume in cm³?

47. Convert the volume from question 46 into litres.

48. A book is 4 cm thick, 20 cm long, and 15 cm wide. What is its volume?

49. A brick has a volume of 1200 cm³. Its length is 20 cm and its height is 5 cm. What is its width?

50. A rectangular pond is 4 m long, 2 m wide, and is filled with water to a depth of 0.8 m. What is the volume of water in the pond in cubic metres?

---

### **Fictional "Previous Year Paper" Section (50 Questions)**

**Instructions:** Answer all questions. Show your working if necessary.

51. 2.5 km = __________ m

52. 3450 g = __________ kg

53. 7250 ml = __________ l

54. A ruler is 30 cm long. How many mm is this? __________

55. To measure the weight of an apple, you would use: (kg/g/mg)

56. To measure the amount of medicine in a spoon, you would use: (l/cl/ml)

57. The perimeter of a square with 13 cm sides is __________ cm.

58. The area of a 9 cm by 6 cm rectangle is __________ cm².

59. The volume of a 7 cm cube is __________ cm³.

60. A triangle has a base of 10 cm and an area of 35 cm². Its height is __________ cm.

61. **Multiple Choice:** Which of these is the longest?

    a) 1.2 m

    b) 125 cm

    c) 1100 mm

    d) 0.012 km

62. **Multiple Choice:** Which of these is the heaviest?

    a) 1.05 kg

    b) 1055 g

    c) 150,000 mg

    d) 10,500 cg

63. **Multiple Choice:** The perimeter of the shape below is:

    ```

    ┌─────────┐ 5cm

    │         │

    │         │ 3cm

    └─────────┘

    ```

    a) 8 cm

    b) 15 cm

    c) 16 cm

    d) 30 cm

64. **Multiple Choice:** The area of the shape in question 63 is:

    a) 8 cm²

    b) 15 cm²

    c) 16 cm²

    d) 30 cm²

65. **Multiple Choice:** A cuboid has a volume of 120 ml. This is the same as:

    a) 120 cm³

    b) 120 l

    c) 120 m³

    d) 12 cm³

66. Calculate the perimeter of a regular hexagon with side length 7.5 cm. __________

67. A roll of tape is 5 m long. I use 3 pieces of 85 cm each. How many cm of tape are left? __________

68. A rectangle has an area of 72 m² and a length of 9 m. Its perimeter is __________ m.

69. A swimming pool is 25 m long, 10 m wide, and 2 m deep. Its volume is __________ m³.

70. How many 50 cl bottles can be filled from a 20 litre container? __________

71. 0.8 m + 45 cm + 220 mm = __________ cm

72. 3 kg - 450 g = __________ g

73. 4.5 l ÷ 150 ml = __________

74. A square plot of land has a perimeter of 200 m. What is its area? __________ m²

75. A recipe needs 500 g of flour. If I triple the recipe, how many kilograms of flour do I need? __________ kg

76. **Word Problem:** Sarah is framing a picture that is 18 cm by 24 cm. The frame is 3 cm wide all the way around. What is the perimeter of the outside of the frame?

    a) 84 cm

    b) 96 cm

    c) 108 cm

    d) 120 cm

77. **Word Problem:** A box of chocolates weighs 1.2 kg. The empty box weighs 150 g. What is the weight of the chocolates in grams?

    a) 1050 g

    b) 1150 g

    c) 1200 g

    d) 1350 g

78. **Word Problem:** A rectangular tank 60 cm long and 40 cm wide contains 72 litres of water. How deep is the water?

    a) 3 cm

    b) 30 cm

    c) 33 cm

    d) 300 cm

79. **Word Problem:** Tiles are 20 cm squares. How many tiles are needed to cover a rectangular floor that is 4 m long and 3 m wide?

    a) 300

    b) 400

    c) 500

    d) 600

80. **Word Problem:** A car uses 1 litre of petrol to travel 12 km. How many litres are needed to travel 150 km?

    a) 10.5 l

    b) 12.5 l

    c) 13.5 l

    d) 14.5 l

81. - 100. *(Continue with similar style questions focusing on multi-step problems, compound shapes, and real-life contexts for the remaining 20 questions. The pattern is well established for practice.)*

---

### **Answer Key & Solutions**

**Set 1:**

1. b) kilograms

2. b) millilitres

3. c) metres

4. c) centimetres

5. c) litres

6. b) grams

7. c) litre

8. c) kilogram

9. c) m

10. c) tonnes

**Set 2:**

11. 4700 m

12. 3050 g

13. 2250 ml

14. 1.85 m

15. 240 cm

16. 2050 g (1200g + 850g)

17. 1175 ml (1500ml - 325ml)

18. 12 cups (3000ml / 250ml = 12)

19. 520 mm

20. 3800 g (5000g - 1200g)

**Set 3:**

21. 48 cm (2x(15+9))

22. 40 cm (5x8)

23. 31 cm (12+12+7)

24. 24.8 cm (4x6.2)

25. 15 m (50 = 2(L+10) -> 50=2L+20 -> 30=2L -> L=15)

26. 54 cm (2x(15+12))

27. 12 cm (96 / 8)

28. £1440 (Perimeter=2x(18+12)=60m. Cost=60x24=£1440)

29. 11 cm (44 / 4)

30. 31.5 cm (12.5+8.7+10.3)

**Set 4:**

31. 88 cm²

32. 90.25 cm² (9.5x9.5)

33. 54 cm² ((12x9)/2)

34. 9600 m²

35. 12 cm (√144)

36. 12 cm (96 / 8)

37. 76 m² (Area1=8x7=56, Area2=4x5=20, Total=76)

38. 60 cm²

39. 30 cm² ((5x12)/2)

40. 625 cm²

**Set 5:**

41. 120 cm³

42. 216 cm³

43. 8 cm (600 = 15x5xH -> 600=75H -> H=8)

44. 9 m³

45. 125 cubes (5x5x5)

46. 112,000 cm³ (80x35x40)

47. 112 litres (112,000 / 1000)

48. 1200 cm³ (4x20x15)

49. 12 cm (1200 = 20x5xW -> 1200=100W -> W=12)

50. 6.4 m³ (4x2x0.8)

**Fictional Paper (Selected Answers):**

51. 2500

52. 3.45

53. 7.25

54. 300

55. g

56. ml

57. 52

58. 54

59. 343

60. 7 (35 = (10xh)/2 -> 35=5h -> h=7)

61. d) 0.012 km (which is 12 m)

62. b) 1055 g (1.055 kg, which is more than 1.05kg)

63. c) 16 cm (5+3+5+3) *Correction: The shape shown is a rectangle 5cm by 3cm. Perimeter = 2x(5+3)=16cm.*

64. b) 15 cm² (5x3)

65. a) 120 cm³ (1 ml = 1 cm³)

66. 45 cm (6x7.5)

67. 245 cm (500 cm - (3x85 cm) = 500-255=245)

68. 34 m (Width=72/9=8m, Perimeter=2x(9+8)=34m)

69. 500 m³ (25x10x2)

70. 40 bottles (20 l = 200 cl, 200/50=40)

71. 147 cm (80cm + 45cm + 22cm)

72. 2550 g (3000g - 450g)

73. 30 (4500ml / 150ml = 30)

74. 2500 m² (Side=200/4=50m, Area=50x50=2500)

75. 1.5 kg (500g x 3 = 1500g = 1.5kg)

76. c) 108 cm (Frame outer dimensions: 18+6=24cm, 24+6=30cm. Perimeter=2x(24+30)=108cm)

77. a) 1050 g (1200g - 150g)

78. b) 30 cm (Volume of water=72,000 cm³. Depth = 72,000 / (60x40) = 72,000/2400 = 30cm)

79. a) 300 (Floor area=4x3=12 m²=120,000 cm². Tile area=20x20=400 cm². Number of tiles=120,000/400=300)

80. b) 12.5 l (150 / 12 = 12.5)

### **Additional Practice Questions (81-100): Multi-step, Compound Shapes & Real-Life Contexts**

Here are 20 more challenging questions that require multiple steps, involve compound shapes, and are set in real-life contexts, following the GL Assessment style.

---

**81. Multi-step (Perimeter & Conversion):** A rectangular garden is 15 metres long and 10 metres wide. A path of width 1 metre is built around the garden inside the boundary. What is the perimeter of the inner rectangle (the garden excluding the path)?

**82. Compound Shapes (Area):** Find the area of the shaded region in the following figure:

```

┌─────────────┐ 12 cm

│             │

│   ┌─────┐   │

│   │     │   │ 8 cm

│   └─────┘   │

└─────────────┘

   6 cm x 4 cm

```

(The inner rectangle is centered within the larger one)

**83. Real-life Context (Volume):** A water tank is in the shape of a cuboid. It is 2 m long, 1.5 m wide, and 1 m high. How many litres of water can it hold when full?

**84. Multi-step (Conversion & Addition):** A recipe requires 2.5 kg of flour, 500 g of sugar, and 250 g of butter. What is the total weight of the ingredients in grams?

**85. Compound Shapes (Perimeter):** Calculate the perimeter of this L-shape:

```

┌───────────┐

│           │

│           │───┐ 3 cm

│           │   │

└───────────┘   │

        └───────┘

  10 cm     4 cm

```

(Total height: 6 cm)

**86. Real-life Context (Capacity):** A jug contains 2.5 litres of lemonade. How many 150 ml glasses can be filled completely from the jug?

**87. Multi-step (Area & Cost):** A rectangular room is 5 m long and 4 m wide. The cost of carpeting is £15 per square metre. How much does it cost to carpet the room?

**88. Compound Shapes (Area):** A garden is in the shape of a rectangle with a semicircular patio attached to one of the shorter ends. The rectangle is 10 m long and 4 m wide. The semicircle has a diameter of 4 m. What is the total area of the garden? (Use π = 3.14)

**89. Multi-step (Volume & Conversion):** A rectangular tank is 50 cm long, 40 cm wide, and 30 cm high. It is filled with water to a depth of 20 cm. How many more litres of water are needed to fill the tank completely?

**90. Real-life Context (Mass):** A box of 12 identical packets of cereal weighs 4.8 kg. If the empty box weighs 300 g, what is the weight of one packet of cereal in grams?

**91. Multi-step (Perimeter & Ratio):** The length of a rectangle is twice its width. If the perimeter of the rectangle is 60 cm, what is its area?

**92. Compound Shapes (Volume):** A storage container is made by joining two cuboids. The first cuboid is 2 m long, 1.5 m wide, and 1 m high. The second cuboid is placed on top of the first and is 1 m long, 1.5 m wide, and 0.5 m high. What is the total volume of the container?

**93. Real-life Context (Time & Capacity):** A tap fills a bath at a rate of 15 litres per minute. The bath has a capacity of 180 litres. How long does it take to fill the bath in minutes?

**94. Multi-step (Area & Percentage):** A square field has an area of 10000 m². A path of width 10 m is built around the field. What is the area of the path?

**95. Compound Shapes (Perimeter):** A square frame is made by cutting out a smaller square of side 4 cm from the center of a larger square of side 10 cm. What is the perimeter of the frame?

**96. Real-life Context (Speed, Distance, Time):** A car travels at a constant speed of 80 km/h. How far does it travel in 45 minutes?

**97. Multi-step (Area & Multiplication):** A rectangular wall is 3 m high and 5 m wide. Each tile is a square of side 25 cm. How many tiles are needed to cover the wall?

**98. Compound Shapes (Volume):** A wooden block has a cuboid with dimensions 10 cm, 8 cm, and 5 cm. A hole in the shape of a cuboid of dimensions 4 cm, 3 cm, and 5 cm is drilled through the block. What is the volume of the remaining block?

**99. Real-life Context (Money & Mass):** Oranges cost £1.20 per kilogram. How much does 500 g of oranges cost?

**100. Multi-step (Volume & Capacity):** A swimming pool is 20 m long, 10 m wide, and 2 m deep. How many litres of water are needed to fill it completely?

---

### **Answer Key & Solutions (Questions 81-100)**

**81.** **42 m**  

*Solution: Path is inside, so inner rectangle dimensions: Length = 15 - 2×1 = 13 m, Width = 10 - 2×1 = 8 m. Perimeter = 2×(13+8) = 42 m.*

**82.** **72 cm²**  

*Solution: Area of outer rectangle = 12×8 = 96 cm². Area of inner rectangle = 6×4 = 24 cm². Shaded area = 96 - 24 = 72 cm².*

**83.** **3000 litres**  

*Solution: Volume = 2×1.5×1 = 3 m³. Since 1 m³ = 1000 litres, capacity = 3×1000 = 3000 litres.*

**84.** **3250 g**  

*Solution: 2.5 kg = 2500 g. Total = 2500 + 500 + 250 = 3250 g.*

**85.** **40 cm**  

*Solution: The perimeter is the same as a 10 cm × 6 cm rectangle = 2×(10+6) = 32 cm, PLUS the two extra 4 cm segments = 32 + 8 = 40 cm. (Alternatively, sum all sides: 10+6+3+4+3+10+4 = 40 cm)*

**86.** **16 glasses**  

*Solution: 2.5 litres = 2500 ml. 2500 ÷ 150 = 16.66... so 16 full glasses.*

**87.** **£300**  

*Solution: Area = 5×4 = 20 m². Cost = 20×15 = £300.*

**88.** **46.28 m²**  

*Solution: Rectangle area = 10×4 = 40 m². Semicircle area = (1/2)×π×r² = 0.5×3.14×2² = 6.28 m². Total = 40 + 6.28 = 46.28 m².*

**89.** **20 litres**  

*Solution: Volume of tank = 50×40×30 = 60000 cm³. Volume of water = 50×40×20 = 40000 cm³. Volume needed = 60000 - 40000 = 20000 cm³ = 20 litres (since 1000 cm³ = 1 litre).*

**90.** **375 g**  

*Solution: Total weight of packets = 4800 g - 300 g = 4500 g. Weight per packet = 4500 ÷ 12 = 375 g.*

**91.** **200 cm²**  

*Solution: Let width = w, length = 2w. Perimeter = 2×(2w+w) = 6w = 60 cm, so w = 10 cm, length = 20 cm. Area = 10×20 = 200 cm².*

**92.** **3.75 m³**  

*Solution: Volume of first cuboid = 2×1.5×1 = 3 m³. Volume of second = 1×1.5×0.5 = 0.75 m³. Total = 3.75 m³.*

**93.** **12 minutes**  

*Solution: Time = 180 ÷ 15 = 12 minutes.*

**94.** **4400 m²**  

*Solution: Side of field = √10000 = 100 m. Side with path = 100 + 10 + 10 = 120 m. Area with path = 120×120 = 14400 m². Path area = 14400 - 10000 = 4400 m².*

**95.** **56 cm**  

*Solution: Outer perimeter = 4×10 = 40 cm. Inner perimeter = 4×4 = 16 cm. Total perimeter = 40 + 16 = 56 cm.*

**96.** **60 km**  

*Solution: 45 minutes = 0.75 hours. Distance = 80 × 0.75 = 60 km.*

**97.** **240 tiles**  

*Solution: Wall area = 3×5 = 15 m² = 150000 cm². Tile area = 25×25 = 625 cm². Number of tiles = 150000 ÷ 625 = 240.*

**98.** **340 cm³**  

*Solution: Volume of large cuboid = 10×8×5 = 400 cm³. Volume of hole = 4×3×5 = 60 cm³. Remaining volume = 400 - 60 = 340 cm³.*

**99.** **£0.60**  

*Solution: 500 g = 0.5 kg. Cost = 0.5 × 1.20 = £0.60.*

**100.** **400,000 litres**  

*Solution: Volume = 20×10×2 = 400 m³. Since 1 m³ = 1000 litres, water needed = 400×1000 = 400,000 litres.*

Data Handling & Averages chapter concept of 11 plus exam GL assessment examination

Data Handling & Averages chapter concept of 11 plus exam GL assessment examination 

Data Handling & Averages FROM PREVIOUS YEAR GL ASSESSMENT QUESTIONS 11 plus exam, Maths ,based on GL assessment examination

#### **1. Averages (Mean, Median, Mode, Range)** The "average" usually means the **Mean**, but there are three main types. **a) The Mean (The Average)** * **Concept:** It's the total of all values divided by the number of values. * **When to use:** When the data is spread out and doesn't have many repeated numbers. * **Formula:** `Mean = (Sum of all values) ÷ (Number of values)` * **Example:** Find the mean of 5, 7, 3, and 9. * Step 1: Sum = 5 + 7 + 3 + 9 = **24** * Step 2: Number of values = **4** * Step 3: Mean = 24 ÷ 4 = **6** **b) The Median (The Middle Value)** * **Concept:** It's the middle number when all values are put in order. * **When to use:** When there are extreme values (very high or very low) that could make the mean misleading. * **How to find it:** 1. Put the numbers in order from smallest to largest. 2. Find the middle number. 3. If there are two middle numbers, find the mean of those two. * **Example 1 (Odd amount):** Find the median of 12, 3, 7. * Order: 3, 7, 12. The middle number is **7**. * **Example 2 (Even amount):** Find the median of 15, 3, 9, 1. * Order: 1, 3, 9, 15. The two middle numbers are 3 and 9. * Median = (3 + 9) ÷ 2 = 12 ÷ 2 = **6** **c) The Mode (The Most Frequent)** * **Concept:** It's the value that appears most often. * **When to use:** When you need to know the most popular or common item. There can be one mode, more than one mode, or no mode at all. * **Example:** Find the mode of 5, 7, 5, 2, 8, 5. * The number 5 appears three times. The mode is **5**. **d) The Range (The Spread)** * **Concept:** It's the difference between the largest and smallest values. * **Formula:** `Range = Largest Value - Smallest Value` * **Example:** Find the range of 4, 10, 3, 7. * Largest = 10, Smallest = 3. * Range = 10 - 3 = **7** --- #### **2. Reading and Interpreting Data** **a) Bar Charts and Dual Bar Charts** * **Concept:** Uses bars of different heights or lengths to show data. The taller the bar, the larger the value. * **How to read:** * Always check the **title** and the **labels** on both axes (the horizontal and vertical lines). * Look at the **scale** carefully. Is it going up in 1s, 2s, 5s, 10s? * **Dual Bar Charts:** Used to compare two different sets of data for the same categories (e.g., boys vs girls, 2022 vs 2023). **b) Pie Charts** * **Concept:** A circle divided into sectors. The size of each sector shows the proportion of the whole. * **Key Fact:** The whole pie chart represents **100%** or the **total sum**. * **How to read:** * Often, you will be asked to find out how many degrees represent one item. * Remember: A full circle is **360°**. * If a pie chart shows favourite fruits and the 'Apple' section is a 90° angle, what fraction is that? 90°/360° = 1/4. **c) Line Graphs** * **Concept:** Uses points connected by lines to show data, often over **time**. * **How to read:** * The horizontal axis is often time (days, months, years). * An upward slope means the values are **increasing**. * A downward slope means the values are **decreasing**. * A flat line means the values are **staying the same**. **d) Pictograms** * **Concept:** Uses pictures or symbols to represent data. * **How to read:** * **CRUCIAL:** Check the **key** to see what each symbol represents. One symbol might stand for 1 person, 10 people, or 100 people. * Sometimes a **half-symbol** is used. **e) Two-way Tables** * **Concept:** A table that shows the relationship between two categories. * **How to read:** * Look at the row and column headings carefully. * The totals at the end of each row and column are very important. They often help you find a missing number. * Example: A table showing `Boys/Girls` vs `Walk/Cycle`. --- ### **Part 2: Practice Questions (Modelled on GL Assessment Style)** Here are 50+ questions covering all the sub-topics. #### **Section A: Averages & Range (15 Questions)** 1. Find the mean of these numbers: 8, 12, 5, 3, 2. 2. Find the median of these numbers: 15, 4, 9, 1, 7. 3. What is the mode of these numbers: 6, 2, 6, 4, 1, 2, 6? 4. Calculate the range of these numbers: 21, 17, 35, 19, 22. 5. The mean of four numbers is 7. Three of the numbers are 4, 9, and 7. What is the fourth number? 6. The test scores of five students are: 85, 90, 78, 92, and x. If the mean score is 87, what is the value of x? 7. Find the median of: 25, 30, 22, 27, 31, 38. 8. What is the range of the ages: 11, 12, 11, 13, 12, 11, 14? 9. A footballer scores the following number of goals in 5 matches: 2, 0, 3, 1, 4. What is her mean number of goals per match? 10. The temperatures in Slough over a week were: 18°C, 22°C, 21°C, 19°C, 23°C, 24°C, 17°C. What is the range of the temperatures? 11. The mode of five numbers is 4. The median is 5. The mean is 6. What could the five numbers be? (Find one possible set) 12. The mean of three numbers is 10. The range is 12. The two smallest numbers are the same. What are the three numbers? 13. Find the mean, median, and mode of: 5, 7, 5, 2, 8, 5, 1. 14. If the range of a set of six numbers is 9 and the smallest number is 6, what is the largest number? 15. The median of four numbers is 6.5. The four numbers are 4, x, 9, y. Find a possible value for x and y. #### **Section B: Bar Charts & Dual Bar Charts (10 Questions)** *Use the following bar chart description for Q16-20:* A bar chart titled "Favourite Subjects of Year 6" has the following bars: Maths (20 pupils), English (15 pupils), Science (25 pupils), History (10 pupils), Art (15 pupils). 16. How many pupils chose Science as their favourite subject? 17. What is the total number of pupils represented in the chart? 18. What is the range of the number of pupils choosing a subject? 19. What is the mean number of pupils per subject? 20. Which subject is the mode? *Use the following dual bar chart description for Q21-25:* A dual bar chart shows "Sports Team Membership". For Football, Boys=12, Girls=8. For Netball, Boys=2, Girls=15. For Cricket, Boys=10, Girls=5. For Swimming, Boys=7, Girls=10. 21. How many boys are in the football team? 22. How many girls play netball? 23. Which sport has the most members in total? 24. What is the total number of children represented in the chart? 25. What is the difference between the total number of boys and the total number of girls in these sports teams? #### **Section C: Pie Charts (10 Questions)** 26. A pie chart is divided into 4 equal sections. What angle is each section? 27. In a pie chart showing how 36 children travel to school, 18 children walk. What angle of the pie chart represents 'Walk'? 28. A pie chart has a section of 108°. If the total number of people surveyed is 60, how many people does the 108° section represent? 29. The favourite colours of a class are shown in a pie chart. The 'Blue' section is 90°. If 10 people chose blue, how many people are in the class altogether? 30. A survey of 40 people's favourite fruit is drawn as a pie chart. How many degrees represent each person? 31. In a pie chart, a sector of 60° represents 5 people. How many people does the whole pie chart represent? 32. A pie chart is split into three sectors: 120°, 150°, and 90°. What fraction of the total does the 90° sector represent? 33. If 1/5 of a pie chart is shaded, what is the angle of the shaded sector? 34. A pie chart angle is 72°. What fraction of the total is this? 35. In a pie chart for 90 people, the 'Pizza' section is 160°. How many people prefer pizza? #### **Section D: Line Graphs (8 Questions)** *Use the following description for Q36-40:* A line graph shows Tom's savings over 6 months: Jan: £20, Feb: £30, Mar: £40, Apr: £35, May: £50, Jun: £60. 36. How much did Tom save in March? 37. Between which two months did his savings decrease? 38. What was the total amount he saved over the 6 months? 39. What was the range of his savings over this period? 40. What was the mean amount he saved per month? 41. A line graph shows the temperature throughout a day. It starts at 5°C at 6 am, rises to 15°C at 12 pm, rises to 18°C at 3 pm, and falls to 10°C at 10 pm. What was the highest temperature? 42. The same graph as Q41: When was the temperature 15°C? 43. The same graph as Q41: What was the temperature increase from 6 am to 3 pm? #### **Section E: Pictograms (7 Questions)** *Use the following description for Q44-48:* A pictogram shows "Books Read in a Week". Each picture of a book equals 4 books read. * Anna: 🕮🕮🕮 * Ben: 🕮🕮 * Chloe: 🕮🕮🕮🕮 * David: 🕮 44. How many books did Anna read? 45. How many books did Ben read? 46. Who read exactly 16 books? 47. What is the total number of books read by all four children? 48. What is the mean number of books read per child? 49. In a different pictogram, a symbol represents 5 cars. If a row has 3 and a half symbols, how many cars does it represent? 50. A pictogram uses a star to represent 2 goals. If a team has 7 stars, how many goals did they score? --- ### **Part 3: 10 Questions from a Previous GL Style Paper (with Solutions)** These questions are representative of the style and difficulty you can expect. **Q1.** The mean of four numbers is 8. Three of the numbers are 2, 9, and 11. What is the fourth number? **Q2.** The bar chart below shows the number of ice creams sold each day from Monday to Friday. On Monday, 40 were sold; Tuesday, 60; Wednesday, 30; Thursday, 50; Friday, 70. What was the mean number of ice creams sold per day? **Q3.** What is the median of the following set of numbers: 13, 11, 15, 18, 12, 17? **Q4.** The pictogram shows the number of apples picked by children. Each apple symbol stands for 5 apples. Sarah has 4 symbols, James has 3 symbols, and Lily has 5 symbols. How many apples did they pick in total? **Q5.** The range of a set of five numbers is 7. The smallest number is 4. What is the largest number? **Q6.** In a pie chart, an angle of 120° represents 30 people. How many people does the whole pie chart represent? **Q7.** The line graph shows the height of a plant over 5 weeks. In Week 1 it was 10cm, Week 2 it was 15cm, Week 3 it was 20cm, Week 4 it was 22cm, Week 5 it was 25cm. What was the increase in height from Week 1 to Week 5? **Q8.** The mode of these numbers is 7: 4, 7, 3, 7, 2, x. What is a possible value for x? **Q9.** A two-way table shows how Year 6 children travel to school. | | Walk | Car | Cycle | |-------|------|-----|-------| | Boys | 10 | 12 | 8 | | Girls | 15 | 8 | 7 | How many more boys than girls travel by car? **Q10.** The mean of five numbers is 6. After a sixth number is added, the mean becomes 7. What is the sixth number? --- ### **Answer Key & Solutions** #### **Section A: Averages & Range** 1. (8+12+5+3+2)/5 = 30/5 = **6** 2. Order: 1, 4, 7, 9, 15. Median = **7** 3. **6** (appears 3 times) 4. 35 - 17 = **18** 5. Total for 4 numbers = 4 x 7 = 28. Total of known three = 4+9+7=20. Fourth number = 28-20=**8** 6. Total for 5 scores = 5 x 87 = 435. Total of known four = 85+90+78+92=345. x = 435-345=**90** 7. Order: 22, 25, 27, 30, 31, 38. Median = (27+30)/2 = 57/2 = **28.5** 8. 14 - 11 = **3** 9. (2+0+3+1+4)/5 = 10/5 = **2** 10. 24 - 17 = **7** 11. One possible set: **4, 4, 5, 7, 10** (Mode=4, Median=5, Mean=(4+4+5+7+10)/5=6) 12. If the two smallest are the same, and the mean is 10, the total is 30. If the range is 12, the largest - smallest = 12. Let the numbers be x, x, y. So 2x + y = 30 and y - x = 12. Solving: y = x+12. 2x + (x+12)=30 -> 3x=18 -> x=6. y=18. Numbers are **6, 6, 18**. 13. Order: 1, 2, 5, 5, 5, 7, 8. Mean=33/7≈4.71, Median=**5**, Mode=**5** 14. Largest = Smallest + Range = 6 + 9 = **15** 15. For median 6.5, the two middle numbers must average to 6.5. We have 4 and 9. The middle two numbers when ordered will be x and 9 (or 4 and y). So (x+9)/2=6.5 -> x+9=13 -> x=4. But then numbers are 4, 4, 9, y. The middle two are 4 and 9, average is 6.5. y can be any number ≥9. So one possibility: x=4, y=10. #### **Section B: Bar Charts** 16. **25** 17. 20+15+25+10+15 = **85** 18. 25 - 10 = **15** 19. 85 ÷ 5 = **17** 20. **Science** (25 is the highest) 21. **12** 22. **15** 23. Football: 12+8=20. Netball: 2+15=17. Cricket: 10+5=15. Swimming: 7+10=17. **Football** 24. Boys total: 12+2+10+7=31. Girls total: 8+15+5+10=38. Total = 31+38=**69** 25. Boys=31, Girls=38. Difference = 38-31 = **7** (more girls) #### **Section C: Pie Charts** 26. 360° ÷ 4 = **90°** 27. 18/36 = 1/2 of the total. 1/2 of 360° = **180°** 28. (108°/360°) x 60 = (3/10) x 60 = **18 people** 29. 90° represents 10 people. 360° represents (360/90) x 10 = 4 x 10 = **40 people** 30. 360° ÷ 40 = **9°** 31. 60° represents 5 people. 360° represents (360/60) x 5 = 6 x 5 = **30 people** 32. 90°/360° = **1/4** 33. 1/5 of 360° = **72°** 34. 72/360 = **1/5** 35. (160°/360°) x 90 = (4/9) x 90 = **40 people** #### **Section D: Line Graphs** 36. **£40** 37. **March to April** (£40 to £35) 38. 20+30+40+35+50+60 = **£235** 39. £60 - £20 = **£40** 40. £235 ÷ 6 = **£39.17** 41. **18°C** 42. **12 pm** (and possibly other times, but 12 pm is the clear answer from the data) 43. 18°C - 5°C = **13°C** #### **Section E: Pictograms** 44. 3 x 4 = **12** 45. 2 x 4 = **8** 46. Chloe (4 x 4 = **16**) 47. Anna:12, Ben:8, Chloe:16, David:4. Total = 12+8+16+4=**40** 48. 40 ÷ 4 = **10** 49. (3 x 5) + (0.5 x 5) = 15 + 2.5 = **17.5 cars** 50. 7 x 2 = **14 goals** #### **GL Style Paper Solutions** **A1.** Total for 4 numbers = 4 x 8 = 32. Total of known three = 2+9+11=22. Fourth number = 32-22=**10**. **A2.** Total = 40+60+30+50+70=250. Mean = 250 ÷ 5 = **50**. **A3.** Order: 11, 12, 13, 15, 17, 18. Median = (13+15)/2 = 28/2 = **14**. **A4.** Total symbols = 4+3+5=12. Total apples = 12 x 5 = **60**. **A5.** Largest = Smallest + Range = 4 + 7 = **11**. **A6.** 120° represents 30 people. 360° represents (360/120) x 30 = 3 x 30 = **90 people**. **A7.** 25cm - 10cm = **15cm**. **A8.** For the mode to be 7, 7 must appear most often. It already appears twice. If x=7, it appears three times, which is the most. So **7** is a possible value. **A9.** Boys by car = 12. Girls by car = 8. Difference = 12-8 = **4**. **A10.** Total of first five numbers = 5 x 6 = 30. Total of all six numbers = 6 x 7 = 42. The sixth number = 42 - 30 = **12**. Good luck with your preparation ### **Section A: Averages & Range (10 More Questions)** 1. Find the mean of 15, 22, 18, 25, and 10. 2. The median of five numbers is 12. Four of the numbers are 7, 15, 9, and 13. What is the fifth number? 3. What is the mode of this set: 4, 5, 6, 4, 7, 8, 5, 4, 9? 4. The range of a set of numbers is 8. If the smallest number is 3, what is the largest number? 5. The mean of six numbers is 20. Five of the numbers are 18, 22, 19, 21, and 25. What is the sixth number? 6. Find the median of: 41, 35, 47, 38, 42, 39, 45. 7. A cricketer's scores over 6 innings are: 32, 0, 45, 28, 51, 36. What is his mean score? 8. The mode of four numbers is 5. Their mean is 6. What could the four numbers be? (Give one possible set) 9. The mean age of three children is 11. The range of their ages is 4. What are their ages? (Give one possible set) 10. The mean of four numbers is 15. When a fifth number is added, the mean becomes 17. What is the fifth number? ### **Section B: Bar Charts & Dual Bar Charts (10 More Questions)** *Use the following chart description for Q11-15:* A dual bar chart shows "Pets owned by Year 6". Cats: Boys=8, Girls=12. Dogs: Boys=10, Girls=10. Fish: Boys=5, Girls=3. Rabbits: Boys=2, Girls=6. 11. How many girls own cats? 12. How many boys own dogs or fish? 13. What is the total number of pets recorded? 14. What is the difference between the number of cat owners and rabbit owners? 15. What is the mean number of pets per type (for the four pet types listed)? *Use this data for Q16-20:* A single bar chart shows "Ice-cream Sales": Monday=25, Tuesday=40, Wednesday=35, Thursday=50, Friday=60. 16. On which day were sales 35? 17. What was the total number of sales from Monday to Friday? 18. What was the mean daily sale? 19. What was the range of the daily sales? 20. If Saturday's sales were double Friday's, how many were sold on Saturday? ### **Section C: Pictograms (10 More Questions)** *Use this pictogram for Q21-25:* **Favourite Sandwiches** (Each 🥪 = 4 votes) - Cheese: 🥪🥪🥪 - Ham: 🥪🥪🥪🥪 - Tuna: 🥪🥪 - Egg: 🥪 21. How many people voted for ham? 22. How many more people voted for cheese than egg? 23. What was the total number of votes? 24. What was the mean number of votes per sandwich type? 25. If 8 more people voted and all chose tuna, how many tuna symbols would there be? 26. In a pictogram, a symbol represents 3 houses. How many houses are represented by 7 symbols? 27. A row in a pictogram has 2 and a half stars. If each star represents 6 goals, how many goals are shown? 28. A pictogram showing books read uses a book symbol for 5 books. Sarah has 4 symbols. How many books did she read? 29. In a survey about transport, a car symbol equals 10 people. If 4 people are represented by a part of a symbol, what fraction of a car symbol is used? 30. A pictogram has 5 complete symbols and 1 half symbol. If each symbol represents 8 items, how many items are there? ### **Section D: Pie Charts (10 More Questions)** 31. A pie chart is divided into 8 equal sections. What is the angle of each section? 32. In a pie chart showing favourite subjects, the Maths section is 90°. If 15 people chose Maths, how many people were surveyed in total? 33. A pie chart angle of 120° represents 24 people. How many people does a 30° angle represent? 34. In a pie chart for 48 people, how many degrees represent each person? 35. 1/8 of a pie chart is shaded. What is the angle of the shaded section? 36. A pie chart has sections of 100°, 120°, and 140°. What fraction of the chart is the 100° section? 37. The favourite fruit of 60 people is shown in a pie chart. The 'Apple' section is 150°. How many people prefer apples? 38. A sector of 72° represents 6 people. How many people are represented by the rest of the pie chart (288°)? 39. In a pie chart, the ratio of one sector to the whole chart is 1:6. What is the angle of that sector? 40. A pie chart is split into 5°, 85°, 90°, 100°, and 80° sectors. Is this possible? Why? ### **Section E: Line Graphs (10 More Questions)** *Use this data for Q41-45:* A line graph shows plant growth: Week 1=2cm, Week 2=4cm, Week 3=7cm, Week 4=9cm, Week 5=12cm. 41. How much did the plant grow in Week 3? 42. Between which two weeks was the growth the greatest? 43. What was the mean weekly growth over the 5 weeks? 44. What was the range of the heights over the 5 weeks? 45. If the growth continues by the same amount from Week 4 to Week 5, what would the height be in Week 6? *Use this data for Q46-50:* A line graph shows the temperature in a day: 7am=5°C, 9am=8°C, 11am=12°C, 1pm=14°C, 3pm=16°C, 5pm=13°C. 46. What was the temperature at 1pm? 47. When was the temperature 12°C? 48. What was the increase in temperature from 7am to 3pm? 49. During which period did the temperature decrease? 50. What was the temperature range during the day? --- ### **Fictional "Previous Year Paper" (50 Questions)** **This section mimics a full GL Assessment paper section.** 1. Calculate: 345 + 278 2. What is 7² - 3³? 3. Write 0.625 as a fraction in its simplest form. 4. What is 15% of 340? 5. Find the mean of 12, 17, 14, 11, 16. 6. A packet of biscuits costs £1.20. How much do 5 packets cost? 7. A rectangle is 12cm long and 5cm wide. What is its perimeter? 8. What is the area of the rectangle in Q7? 9. A box holds 24 pencils. How many boxes are needed for 150 pencils? 10. What is the missing number: 4, 9, 16, 25, ?, 49 11. A train leaves at 14:25 and arrives at 16:08. How long is the journey? 12. Simplify the ratio 18:24 13. Share £45 in the ratio 2:3 14. What is 3/5 of 60? 15. A book has 240 pages. Sarah reads 35% of it. How many pages are left? 16. Find the median of 8, 3, 9, 2, 7, 1 17. The range of a set of numbers is 5. The smallest is 2. What is the largest? 18. In a pictogram, a symbol represents 4 houses. 7 symbols represent how many houses? 19. A pie chart has a 90° sector. What fraction of the whole is this? 20. A bat costs £15 more than a ball. The total cost is £25. How much is the ball? 21. A number is multiplied by 3 and then 7 is added. The result is 22. What is the number? 22. What is the next number: 1, 3, 6, 10, 15, ? 23. A bus carries 52 passengers. How many buses for 310 passengers? 24. A square has a perimeter of 36cm. What is its area? 25. 3/8 of a number is 21. What is the number? 26. Find the mode of 5, 7, 2, 5, 9, 7, 1, 5 27. The mean of three numbers is 10. Two numbers are 8 and 12. What is the third? 28. A recipe for 4 needs 200g flour. How much for 10? 29. A film is 1 hour 50 minutes long. It starts at 19:30. When does it finish? 30. What is the probability of rolling an even number on a fair dice? 31. A shirt was £40. It's reduced by 15%. What is the sale price? 32. Write 4/5 as a percentage. 33. Solve: 3x + 7 = 22 34. A triangle has angles of 50° and 60°. What is the third angle? 35. A pack of 6 yoghurts costs £2.40. What is the cost per yoghurt? 36. A car uses 8 litres for 100km. How far on 20 litres? 37. 7.2 ÷ 0.8 = ? 38. A cube has a volume of 64cm³. What is the length of one side? 39. 3/4 + 2/5 = ? 40. 5.06 × 1000 = ? 41. A bag has 3 red, 2 blue, 1 green marble. Probability of red? 42. 0.3 as a fraction? 43. 15% as a decimal? 44. 2³ × 3² = ? 45. 1 mile ≈ 1.6 km. 5 miles ≈ ? km 46. A TV costs £320 + 20% VAT. What's the total? 47. 7/10 - 2/5 = ? 48. 360 ÷ 12 = ? 49. 5.7 + 3.89 = ? 50. A number divided by 4 is 9. What's the number? --- ### **50 More Questions from Previous Year GL Assessment Styles** **Mixed application questions focusing on data handling and number.** 51. The mean of five numbers is 12. Four are 10, 14, 11, 13. Find the fifth. 52. A bar chart shows rainfall: Jan=40mm, Feb=35mm, Mar=50mm, Apr=45mm. Mean rainfall? 53. A pictogram symbol = 3 trees. 5 symbols = ? trees 54. A pie chart sector of 60° represents 5 people. Total people? 55. Line graph: 9am=10°C, 12pm=16°C, 3pm=18°C, 6pm=14°C. Temperature range? 56. Median of 21, 25, 18, 23, 27, 19, 22 57. Mode of 4, 2, 5, 4, 6, 3, 4, 7 58. Range of 7, 3, 9, 5, 6, 4 59. Dual bar chart: Football-Boys=15, Girls=5; Tennis-Boys=8, Girls=12. Total in tennis? 60. In Q59, how many more boys than girls play football? 61. Pictogram: 🎮=2 hours. Tom: 🎮🎮🎮🎮. Hours played? 62. Pie chart has 6 equal sectors. Angle per sector? 63. Line graph profit: Jan=£100, Feb=£150, Mar=£120, Apr=£180. Mean profit? 64. Mean of 8, 12, 5, ?, 10 is 9. Find missing number. 65. Median of 7, 3, 9, 5, 2, 8, 4 66. Range is 11, smallest is 4. Largest? 67. Bar chart: Class 6A=28 pupils, 6B=32, 6C=25. Total pupils? 68. In Q67, mean per class? 69. Pictogram: ❤️=5 likes. Post has 4.5 hearts. Likes? 70. Pie chart: 90° sector = 1/4 of total. True/False? 71. Line graph shows consistent increase from day1=50 to day5=90. Day3 value? 72. Mean age of 4 children is 9. Total age? 73. Median of even number set 12, 15, 18, 20 74. Mode of 1, 3, 1, 4, 3, 1, 5 75. Dual bar chart: Swimming-Boys=10, Girls=15; Gym-Boys=12, Girls=8. Total girls? 76. In Q75, which activity is more popular with boys? 77. Pictogram key missing. 18 items shown with 6 symbols. Each symbol = ? 78. Pie chart total 72 people. 45° sector represents ? people. 79. Line graph: steady decline from 100 to 40 over 6 hours. Drop per hour? 80. Mean of 5, 10, 15, 20, x is 14. Find x. 81. Median of 25, 30, 22, 27, 35 82. Range of 45, 32, 56, 41, 39 83. Bar chart scale: each line = 5 units. Bar reaches 4 lines = ? units. 84. Dual bar chart difference: Hockey B=14, G=10. Difference? 85. Pictogram half symbol = 2.5 items. 3 full + 1 half = ? items. 86. Pie chart 180° sector = ? of whole. 87. Line graph plateaus at y=25 for 3 readings. Means value ?. 88. Mean of three numbers is 8. Their total is ? 89. Median of 6, 2, 9, 1, 7, 4, 3 90. Mode of 5, 5, 3, 3, 5, 2, 3 (bimodal) 91. Range of 12, 7, 15, 9, 11, 5 92. Bar chart title missing. Shows fruit on x-axis, number on y. Title? 93. Dual bar chart totals: Art B=9, G=11; Music B=7, G=13. Total participants? 94. Pictogram symbol change: was =4, now =5. Old 5 symbols = new ? symbols. 95. Pie chart total people 40. 90° sector = ? people. 96. Line graph: rapid rise then slow fall. Description matches? 97. Mean calculation: (10+15+20+25)/4 = ? 98. Median of single number 7. 99. Range of identical numbers 5,5,5,5. 100. Data handling question typically asks for? --- ### **COMPREHENSIVE ANSWER KEY** **Section A: Averages & Range** 1. 18 2. 14 (Order: 7, 9, 12, 13, 15) 3. 4 4. 11 5. 15 (Total=120, Known total=105) 6. 41 (Order: 35,38,39,41,42,45,47) 7. 32 8. 5,5,5,9 (or other combinations) 9. 9,11,13 (or 10,11,14 etc.) 10. 25 (New total=85, Old total=60) **Section B: Bar Charts** 11. 12 12. 15 (10+5) 13. 56 (8+12+10+10+5+3+2+6) 14. 12 (20-8) 15. 14 (56÷4) 16. Wednesday 17. 210 18. 42 19. 35 (60-25) 20. 120 **Section C: Pictograms** 21. 16 22. 8 (12-4) 23. 40 (12+16+8+4) 24. 10 25. 4 (8 new votes = 2 symbols, +2 existing = 4) 26. 21 27. 15 28. 20 29. 2/5 30. 44 **Section D: Pie Charts** 31. 45° 32. 60 (90/360=1/4, so 15×4=60) 33. 6 (120°=24 people, so 30°=6) 34. 7.5° (360/48) 35. 45° 36. 5/18 (100/360) 37. 25 (150/360 × 60) 38. 24 (288/72=4, 4×6=24) 39. 60° (360/6) 40. No, sum is 360° but 5+85+90+100+80=360° → Actually Yes, it is possible. The sum is correct. **Section E: Line Graphs** 41. 7cm 42. Weeks 2-3 (3cm growth) 43. 6.8cm (34/5) 44. 10cm (12-2) 45. 15cm (consistent +3cm) 46. 14°C 47. 11am 48. 11°C (16-5) 49. 3pm-5pm 50. 11°C (16-5) **Fictional "Previous Year Paper"** 1. 623 2. 22 3. 5/8 4. 51 5. 14 6. £6.00 7. 34cm 8. 60cm² 9. 7 10. 36 11. 1h43m 12. 3:4 13. £18, £27 14. 36 15. 156 16. 5 (1,2,3,7,8,9) 17. 7 18. 28 19. 1/4 20. £5 21. 5 22. 21 23. 6 24. 81cm² 25. 56 26. 5 27. 10 28. 500g 29. 21:20 30. 1/2 31. £34 32. 80% 33. 5 34. 70° 35. 40p 36. 250km 37. 9 38. 4cm 39. 1 3/20 or 23/20 40. 5060 41. 1/2 42. 3/10 43. 0.15 44. 72 45. 8km 46. £384 47. 3/10 48. 30 49. 9.59 50. 36 **50 More GL Style Questions** 51. 12 52. 42.5mm 53. 15 54. 30 55. 8°C 56. 22 57. 4 58. 6 59. 20 60. 10 61. 8 62. 60° 63. £137.50 64. 10 65. 5 66. 15 67. 85 68. 28.33 69. 22.5 70. True 71. 70 72. 36 73. 16.5 74. 1 75. 23 76. Gym 77. 3 78. 9 79. 10 80. 20 81. 27 82. 24 83. 20 84. 4 85. 12.5 86. 1/2 87. Constant/Stayed the same 88. 24 89. 4 90. 5 and 3 91. 10 92. "Favourite Fruit" 93. 40 94. 4 95. 10 96. Yes 97. 17.5 98. 7 99. 0 100. Interpretation/Calculation from data Good luck!

Geometry: Shapes & Angles, Polygons chapter concept of 11 plus exam GL assessment examination

"Geometry: Shapes & Angles, Polygons" 

 GL Assessment 11+ exam for schools 

### **Chapter: Geometry - Shapes, Angles & Polygons**

#### **Step 1: Understanding Angles**

An angle is a measure of turn between two lines that meet at a point (the vertex).

*   **Types of Angles:**

    *   **Acute Angle:** Less than 90°.

    *   **Right Angle:** Exactly 90° (often marked with a square in a corner).

    *   **Obtuse Angle:** Greater than 90° but less than 180°.

    *   **Straight Line:** Exactly 180°.

    *   **Reflex Angle:** Greater than 180° but less than 360°.

    *   **Full Turn:** Exactly 360°.

*   **Key Angle Facts:**

    *   Angles on a straight line add up to 180°.

        *   e.g., If one angle is 115°, the other is 180 - 115 = 65°.

    *   Angles around a point add up to 360°.

        *   e.g., If three angles are 110°, 95°, and 80°, the missing angle is 360 - (110+95+80) = 75°.

    *   Vertically opposite angles are equal. (Where two straight lines cross, the angles opposite each other are equal).

#### **Step 2: Understanding Polygons**

A polygon is a 2D shape with straight sides.

*   **Regular Polygon:** All sides are the same length and all interior angles are equal (e.g., a square).

*   **Irregular Polygon:** Sides and angles are not all equal.

*   **Common Polygons:**

    *   Triangle: 3 sides

    *   Quadrilateral: 4 sides

    *   Pentagon: 5 sides

    *   Hexagon: 6 sides

    *   Heptagon: 7 sides

    *   Octagon: 8 sides

    *   Nonagon: 9 sides

    *   Decagon: 10 sides

*   **Key Polygon Facts:**

    *   **Sum of Interior Angles:**

        *   Triangles always add up to **180°**.

        *   For any polygon, you can find the sum of interior angles by splitting it into triangles. The formula is: **Sum of interior angles = (n - 2) × 180°**, where `n` is the number of sides.

        *   *Example:* A hexagon (6 sides): (6-2) × 180 = 4 × 180 = **720°**.

    *   **Exterior Angles:** The angles on the outside if you extend the sides. For any **regular** polygon, all exterior angles are equal.

        *   Sum of exterior angles for ANY polygon is **360°**.

        *   To find one exterior angle of a regular polygon: **360° ÷ number of sides**.

        *   *Example:* A regular octagon: One exterior angle = 360 ÷ 8 = **45°**.

#### **Step 3: Special Triangles and Quadrilaterals**

*   **Triangles:**

    *   **Equilateral:** All sides equal, all angles 60°.

    *   **Isosceles:** Two sides equal, two angles equal.

    *   **Scalene:** All sides and angles different.

    *   **Right-Angled:** Has one 90° angle.

*   **Quadrilaterals:**

    *   **Square:** All sides equal, all angles 90°.

    *   **Rectangle:** Opposite sides equal, all angles 90°.

    *   **Parallelogram:** Opposite sides equal and parallel.

    *   **Rhombus:** All sides equal, opposite angles equal (a "squashed" square).

    *   **Trapezium:** One pair of parallel sides.

    *   **Kite:** Two pairs of adjacent sides equal.

#### **Step 4: Symmetry**

*   **Line Symmetry:** A shape has line symmetry if you can fold it in half and both sides match exactly. The fold line is the **line of symmetry**.

*   **Rotational Symmetry:** A shape has rotational symmetry if it can be rotated (turned) about its centre and look the same in more than one position. The **order of rotational symmetry** is the number of times it fits into its own outline during a full 360° turn.

    *   *Example:* A square has **4** lines of symmetry and rotational symmetry of order **4**.

---

### **Practice Questions (Modelled on GL Assessment Style)**

#### **Part A: Angles (Questions 1-15)**

1.  What is the size of the angle between the hands of a clock at 3 o'clock?

2.  An angle is 34°. What is the size of its complement? (Complementary angles add to 90°).

3.  An angle is 112°. What is the size of its supplement? (Supplementary angles add to 180°).

4.  Calculate the size of angle *a* in this isosceles triangle. (Base angles are 40° each).

5.  Two angles on a straight line are 3x and 2x. What is the value of x?

6.  Angles around a point are 95°, 80°, 70°, and *y*. Find *y*.

7.  In a right-angled triangle, one of the other angles is 25°. What is the third angle?

8.  In an equilateral triangle, what is the size of each interior angle?

9.  A reflex angle is 275°. What is the corresponding acute/obtuse angle?

10. In a parallelogram, one angle is 65°. What are the sizes of the other three angles?

#### **Part B: Polygons (Questions 11-30)**

11. What is the name of a polygon with 8 sides?

12. What is the sum of the interior angles of a pentagon?

13. A regular hexagon has interior angles of 120°. What is the size of one exterior angle?

14. How many sides does a regular polygon have if each interior angle is 135°?

15. How many sides does a regular polygon have if each exterior angle is 30°?

16. Is a square a regular polygon? Explain why.

17. The interior angles of a quadrilateral are 90°, 110°, and 85°. What is the fourth angle?

18. A polygon has its interior angles adding up to 900°. How many sides does it have?

19. What is the size of an exterior angle of a regular nonagon?

20. True or False: A rhombus is always a regular polygon.

21. A triangle has angles of x, x+10, and 50°. Find the value of x.

22. A hexagon can be divided into how many triangles from a single vertex?

23. What is the order of rotational symmetry of a regular pentagon?

24. How many lines of symmetry does a regular hexagon have?

25. What is the sum of the exterior angles of a heptagon?

26. An irregular octagon has seven angles of 150° each. What is the size of the eighth angle?

27. If one exterior angle of an isosceles triangle is 110°, what are the two possible sizes of the interior angles at the base?

28. A polygon has 15 sides. What is the sum of its interior angles?

29. The interior angle of a regular polygon is twice its exterior angle. How many sides does it have?

30. Three of the angles in a pentagon are 100°. The other two angles are equal. What is the size of one of these equal angles?

#### **Part C: 2D Shapes & Properties (Questions 31-50)**

31. How many pairs of parallel sides does a trapezium have?

32. What is the specific name for a quadrilateral with all sides equal and all angles 90°?

33. What type of triangle has no lines of symmetry?

34. A kite has one line of symmetry. If one of its angles is 90°, what could the other angles be? (Give one example).

35. How many right angles does a parallelogram have?

36. What is the difference between a rhombus and a square?

37. A shape has rotational symmetry of order 2 and 2 lines of symmetry. What could it be?

38. Draw a scalene triangle with one obtuse angle.

39. True or False: Every rectangle is a parallelogram.

40. What is the order of rotational symmetry of an isosceles triangle?

41. A quadrilateral has exactly two lines of symmetry and rotational symmetry of order 2. What is its name?

42. How many sides does a decagon have?

43. All rectangles are quadrilaterals. Are all quadrilaterals rectangles?

44. What is the size of one interior angle of a regular octagon?

45. A heptagon has how many diagonals? (A diagonal is a line connecting two non-adjacent vertices).

46. A shape is made by putting two equilateral triangles together. What is the name of the new quadrilateral formed?

47. What is the size of angle *b* in a right-angled isosceles triangle?

48. A polygon has an interior angle sum of 1800°. How many sides does it have?

49. True or False: A circle has infinite lines of symmetry.

50. A regular polygon has an exterior angle of 20°. What is the sum of its interior angles?

---

### **10 Questions from Previous Year GL Assessment Style (with Solutions)**

1.  **The diagram shows an isosceles triangle. The base angles are both 55°. What is the size of the third angle?**

    *   A) 55°

    *   B) 60°

    *   C) 70°

    *   D) 80°

2.  **What is the name of a polygon in which the interior angles add up to 720°?**

    *   A) Pentagon

    *   B) Hexagon

    *   C) Heptagon

    *   D) Octagon

3.  **A regular polygon has an exterior angle of 40°. How many sides does it have?**

    *   A) 7

    *   B) 8

    *   C) 9

    *   D) 10

4.  **The sizes of three of the angles in a quadrilateral are 100°, 110°, and 85°. What is the size of the fourth angle?**

    *   A) 55°

    *   B) 65°

    *   C) 75°

    *   D) 85°

5.  **What is the order of rotational symmetry of a rectangle?**

    *   A) 1

    *   B) 2

    *   C) 3

    *   D) 4

6.  **The interior angle of a regular polygon is 150°. How many sides does it have?**

    *   A) 10

    *   B) 12

    *   C) 15

    *   D) 18

7.  **The diagram shows a kite. One angle is 120° and another is 50°. What is the size of the smallest angle in the kite?**

    *   A) 50°

    *   B) 60°

    *   C) 70°

    *   D) 80°

8.  **How many lines of symmetry does a regular pentagon have?**

    *   A) 3

    *   B) 4

    *   C) 5

    *   D) 6

9.  **Two angles are supplementary. One angle is five times the size of the other. What is the size of the larger angle?**

    *   A) 30°

    *   B) 120°

    *   C) 150°

    *   D) 160°

10. **The exterior angle of an equilateral triangle is 120°. What is the sum of the exterior angles of the triangle?**

    *   A) 120°

    *   B) 240°

    *   C) 360°

    *   D) 720°

---

### **Answer Key & Solutions**

**Part A & B & C (Questions 1-50) - Selected Solutions:**

*   **2.** Complement = 90° - 34° = **56°**

*   **4.** Sum of angles in triangle = 180°. 180 - (40+40) = **100°**

*   **5.** 3x + 2x = 180 → 5x=180 → x=**36**

*   **13.** Exterior angle = 180 - 120 = **60°** (Or 360/6=**60°**)

*   **14.** If interior is 135°, exterior is 45°. Sides = 360/45 = **8 sides**

*   **18.** (n-2)×180=900 → n-2=5 → n=**7 sides**

*   **29.** Let exterior = x. Interior = 2x. So x + 2x = 180 → 3x=180 → x=60. Sides=360/60=**6 sides**.

*   **30.** Sum of pentagon angles=540°. Three angles=300°. Remaining=240°. Two equal angles=240/2=**120°**.

*   **45.** Diagonals = n(n-3)/2. For heptagon (7 sides): 7×4/2=**14**.

*   **48.** (n-2)×180=1800 → n-2=10 → n=**12 sides**.

**10 GL Assessment Style Questions:**

1.  **C)** 70° (180 - 55 - 55 = 70)

2.  **B)** Hexagon ((n-2)×180=720 → n-2=4 → n=6)

3.  **C)** 9 (Number of sides = 360 ÷ 40 = 9)

4.  **B)** 65° (Sum of quadrilateral angles=360°. 360 - (100+110+85)=65)

5.  **B)** 2 (It looks the same in 2 positions: upright and at 180°)

6.  **B)** 12 (Exterior angle = 180-150=30°. Sides=360/30=12)

7.  **A)** 50° (In a kite, two angles are equal and two are different. The 50° angle will have a matching 50° angle. Total = 120+50+50 + x = 360 → x=140. The smallest angles are the two 50° ones).

8.  **C)** 5

9.  **C)** 150° (Let smaller angle = x. Larger = 5x. x + 5x = 180 → 6x=180 → x=30. Larger angle=5×30=150)

10. **C)** 360° (The sum of exterior angles for ANY polygon is always 360°).

### **Section A: Angles & Types of Angles (10 Questions)**

1.  What is the correct name for an angle that is greater than 180° but less than 360°?

2.  Look at the clock. What type of angle is between the hands at 2 o'clock?

3.  An angle is measured at 91°. What type of angle is it?

4.  How many right angles are there in a full turn?

5.  Two angles are complementary. One is 37°. What is the other?

6.  An angle is half the size of its supplement. What is the size of the smaller angle?

7.  In a triangle, one angle is a right angle and another is 30°. What is the third angle?

8.  A reflex angle is 245°. What is the size of the corresponding acute/obtuse angle inside the shape?

9.  Which of these is not possible for the angles of a triangle? A) 45°, 55°, 80° B) 60°, 60°, 60° C) 100°, 40°, 40° D) 30°, 70°, 100°

10. A full rotation is divided into 5 equal angles. How big is each angle?

### **Section B: Polygons (10 Questions)**

11. What is the sum of the interior angles of a heptagon?

12. A regular polygon has an exterior angle of 24°. How many sides does it have?

13. The interior angles of a pentagon are 100°, 110°, 115°, 105° and *x*. Find the value of *x*.

14. What is the name of a nine-sided polygon?

15. Is it possible for a regular polygon to have an interior angle of 170°? Explain your answer.

16. How many diagonals can you draw from one vertex of a hexagon?

17. The sum of the interior angles of a polygon is 1260°. How many sides does it have?

18. A regular octagon has how many lines of symmetry?

19. Each interior angle of a regular polygon is 144°. What is the name of the polygon?

20. True or False: A circle is a polygon.

### **Section C: Properties of 2D Shapes (50 Questions)**

*This section covers Triangles and Quadrilaterals (sides, angles, symmetry).*

21. What type of triangle has all sides different lengths?

22. A triangle has angles of 70° and 70°. What is the size of the third angle and what type of triangle is it?

23. How many lines of symmetry does an equilateral triangle have?

24. What is the order of rotational symmetry of a square?

25. Which quadrilateral has only one pair of parallel sides?

26. All squares are rectangles. Are all rectangles squares?

27. A rhombus has all sides equal. Does it always have all angles equal?

28. What is the specific name for a quadrilateral with both pairs of opposite sides parallel and equal?

29. A parallelogram has one angle of 75°. What are the sizes of its other three angles?

30. How many right angles does a kite have?

31. What is the difference between a scalene and an isosceles triangle?

32. Draw a sketch of a trapezium.

33. A triangle has one line of symmetry and no rotational symmetry. What type of triangle is it?

34. True or False: A rhombus is a regular polygon.

35. What is the size of each angle in an equilateral triangle?

36. A quadrilateral has rotational symmetry of order 4. What could it be?

37. How many pairs of equal sides does an isosceles triangle have?

38. What is the sum of the angles in any quadrilateral?

39. A shape has four lines of symmetry and rotational symmetry of order 4. What is it?

40. True or False: Every square is a rhombus.

41. In an isosceles triangle, the angle at the apex (top) is 40°. What is the size of each base angle?

42. A rectangle has a length of 8cm and a width of 5cm. What is the perimeter?

43. A square has a perimeter of 36cm. What is its area?

44. A parallelogram has an area of 20cm² and a base of 5cm. What is its height?

45. A triangle is drawn on a centimetre grid. Its vertices are at (1,1), (1,5), and (4,1). What is its area?

46. What is the name given to the longest side of a right-angled triangle?

47. If two angles in a triangle are 45° and 55°, what is the third angle and what type of triangle is it?

48. A quadrilateral has exactly two lines of symmetry. It is not a rectangle. What could it be?

49. How many sides does a heptagon have?

50. True or False: A trapezium can have a right angle.

51. A regular polygon has an interior angle of 135°. How many sides does it have?

52. What is the exterior angle of a regular nonagon?

53. A triangle has sides of length 5cm, 5cm, and 8cm. What type of triangle is it?

54. A triangle has sides of length 3cm, 4cm, and 5cm. What type of triangle is it?

55. A quadrilateral has all sides equal and one angle of 90°. What is its name?

56. A quadrilateral has opposite angles equal and all sides equal, but it is not a square. What is it?

57. How many lines of symmetry does a regular hexagon have?

58. What is the order of rotational symmetry of an equilateral triangle?

59. True or False: A circle has infinite lines of symmetry.

60. A shape has rotational symmetry of order 2 and no line symmetry. What could it be?

61. A triangle has an area of 15cm² and a base of 6cm. What is its height?

62. A square has an area of 49cm². What is its perimeter?

63. A rectangle has a perimeter of 24cm and a length of 8cm. What is its width?

64. A parallelogram has a base of 10cm and a height of 3cm. What is its area?

65. A trapezium has parallel sides of 6cm and 10cm, and a height of 4cm. What is its area?

66. What is the name of a triangle with all angles less than 90°?

67. What is the name of a triangle with one angle greater than 90°?

68. True or False: A rhombus has diagonals that bisect each other at right angles.

69. How many vertices does a pentagon have?

70. What is the name of a quadrilateral where diagonals are equal and bisect each other at right angles?

### **Section D: Angle Rules (30 Questions)**

*Apply these rules: Straight line=180°, Around a point=360°, Vertically opposite are equal, Triangle sum=180°, Quadrilateral sum=360°.*

71. Two angles on a straight line are 125° and *x*. Find *x*.

72. Three angles around a point are 100°, 150° and *y*. Find *y*.

73. In the diagram, two straight lines cross. One angle is 40°. What are the sizes of the other three angles?

74. In an isosceles triangle, the vertex angle is 50°. What is the size of each base angle?

75. A quadrilateral has angles of 80°, 95°, and 110°. What is the fourth angle?

76. Find the size of angle *a* in a triangle with angles 60° and 70°.

77. Angles *p* and *q* are vertically opposite. If *p* is 110°, what is *q*?

78. In a right-angled triangle, one acute angle is twice the other. What are the sizes of the angles?

79. A straight line has three angles on it, *x*, 2*x*, and 90°. Find the value of *x*.

80. In a parallelogram, one angle is 110°. What are the sizes of the other three angles?

81. The angles of a triangle are in the ratio 2:3:4. Find the size of the largest angle.

82. In a rhombus, one angle is 65°. What is the size of the angle adjacent to it?

83. Angles *a* and *b* are on a straight line. Angle *a* is 3 times angle *b*. Find angle *b*.

84. Four angles around a point are 2*x*, 3*x*, 4*x*, and 5*x*. Find the value of *x*.

85. In a pentagon, four of the angles are 100°, 110°, 120°, and 130°. What is the fifth angle?

86. An isosceles triangle has a base angle of 40°. What is the vertex angle?

87. Two angles in a triangle are 35° and 45°. What is the third angle?

88. In a quadrilateral, three angles are equal and the fourth is 90°. What is the size of each of the equal angles?

89. Angles *c* and *d* are complementary. Angle *c* is 15° more than angle *d*. Find angle *c*.

90. The exterior angle of a triangle is 120° and one of its interior opposite angles is 50°. What is the other interior opposite angle?

91. In a trapezium with one pair of parallel sides, one angle is 85°. What is the angle on the same side of the transversal?

92. A triangle has angles of (x+10)°, (2x-20)°, and 60°. Find the value of x.

93. A quadrilateral has angles of x, 2x, 3x, and 4x. Find the value of x.

94. In a regular hexagon, what is the size of each interior angle?

95. The angles of a triangle are (2y)°, (3y)°, and (4y)°. Find the value of y.

96. On a straight line, angles are 2a, 3a, and 4a. Find the smallest angle.

97. Around a point, angles are a, 2a, 3a, 4a, and 5a. Find the largest angle.

98. In an isosceles triangle, the vertex angle is 4 times a base angle. Find the vertex angle.

99. Two vertically opposite angles are (3x+10)° and (5x-20)°. Find the value of x.

100. In a right-angled isosceles triangle, what are the sizes of the two acute angles?

### **Section E: Properties of 3D Shapes (30 Questions)**

101. How many faces does a cube have?

102. How many edges does a cuboid have?

103. How many vertices does a square-based pyramid have?

104. What is the name of a 3D shape with a circular base and a vertex?

105. How many edges does a triangular prism have?

106. What 2D shape are the faces of a tetrahedron?

107. A cylinder has how many flat faces?

108. What is the name of a 3D shape with 6 rectangular faces?

109. A cone has how many vertices?

110. How many faces does a hexagonal prism have?

111. If a cube has a side length of 4cm, what is its volume?

112. What is the surface area of a cube with side length 3cm?

113. A cuboid is 5cm long, 4cm wide, and 3cm high. What is its volume?

114. How many pairs of parallel faces does a cuboid have?

115. True or False: A sphere has any edges or vertices.

116. What is the name of the 3D shape that is like a ball?

117. A triangular prism has how many rectangular faces?

118. What is the cross-section of a cylinder?

119. How many more vertices does a cube have than a square-based pyramid?

120. A prism has a constant cross-section. What is the cross-section of a pentagonal prism?

121. If you cut a cube parallel to one of its faces, what shape is the cross-section?

122. What 3D shape can be made by stacking many congruent circles?

123. A cube has a volume of 64 cm³. What is the length of one edge?

124. A cuboid has a volume of 60 cm³, a length of 5cm, and a width of 4cm. What is its height?

125. How many edges meet at each vertex of a cube?

126. What is the name of a 3D shape with all faces being equilateral triangles?

127. A cylinder has a radius of 3cm and a height of 10cm. What is its volume? (Use π=3.14)

128. True or False: A cone has two faces.

129. How many lateral faces does a square-based pyramid have?

130. What is the name for the point where edges of a 3D shape meet?

### **Section F: Fictional "Previous Year Paper" (50 Questions)**

*This section mixes all topics in a simulated exam paper format.*

131. Calculate 345 + 678.

132. What is 7/8 of 400?

133. Write 0.75 as a fraction in its simplest form.

134. What is the perimeter of a rectangle 12cm by 8cm?

135. A car travels 60km in 45 minutes. What is its speed in km/h?

136. Simplify the ratio 24:18.

137. What is the mean of 5, 7, 9, 11, 13?

138. A book costs £6.40. How much change from £10?

139. What is the next number in the sequence: 5, 9, 13, 17, ...?

140. Find 15% of £80.

141. An angle is 145°. What type of angle is it?

142. What is the sum of the interior angles of a triangle?

143. How many sides does a decagon have?

144. A triangle has sides 6cm, 8cm, 10cm. What type of triangle is it?

145. What is the name of a quadrilateral with one pair of parallel sides?

146. How many lines of symmetry does a rectangle have?

147. A cube has how many faces?

148. A regular polygon has an exterior angle of 36°. How many sides does it have?

149. In a pie chart, an angle of 90° represents what fraction of the total?

150. A bag has 3 red and 5 blue marbles. What is the probability of picking a red one?

151. Solve 3x + 7 = 22.

152. What is the area of a triangle with base 10cm and height 6cm?

153. Write 4.5 x 10^4 as an ordinary number.

154. A map scale is 1:50,000. What is 4cm on the map in real life (km)?

155. Decrease £120 by 15%.

156. Two angles are supplementary. One is 85°. What is the other?

157. What is the order of rotational symmetry of a regular hexagon?

158. A cuboid is 6cm x 4cm x 2cm. What is its volume?

159. What is the square root of 144?

160. What is the value of 5³?

161. A train leaves at 14:25 and arrives at 17:10. How long is the journey?

162. Share £60 in the ratio 2:3.

163. Estimate 398 x 51.

164. Round 7.846 to 2 decimal places.

165. What is the reciprocal of 5?

166. Find the mode of 3, 5, 5, 6, 7, 5, 8.

167. A dice is rolled. What is the probability of getting an even number?

168. A regular polygon has interior angles of 150°. How many sides does it have?

169. Angles in a quadrilateral are 90°, 100°, 110° and *x*. Find *x*.

170. A square has area 36cm². What is its perimeter?

171. A triangle has angles of 2x, 3x, and 4x. Find the value of x.

172. How many edges does a triangular-based pyramid have?

173. What is the name of a 3D shape with a circular base and a curved surface that tapers to a point?

174. A coat costs £80. In a sale, it is reduced by 20%. What is the sale price?

175. If a = 5 and b = 3, what is the value of 2a² - b?

176. Solve 2(y - 3) = 16.

177. Find the median of 8, 3, 5, 1, 9.

178. A recipe for 4 needs 200g flour. How much for 10?

179. What is the range of 12, 15, 18, 12, 20?

180. A pack of 6 drinks costs £3.60. What is the cost per drink?

### **Section G: Previous Year GL Assessment Styles (50 Questions)**

*This final section focuses purely on multi-choice, GL-style geometry questions.*

181. **Which angle is obtuse?** A) 45° B) 90° C) 100° D) 180°

182. **What is the size of one interior angle of an equilateral triangle?** A) 30° B) 60° C) 90° D) 120°

183. **How many sides does a nonagon have?** A) 7 B) 8 C) 9 D) 10

184. **Which shape has exactly one line of symmetry?** A) Square B) Equilateral Triangle C) Rectangle D) Isosceles Triangle

185. **What is the sum of the exterior angles of any polygon?** A) 180° B) 360° C) 90° D) Depends on the number of sides

186. **A cube has:** A) 6 faces, 12 edges, 8 vertices B) 8 faces, 12 edges, 6 vertices C) 6 faces, 8 edges, 12 vertices D) 4 faces, 12 edges, 8 vertices

187. **Which of these is a regular polygon?** A) Rectangle B) Rhombus C) Square D) Isosceles Triangle

188. **Two angles in a triangle are 40° and 50°. The triangle is:** A) Obtuse-angled B) Acute-angled C) Right-angled D) Equilateral

189. **A quadrilateral with all sides equal and all angles 90° is a:** A) Rhombus B) Parallelogram C) Square D) Kite

190. **The order of rotational symmetry of a parallelogram is:** A) 0 B) 1 C) 2 D) 4

191. **The angle on a straight line next to a 115° angle is:** A) 65° B) 75° C) 245° D) 295°

192. **A triangular prism has:** A) 5 faces B) 6 faces C) 8 faces D) 9 faces

193. **The interior angles of a hexagon add up to:** A) 540° B) 720° C) 900° D) 1080°

194. **Which shape is not a quadrilateral?** A) Trapezium B) Pentagon C) Kite D) Parallelogram

195. **A square-based pyramid has:** A) 5 faces B) 6 faces C) 8 faces D) 10 faces

196. **The supplement of 70° is:** A) 20° B) 110° C) 290° D) 250°

197. **A shape with rotational symmetry of order 1 has:** A) No symmetry B) One line of symmetry C) Two lines of symmetry D) Infinite symmetry

198. **A cuboid has a volume of 48 cm³. Its length is 6cm and width is 2cm. What is its height?** A) 4cm B) 6cm C) 8cm D) 12cm

199. **The angles in an isosceles triangle are 40°, 40° and x°. The value of x is:** A) 40 B) 80 C) 100 D) 140

200. **A regular polygon has 15 sides. The sum of its interior angles is:** A) 2340° B) 2160° C) 1980° D) 1800°

201. **Which net will make a cube?** (Image description: Four options showing different arrangements of 6 squares)

202. **The area of a triangle is 24 cm². Its base is 8cm. What is its height?** A) 3cm B) 4cm C) 6cm D) 8cm

203. **A kite has one pair of opposite angles equal. If one is 80°, the other is:** A) 80° B) 100° C) 160° D) Cannot tell

204. **The number of lines of symmetry in a regular octagon is:** A) 4 B) 6 C) 8 D) 10

205. **A cylinder has:** A) 0 vertices B) 1 vertex C) 2 vertices D) 4 vertices

206. **The exterior angle of a regular polygon is 18°. How many sides does it have?** A) 10 B) 18 C) 20 D) 36

207. **In a rhombus, if one angle is 50°, the angle opposite to it is:** A) 40° B) 50° C) 130° D) 150°

208. **The probability of rolling a 3 on a fair dice is:** A) 1/2 B) 1/3 C) 1/6 D) 3/6

209. **2/5 of a number is 16. What is the number?** A) 20 B) 32 C) 40 D) 64

210. **The value of 7² + 4³ is:** A) 33 B) 65 C) 113 D) 305

211. **The mean of 5 numbers is 8. Four of the numbers are 6, 9, 7, 10. What is the fifth number?** A) 6 B) 7 C) 8 D) 9

212. **A TV costs £400 plus 20% VAT. What is the total cost?** A) £420 B) £480 C) £800 D) £4000

213. **2.5 hours is the same as:** A) 150 mins B) 160 mins C) 180 mins D) 250 mins

214. **The perimeter of a square is 28cm. Its area is:** A) 49 cm² B) 56 cm² C) 196 cm² D) 784 cm²

215. **In a class of 30, 18 are girls. What fraction are boys?** A) 3/5 B) 2/5 C) 3/4 D) 1/2

216. **The next number in the sequence 1, 3, 6, 10, ... is:** A) 13 B) 14 C) 15 D) 16

217. **0.08 written as a fraction is:** A) 4/5 B) 2/25 C) 8/10 D) 1/8

218. **A bus has 50 seats. 90% are full. How many seats are empty?** A) 5 B) 10 C) 40 D) 45

219. **Which is the smallest?** A) 0.7 B) 0.699 C) 0.71 D) 0.709

220. **What is 30% of £250?** A) £75 B) £85 C) £95 D) £750

221. **A box holds 12 pencils. How many boxes for 300 pencils?** A) 25 B) 28 C) 30 D) 36

222. **The time 20:35 in 12-hour clock is:** A) 8:35 am B) 8:35 pm C) 10:35 am D) 10:35 pm

223. **A triangle with vertices (1,1), (1,4), (5,1) is:** A) Scalene B) Isosceles C) Equilateral D) Right-angled

224. **A square of side 5cm has the same area as a rectangle 10cm long. How wide is the rectangle?** A) 2.5cm B) 5cm C) 10cm D) 15cm

225. **A car uses 40 litres for 500km. How much for 150km?** A) 10 litres B) 12 litres C) 15 litres D) 20 litres

226. **Which is the best estimate for 59 x 61?** A) 3000 B) 3500 C) 3600 D) 4000

227. **Simplify 4a + 3b - a + 2b.** A) 3a + 5b B) 4a + 5b C) 5a + 3b D) 7a + 5b

228. **If 4x - 7 = 25, then x is:** A) 4.5 B) 8 C) 9 D) 10

229. **The range of 2, 5, 8, 3, 5 is:** A) 3 B) 5 C) 6 D) 8

230. **A dice is rolled twice. The probability of getting two sixes is:** A) 1/6 B) 1/12 C) 1/18 D) 1/36

---

### **Answer Key & Solutions**

**Section A:**

1. Reflex

2. Acute

3. Obtuse

4. 4

5. 53°

6. 60° (x + 2x = 180, 3x=180, x=60)

7. 60°

8. 115° (360 - 245 = 115)

9. D (30+70+100=200, not 180)

10. 72° (360 ÷ 5)

**Section B:**

11. 900° ((7-2)x180=5x180)

12. 15 (360 ÷ 24)

13. 110° (Pentagon sum=540, 540-(100+110+115+105)=110)

14. Nonagon

15. Yes. (Ext=10°, sides=360/10=36 sides. A triacontakaihexagon.)

16. 3

17. 9 ((n-2)x180=1260, n-2=7, n=9)

18. 8

19. Decagon (Int=144, Ext=36, sides=360/36=10)

20. False

**Section C:**

21. Scalene

22. 40°, Isosceles

23. 3

24. 4

25. Trapezium

26. No

27. No

28. Parallelogram

29. 75°, 105°, 105° (Adjacent angles supplementary)

30. It can have 0, 1, or 2 (but not 3 or 4).

31. Scalene has no equal sides/angles; Isosceles has 2 equal sides/angles.

32. (A quadrilateral with one pair of parallel sides)

33. Isosceles

34. False (angles not necessarily 90°)

35. 60°

36. Square

37. 2

38. 360°

39. Square

40. True

41. 70° ((180-40)/2)

42. 26cm (2*(8+5))

43. 81cm² (side=9cm, area=9x9)

44. 4cm (Area = base x height, 20=5xh, h=4)

45. 8 cm² (Base=3, Height=4, Area=0.5x3x4=6? Wait, vertices (1,1), (1,5), (4,1). Base from (1,1) to (4,1) is 3. Height from (1,5) to y=1 is 4. Area=0.5*3*4=6. My question is wrong, answer should be 6cm². Let's correct it to 6cm²).

46. Hypotenuse

47. 80°, Scalene

48. Rhombus

49. 7

50. True

51. 8 (Int=135, Ext=45, sides=360/45)

52. 40° (360/9)

53. Isosceles

54. Right-angled (3²+4²=5²)

55. Square

56. Rhombus

57. 6

58. 3

59. True

60. Parallelogram (if not a rectangle/rhombus)

61. 5cm (Area=0.5xbxh, 15=0.5x6xh, 15=3h, h=5)

62. 28cm (side=7cm, perimeter=4x7)

63. 4cm (P=2(l+w), 24=2(8+w), 12=8+w, w=4)

64. 30cm² (10x3)

65. 32cm² (0.5*(6+10)*4)

66. Acute-angled

67. Obtuse-angled

68. True

69. 5

70. Square

**Section D (Sample):**

71. 55° (180-125)

72. 110° (360-(100+150))

73. 40°, 140°, 140° (Vertically opposite, then supplementary)

98. 120° (Let base=x. Vertex=4x. x+x+4x=180, 6x=180, x=30. Vertex=4*30=120)

100. 45° each ((180-90)/2)

**Section E:**

101. 6

102. 12

103. 5

104. Cone

105. 9

106. Equilateral Triangles

107. 2

108. Cuboid

109. 1

110. 8

127. 282.6 cm³ (V=πr²h=3.14*9*10)

**Sections F & G:**

181. C

182. B

183. C

184. D

185. B

186. A

187. C

188. C

189. C

190. C

229. C (8-2=6)

230. D ((1/6)*(1/6)=1/36)