Thursday, January 1, 2026

Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -2

 

Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -2

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

  1. How many faces does a cube have?

  2. How many edges does a cuboid have?

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

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

  5. How many edges does a triangular prism have?

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

  7. A cylinder has how many flat faces?

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

  9. A cone has how many vertices?

  10. How many faces does a hexagonal prism have?

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

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

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

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

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

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

  17. A triangular prism has how many rectangular faces?

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

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

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

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

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

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

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

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

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

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

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

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

  30. 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.

  1. Calculate 345 + 678.

  2. What is 7/8 of 400?

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

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

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

  6. Simplify the ratio 24:18.

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

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

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

  10. Find 15% of £80.

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

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

  13. How many sides does a decagon have?

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

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

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

  17. A cube has how many faces?

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

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

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

  21. Solve 3x + 7 = 22.

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

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

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

  25. Decrease £120 by 15%.

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

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

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

  29. What is the square root of 144?

  30. What is the value of 5³?

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

  32. Share £60 in the ratio 2:3.

  33. Estimate 398 x 51.

  34. Round 7.846 to 2 decimal places.

  35. What is the reciprocal of 5?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  50. 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.

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

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

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

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

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

  6. 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

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

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

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

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

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

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

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

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

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

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

  17. 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

  18. 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

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

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

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

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

  23. 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

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

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

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

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

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

  29. 2/5 of a number is 16. What is the number? A) 20 B) 32 C) 40 D) 64

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

  31. 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

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

  33. 2.5 hours is the same as: A) 150 mins B) 160 mins C) 180 mins D) 250 mins

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

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

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

  37. 0.08 written as a fraction is: A) 4/5 B) 2/25 C) 8/10 D) 1/8

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

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

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

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

  42. 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

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

  44. 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

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

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

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

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

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

  50. 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 WITH EXPLANATION

Section E: 3D Shapes & Properties

1. How many faces does a cube have?
A cube has 6 faces (all squares).
Answer: 6

2. How many edges does a cuboid have?
A cuboid has 12 edges.
Answer: 12

3. How many vertices does a square-based pyramid have?
Square base (4 vertices) + apex (1) = 5 vertices.
Answer: 5

4. What is the name of a 3D shape with a circular base and a vertex?
Cone.
Answer: Cone

5. How many edges does a triangular prism have?
Triangular prism: 2 triangular faces, 3 rectangular faces → 9 edges.
Check: triangles have 3 edges each but prism has side edges: total edges = 3 × 3 = 9.
Answer: 9

6. What 2D shape are the faces of a tetrahedron?
All faces are equilateral triangles.
Answer: Equilateral triangles

7. A cylinder has how many flat faces?
Two circular flat faces (top and bottom) = 2 flat faces.
Answer: 2

8. What is the name of a 3D shape with 6 rectangular faces?
Cuboid (or rectangular prism).
Answer: Cuboid

9. A cone has how many vertices?
A cone has 1 vertex (apex).
Answer: 1

10. How many faces does a hexagonal prism have?
Hexagonal prism: 2 hexagonal faces + 6 rectangular faces = 8 faces.
Answer: 8

11. If a cube has a side length of 4cm, what is its volume?
Volume = side³ = 4³ = 64 cm³.
Answer: 64 cm³

12. What is the surface area of a cube with side length 3cm?
Surface area = 6 × side² = 6 × 9 = 54 cm².
Answer: 54 cm²

13. A cuboid is 5cm long, 4cm wide, and 3cm high. What is its volume?
Volume = length × width × height = 5 × 4 × 3 = 60 cm³.
Answer: 60 cm³

14. How many pairs of parallel faces does a cuboid have?
A cuboid has 3 pairs of parallel faces.
Answer: 3

15. True or False: A sphere has any edges or vertices.
False — a sphere has no edges and no vertices.
Answer: False

16. What is the name of the 3D shape that is like a ball?
Sphere.
Answer: Sphere

17. A triangular prism has how many rectangular faces?
Triangular prism: 3 rectangular faces (if right prism) + 2 triangular faces.
Answer: 3

18. What is the cross-section of a cylinder?
A cross-section parallel to base is a circle.
Answer: Circle

19. How many more vertices does a cube have than a square-based pyramid?
Cube vertices = 8, pyramid vertices = 5. Difference = 3 more.
Answer: 3

20. A prism has a constant cross-section. What is the cross-section of a pentagonal prism?
Pentagon.
Answer: Pentagon

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

22. What 3D shape can be made by stacking many congruent circles?
Cylinder.
Answer: Cylinder

23. A cube has a volume of 64 cm³. What is the length of one edge?
Edge length = cube root of 64 = 4 cm.
Answer: 4 cm

24. A cuboid has a volume of 60 cm³, a length of 5cm, and a width of 4cm. What is its height?
Height = Volume ÷ (length × width) = 60 ÷ (5 × 4) = 60 ÷ 20 = 3 cm.
Answer: 3 cm

25. How many edges meet at each vertex of a cube?
3 edges meet at each vertex of a cube.
Answer: 3

26. What is the name of a 3D shape with all faces being equilateral triangles?
Tetrahedron (if 4 faces) or possibly octahedron (8 faces) but simplest: tetrahedron.
Given: all faces equilateral triangles → tetrahedron has 4 such triangles.
Answer: Tetrahedron

27. A cylinder has a radius of 3cm and a height of 10cm. What is its volume? (Use Ο€=3.14)
Volume = Ο€r²h = 3.14 × 9 × 10 = 282.6 cm³.
Answer: 282.6 cm³

28. True or False: A cone has two faces.
True — one curved face + one circular flat face = 2 faces.
Answer: True

29. How many lateral faces does a square-based pyramid have?
Lateral faces = faces excluding base = 4 triangular faces.
Answer: 4

30. What is the name for the point where edges of a 3D shape meet?
Vertex (plural vertices).
Answer: Vertex

Section F: Fictional "Previous Year Paper"

  1. 345 + 678 = 1023
    Answer: 1023

  2. 7/8 of 400 = 350
    Answer: 350

  3. 0.75 = 3/4
    Answer: 3/4

  4. Perimeter of rectangle 12cm by 8cm = 2×(12+8) = 40 cm
    Answer: 40 cm

  5. Speed: 45 mins = 0.75 hours → speed = 60 km ÷ 0.75 h = 80 km/h
    Answer: 80 km/h

  6. Simplify 24:18 = 4:3
    Answer: 4:3

  7. Mean of 5,7,9,11,13 = (5+7+9+11+13)/5 = 45/5 = 9
    Answer: 9

  8. Change from £10 for £6.40 = £3.60
    Answer: £3.60

  9. Next in sequence 5,9,13,17 → +4 → 21
    Answer: 21

  10. 15% of £80 = £12
    Answer: £12

  11. 145° = Obtuse angle (between 90° and 180°)
    Answer: Obtuse

  12. Sum of interior angles of a triangle = 180°
    Answer: 180°

  13. Decagon sides = 10
    Answer: 10

  14. Sides 6,8,10 → right-angled (6²+8²=10²)
    Answer: Right-angled

  15. Quadrilateral with one pair of parallel sides = Trapezium
    Answer: Trapezium

  16. Lines of symmetry in a rectangle = 2
    Answer: 2

  17. Cube faces = 6
    Answer: 6

  18. Exterior angle 36° → sides = 360/36 = 10
    Answer: 10

  19. 90° in pie chart = 1/4 of total
    Answer: 1/4

  20. Probability red = 3/(3+5) = 3/8
    Answer: 3/8

  21. 3x + 7 = 22 → 3x=15 → x=5
    Answer: 5

  22. Area of triangle = ½×10×6 = 30 cm²
    Answer: 30 cm²

  23. 4.5×10⁴ = 45,000
    Answer: 45,000

  24. Scale 1:50,000 → 4 cm = 4×50,000 cm = 200,000 cm = 2 km
    Answer: 2 km

  25. Decrease £120 by 15%: 15% of 120 = 18 → 120−18 = 102
    Answer: £102

  26. Supplementary to 85° = 95°
    Answer: 95°

  27. Rotational symmetry of regular hexagon = order 6
    Answer: 6

  28. Cuboid volume 6×4×2 = 48 cm³
    Answer: 48 cm³

  29. √144 = 12
    Answer: 12

  30. 5³ = 125
    Answer: 125

  31. Journey 14:25 to 17:10 = 2h45m = 2.75h or 165 mins
    Answer: 2h45m or 165 mins

  32. Share £60 in 2:3 → 2/5×60=£24, 3/5×60=£36
    Answer: £24 and £36

  33. Estimate 398×51 ≈ 400×50 = 20,000
    Answer: 20,000

  34. 7.846 to 2 d.p. = 7.85
    Answer: 7.85

  35. Reciprocal of 5 = 1/5
    Answer: 1/5

  36. Mode of 3,5,5,6,7,5,8 = 5
    Answer: 5

  37. Probability even on dice = 3/6 = 1/2
    Answer: 1/2

  38. Interior 150° → exterior 30° → sides = 360/30 = 12
    Answer: 12

  39. Quadrilateral: 90+100+110+x=360 → x=60°
    Answer: 60°

  40. Area 36cm² → side = 6cm → perimeter = 24cm
    Answer: 24 cm

  41. 2x+3x+4x=180 → 9x=180 → x=20°
    Answer: 20

  42. Triangular-based pyramid edges = 6
    Answer: 6

  43. Circular base, tapers to point = Cone
    Answer: Cone

  44. £80 reduced by 20% = 80−16=£64
    Answer: £64

  45. a=5, b=3 → 2a²−b = 2×25−3=50−3=47
    Answer: 47

  46. 2(y−3)=16 → y−3=8 → y=11
    Answer: 11

  47. Median of 1,3,5,8,9 = 5
    Answer: 5

  48. Recipe: for 10 people → 200×(10/4)=500g flour
    Answer: 500 g

  49. Range of 12,15,18,12,20 = 20−12=8
    Answer: 8

  50. Cost per drink = £3.60 ÷ 6 = £0.60
    Answer: £0.60

Section G: Multi-Choice GL Style

  1. Obtuse angle: C) 100° (between 90° and 180°)
    Answer: C

  2. Equilateral triangle interior angle: B) 60°
    Answer: B

  3. Nonagon sides: C) 9
    Answer: C

  4. Exactly one line of symmetry: D) Isosceles Triangle
    Answer: D

  5. Sum exterior angles: B) 360° (always)
    Answer: B

  6. Cube facts: A) 6 faces, 12 edges, 8 vertices
    Answer: A

  7. Regular polygon: C) Square
    Answer: C

  8. Triangle with 40°,50° → third 90°: C) Right-angled
    Answer: C

  9. All sides equal, all angles 90°: C) Square
    Answer: C

  10. Rotational symmetry of parallelogram: C) 2
    Answer: C

  11. On straight line next to 115°: A) 65°
    Answer: A

  12. Triangular prism faces: B) 6 faces (5 faces? No, it’s 5 actually? Wait: 2 triangles + 3 rectangles = 5 faces total? Check: triangular prism has 5 faces. But GL often says 5. Given options: A)5 B)6 C)8 D)9 → answer is A) 5 faces.)
    Actually: Standard triangular prism has 5 faces. But some count bases differently — but mathematically: 2 triangular + 3 rectangular = 5 faces.
    Answer: A) 5 faces

  13. Hexagon interior sum: B) 720°
    Answer: B

  14. Not quadrilateral: B) Pentagon
    Answer: B

  15. Square-based pyramid faces: A) 5 faces
    Answer: A

  16. Supplement of 70°: B) 110°
    Answer: B

  17. Rotational symmetry order 1: A) No symmetry
    Answer: A

  18. Cuboid volume 48, length 6, width 2: height = 48/(6×2)=4 → A) 4cm
    Answer: A

  19. Isosceles triangle 40°,40°,x: C) 100°
    Answer: C

  20. 15-sided polygon interior sum: A) 2340°
    Answer: A

  21. Which net makes a cube? (No image, but typical answer is the one with 6 squares arranged in T or cross shape)
    Answer: (Cannot choose without image)

  22. Triangle area 24, base 8: height = (2×24)/8=6 → C) 6cm
    Answer: C

  23. Kite opposite angles equal: one 80°, other: A) 80°
    Answer: A

  24. Lines of symmetry in regular octagon: C) 8
    Answer: C

  25. Cylinder vertices: A) 0 vertices (curved surface, no vertices)
    Answer: A

  26. Exterior angle 18° → sides = 360/18=20 → C) 20
    Answer: C

  27. Rhombus opposite angle to 50°: B) 50°
    Answer: B

  28. Probability of 3 on dice: C) 1/6
    Answer: C

  29. 2/5 of number = 16 → number = 16×(5/2)=40 → C) 40
    Answer: C

  30. 7² + 4³ = 49 + 64 = 113 → C) 113
    Answer: C

  31. Mean of 5 numbers is 8, four are 6,9,7,10 total=32, fifth = 40−32=8 → C) 8
    Answer: C

  32. £400 + 20% VAT = 400×1.2=480 → B) £480
    Answer: B

  33. 2.5 hours = 150 mins → A) 150 mins
    Answer: A

  34. Perimeter square 28cm → side=7cm → area=49cm² → A) 49 cm²
    Answer: A

  35. Boys in class of 30 with 18 girls = 12 boys → fraction=12/30=2/5 → B) 2/5
    Answer: B

  36. Sequence 1,3,6,10 → differences 2,3,4 → next 15 → C) 15
    Answer: C

  37. 0.08 = 8/100=2/25 → B) 2/25
    Answer: B

  38. Bus 90% full of 50 = 45 full, empty=5 → A) 5
    Answer: A

  39. Smallest: B) 0.699
    Answer: B

  40. 30% of £250 = £75 → A) £75
    Answer: A

  41. 300 pencils ÷ 12 per box = 25 boxes → A) 25
    Answer: A

  42. 20:35 in 12-hour = 8:35 pm → B) 8:35 pm
    Answer: B

  43. Vertices (1,1),(1,4),(5,1) → right-angled at (1,1) → D) Right-angled
    Answer: D

  44. Square side 5 area 25 → rectangle length 10 width=25/10=2.5 → A) 2.5cm
    Answer: A

  45. Car 500km uses 40L → 1km=0.08L → 150km=12L → B) 12 litres
    Answer: B

  46. Estimate 59×61 ≈ 60×60=3600 → C) 3600
    Answer: C

  47. Simplify 4a+3b−a+2b = 3a+5b → A) 3a+5b
    Answer: A

  48. 4x−7=25 → 4x=32 → x=8 → B) 8
    Answer: B

  49. Range of 2,5,8,3,5 = 8−2=6 → C) 6
    Answer: C

  50. Probability two sixes = (1/6)×(1/6)=1/36 → D) 1/36
    Answer: D

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Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -4

 Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -4 Part 2: 100+ Practice Questions (GL Assessment Style) ...