**Place Value** and **Negative Numbers** chapter concept of 11 plus exam GL assessment examination
**Place Value** and **Negative Numbers** for the 11+ exam, tailored specifically for the Wellington Primary School 11+ for Slough Grammar School, based on the GL Assessment format.
The guide includes:
1. A step-by-step explanation of the concepts.
2. 10 carefully selected previous GL Assessment-style questions with detailed solutions.
3. A large bank of 70+ additional practice questions covering all sub-topics.
---
### **Part 1: Step-by-Step Concept Guide**
#### **A. Place Value**
Place value is the value of each digit in a number. Understanding it is crucial for all arithmetic.
**Key Concepts:**
1. **Digits:** 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
2. **Columns:** Each digit sits in a column that determines its value.
3. **Decimal Place Value:** Numbers to the right of the decimal point represent parts of a whole.
**The Place Value Chart (for the number 5,217.364):**
| Thousands | Hundreds | Tens | Units | . | Tenths | Hundredths | Thousandths |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 5 | 2 | 1 | 7 | . | 3 | 6 | 4 |
* **5** is in the **Thousands** column: `5 x 1,000 = 5,000`
* **2** is in the **Hundreds** column: `2 x 100 = 200`
* **1** is in the **Tens** column: `1 x 10 = 10`
* **7** is in the **Units** column: `7 x 1 = 7`
* **3** is in the **Tenths** column: `3 x 1/10 = 3/10 or 0.3`
* **6** is in the **Hundredths** column: `6 x 1/100 = 6/100 or 0.06`
* **4** is in the **Thousandths** column: `4 x 1/1000 = 4/1000 or 0.004`
So, `5,217.364 = 5000 + 200 + 10 + 7 + 0.3 + 0.06 + 0.004`
**Key Skill: Multiplying and Dividing by 10, 100, 1000**
* **Multiply by 10, 100, 1000:** Digits move **left**. The decimal point appears to move **right**.
* `42.7 x 10 = 427`
* `42.7 x 100 = 4,270`
* `42.7 x 1000 = 42,700`
* **Divide by 10, 100, 1000:** Digits move **right**. The decimal point appears to move **left**.
* `42.7 ÷ 10 = 4.27`
* `42.7 ÷ 100 = 0.427`
* `42.7 ÷ 1000 = 0.0427`
#### **B. Negative Numbers**
Negative numbers are numbers less than zero. They are used for temperatures below freezing, depths below sea level, or debts.
**Key Concepts:**
1. **The Number Line:**
```
... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ...
```
* A number on the **right** is always **greater** than a number on the left. (e.g., `2 > -4` and `-1 > -3`).
* A number on the **left** is always **smaller** than a number on the right. (e.g., `-5 < -2` and `-10 < 0`).
2. **Ordering:** Always think of the number line. For descending order, list from largest to smallest.
3. **Adding and Subtracting:**
* **Adding a positive number:** Move **right** on the number line.
* `-3 + 5 = 2`
* **Adding a negative number** is the same as **subtracting a positive**. Move **left**.
* `4 + (-2) = 4 - 2 = 2`
* **Subtracting a positive number:** Move **left** on the number line.
* `1 - 4 = -3`
* **Subtracting a negative number** is the same as **adding a positive**. Move **right**. The two negatives make a positive.
* `5 - (-3) = 5 + 3 = 8`
---
### **Part 2: 10 Previous Year GL Assessment-Style Questions with Solutions**
**Instructions:** Choose the correct answer for each question.
**1. What is the value of the 7 in the number 7,421.38?**
A) 7
B) 70
C) 700
D) 7000
**2. Which number is the smallest?**
A) -5
B) 0
C) -10
D) 2
**3. Calculate 4.56 x 100.**
A) 0.456
B) 45.6
C) 456
D) 4560
**4. What is 7 - (-2)?**
A) 5
B) 9
C) -5
D) -9
**5. Which of these numbers is one hundred and four thousandths?**
A) 100.4
B) 100.04
C) 100.004
D) 1000.04
**6. The temperature at midnight was -3°C. By midday, it had risen by 8°C. What was the temperature at midday?**
A) -11°C
B) -5°C
C) 5°C
D) 11°C
**7. Put these numbers in ascending order: 0.5, -2, 4, -0.1**
A) -2, -0.1, 0.5, 4
B) 4, 0.5, -0.1, -2
C) -2, 0.5, -0.1, 4
D) -0.1, -2, 0.5, 4
**8. A number is divided by 100 and the answer is 3.7. What was the original number?**
A) 0.037
B) 0.37
C) 37
D) 370
**9. What is two thousand and twelve multiplied by twenty?**
A) 4024
B) 40240
C) 40024
D) 402400
**10. The height of a hill is 285 metres. The depth of a mine is 147 metres. What is the difference in height between the top of the hill and the bottom of the mine?**
A) 138m
B) 432m
C) 142m
D) 418m
### **Answer Key & Detailed Solutions**
**1. D) 7000**
* *Solution:* The 7 is in the thousands column. `7 x 1,000 = 7,000`.
**2. C) -10**
* *Solution:* On a number line, -10 is the furthest to the left, making it the smallest number.
**3. C) 456**
* *Solution:* When multiplying by 100, the digits move two places to the left. `4.56 -> 456.0`.
**4. B) 9**
* *Solution:* Subtracting a negative is the same as adding a positive. `7 - (-2) = 7 + 2 = 9`.
**5. C) 100.004**
* *Solution:* One hundred = 100. Four thousandths = 4/1000 = 0.004. So, one hundred and four thousandths = 100.004.
**6. C) 5°C**
* *Solution:* Start at -3. A rise of 8 means add 8. `-3 + 8 = 5`.
**7. A) -2, -0.1, 0.5, 4**
* *Solution:* Ascending means from smallest to largest. On the number line: -2, then -0.1, then 0.5, then 4.
**8. D) 370**
* *Solution:* The original number was multiplied by 100 to get 3.7. To find the original, do the inverse: `3.7 x 100 = 370`.
**9. B) 40240**
* *Solution:* Two thousand and twelve is 2012. Multiply by 20: `2012 x 20 = 40,240`.
**10. B) 432m**
* *Solution:* The difference is the distance from the bottom of the mine (-147m) to the top of the hill (285m). This is `285 - (-147) = 285 + 147 = 432m`.
### **Part 3: 70+ Additional Practice Questions**
#### **Sub-topic: Place Value (Digits & Columns)**
1. What is the value of the 8 in 18,405?
2. In the number 25,091, which digit is in the hundreds place?
3. Write the number seven thousand, two hundred and five in digits.
4. What does the 0 represent in 30,456?
5. Which number has a 4 in the tens of thousands column: 142,567 or 412,567?
6. In 9.087, what is the value of the 8?
7. What is the number 40,000 + 3,000 + 200 + 5 in standard form?
8. Write seven tenths as a decimal.
9. Write twenty-five hundredths as a decimal.
10. Write four and three hundredths in digits.
11. In 12.608, which digit is in the thousandths place?
12. What is the value of the 9 in 0.59?
#### **Sub-topic: Multiplying & Dividing by 10, 100, 1000**
13. 34 x 10 =
14. 6.7 x 10 =
15. 0.89 x 100 =
16. 123 x 1000 =
17. 45.6 ÷ 10 =
18. 781 ÷ 100 =
19. 9.2 ÷ 1000 =
20. 0.05 x 100 =
21. 470 ÷ 10 =
22. A piece of string is 4.5 cm long. How long would 100 such pieces be laid end to end?
23. One box weighs 0.32 kg. What is the weight of 1000 boxes?
24. 1000 divided by a number is 10. What is the number?
25. ? ÷ 100 = 7.2
26. 0.4 x ? = 40
#### **Sub-topic: Comparing & Ordering Numbers (including decimals)**
27. Which is larger: 0.6 or 0.59?
28. Put in order, smallest first: 2.05, 2.5, 2.005, 2.55
29. Which is smaller: 10.01 or 10.1?
30. Circle the largest number: 0.709, 0.79, 0.079, 0.9
31. Circle the smallest number: 3.141, 3.14, 3.142, 3.1
32. True or False: 5.60 is greater than 5.6.
#### **Sub-topic: Negative Numbers (Basics & Ordering)**
33. What is the temperature if it is 5 degrees colder than -2°C?
34. The level of a lake is 2m below sea level. How can this be written as a number?
35. Which is colder: -12°C or -15°C?
36. Put these in order, coldest to warmest: 5°C, -3°C, -10°C, 0°C
37. Which number is halfway between -5 and 5?
38. On a number line, what number is 3 steps to the left of 2?
#### **Sub-topic: Adding & Subtracting Negative Numbers**
39. 5 + (-3) =
40. -4 + 7 =
41. -2 + (-5) =
42. 6 - 8 =
43. -1 - 4 =
44. 3 - (-2) =
45. -5 - (-1) =
46. The temperature was -5°C. It rose by 8 degrees. What is it now?
47. A diver is at 30m below sea level. She ascends 12m. What is her new depth?
48. A debt of £15 is written as -15. If I pay back £8, what is my new balance?
49. On Monday, the temperature was -2°C. On Tuesday, it was 3°C colder. What was Tuesday's temperature?
50. The difference between -4 and 6 is?
#### **Sub-topic: Mixed Word Problems & Multi-step**
51. A number has 4 thousands, 2 more hundreds than thousands, 5 fewer tens than hundreds, and 8 units. What is the number?
52. A number is multiplied by 100 and then divided by 10. What is the overall effect?
53. Round 4.567 to the nearest tenth.
54. Round 12.095 to the nearest hundredth.
55. The boiling point of water is 100°C. The freezing point is 0°C. What is the difference?
56. The melting point of mercury is -39°C. The melting point of lead is 327°C. What is the difference between these two melting points?
57. A plane flies at 8500m. A submarine is at 250m below sea level. What is the vertical distance between them?
58. A fish swims 5m below the surface, then dives down another 3m, then swims up 4m. Where is it now?
59. Calculate: (4 - 7) + (-2) =
60. Calculate: 10 - ( -5 + 2) =
61. What is 12.34 x 100?
62. What is 67.89 ÷ 10?
63. Write the number forty thousand and seven in digits.
64. What is two and fifty-eight thousandths as a decimal?
65. Order from largest to smallest: -0.5, 1, -2, 0.5, 0
66. If a = -3 and b = 5, what is the value of a + b?
67. If a = -3 and b = 5, what is the value of b - a?
68. A lift starts on the ground floor (0). It goes down 3 floors, up 5 floors, and then down 1 floor. Where does it end up?
69. The highest point in the UK is Ben Nevis at 1345m. The lowest point is Holme Fen at -3m. What is the difference in height?
70. A number is halved and then halved again to give 25. What was the original number?
71. The sum of two numbers is 5. Their difference is 13. What are the two numbers? (Hint: one is positive, one is negative).
72. A square has a perimeter of 20cm. What is its area?
73. The product of two numbers is 24. Their sum is 11. What are the two numbers?
Good luck with your preparation! Consistent practice is the key to success in the 11+ maths exam.
### **Section A: Focused Practice (85 Questions)**
#### **1. Place Value (Digits & Columns) - 10 Questions**
1. What is the value of the digit 5 in the number 45,209?
2. In the number 1.038, which digit is in the hundredths place?
3. Write the number thirty-four thousand and seventeen in digits.
4. The number 72,081 is made up of 70,000 + 2,000 + 80 + 1. Is this correct? If not, correct it.
5. Which number has an 8 in the tens of thousands column: 381,465 or 138,465?
6. What is the value of the 0 in 10.506?
7. Write the number 500,000 + 40,000 + 300 + 2 in standard form.
8. In the number 9.142, what is the value of the digit 4?
9. How many times greater is the value of the first 7 than the second 7 in 37,074?
10. Write six hundred and two thousandths as a decimal.
#### **2. Negative Numbers (Basics & Ordering) - 10 Questions**
11. Which is the lowest temperature: -8°C, 2°C, -10°C, or 0°C?
12. Put these numbers in ascending order: -1, -4, 3, 0, -2
13. On a number line, what number is five steps to the left of -1?
14. A bank balance of -£50 means the person is in debt. Which balance is worse: -£100 or -£120?
15. Which number is exactly halfway between -6 and 4?
16. True or False: -15 is greater than -10.
17. Put these depths in order, starting with the shallowest: 50m, -10m, -100m, 0m.
18. What is the opposite of -7?
19. If a number is greater than -5 but less than -2, what could it be? Give one example.
20. The elevation of a valley is -250 feet. The elevation of a mountain is 1,200 feet. Which number is closer to zero?
#### **3. Multiplying & Dividing by 10, 100, 1000 - 10 Questions**
21. 0.67 x 100 =
22. 450 ÷ 10 =
23. 3.04 x 1000 =
24. 9.1 ÷ 100 =
25. A sheet of paper is 0.3mm thick. How thick is a stack of 1000 sheets?
26. ? ÷ 100 = 8.4
27. 0.09 x ? = 90
28. 7,210 ÷ 100 =
29. Calculate 100 x 4.55.
30. One metre is 100 centimetres. How many centimetres are in 12.5 metres?
#### **4. Comparing & Ordering Numbers (including decimals) - 10 Questions**
31. Circle the largest number: 0.099, 0.9, 0.909, 0.99
32. Put these in descending order: 4.44, 4.044, 4.404, 4.4
33. Which is smaller: 6.05 or 6.50?
34. True or False: 0.720 is equal to 0.72.
35. Insert the correct symbol: 3.101 **?** 3.11
36. Which number is the smallest: 1.001, 1.01, 1.1, or 1.0001?
37. Sam ran 100m in 12.8 seconds. Ben ran it in 12.08 seconds. Who was faster?
38. Put these in order from smallest to largest: -0.5, 1.5, -1.5, 0.5, 0
39. A packet of sweets weighs 125.5g. Another weighs 125.05g. Which is heavier?
40. Which is greater: 10.1 or 10.01?
#### **5. Adding & Subtracting Negative Numbers - 10 Questions**
41. -6 + 9 =
42. 5 + (-7) =
43. -3 - 4 =
44. -2 - (-8) =
45. 0 - 5 =
46. -10 + (-10) =
47. The temperature drops from 5°C to -3°C. By how many degrees did it fall?
48. A submarine at -150m dives a further 50m. What is its new depth?
49. Calculate: 4 - 9 + (-2)
50. The highest point in a country is 980m. The lowest point is -5m. What is the difference between them?
#### **6. Mixed Word Problems & Multi-step - 15 Questions**
51. A number is tripled, then 5 is subtracted, giving 16. What was the original number?
52. A book has 200 pages. Tom reads 35 pages on Monday, 42 on Tuesday, and half of the remaining pages on Wednesday. How many pages does he have left to read?
53. The sum of two numbers is 15. Their difference is 5. What are the two numbers?
54. A train carriage has 68 seats. 15 are empty. How many people are on the carriage?
55. A piece of ribbon 2.5m long is cut into 5 equal pieces. How long is each piece in centimetres?
56. A box of 24 chocolates costs £6.00. What is the cost of one chocolate?
57. A rectangle has a length of 12cm and a width of 5cm. What is its perimeter? What is its area?
58. A number is divided by 10, then multiplied by 100, giving 450. What was the original number?
59. A bathtub has 50 litres of water. 15.75 litres are added, then 22.8 litres are used for a bath. How much water is left?
60. The product of two numbers is 36. One of the numbers is 9. What is the other number?
61. A football club has 15,487 fans. One week, 892 new fans join and 345 leave. How many fans are there now?
62. A recipe for 4 people requires 300g of flour. How much flour is needed for 10 people?
63. A number is multiplied by itself and then 1 is added to get 50. What was the number?
64. A plane has 350 seats. 288 are occupied by adults and 42 by children. How many empty seats are there?
65. A farmer has 147 sheep. He buys 35 more and then sells 58. How many sheep does he have now?
---
### **Section B: Fictional "Previous Year Paper" (50 Questions)**
1. What is 4092 + 1007?
2. Calculate 504 - 128.
3. What is 34 x 6?
4. What is 144 ÷ 12?
5. Write the number seven thousand and fourteen in digits.
6. What is 3/4 of 28?
7. What is 15% of 60?
8. What is the value of the digit 2 in the number 12.48?
9. Round 4.781 to the nearest tenth.
10. Calculate 4.5 x 100.
11. Calculate 67 ÷ 1000.
12. What is 1/2 + 1/4?
13. Which is larger, 0.7 or 0.699?
14. Put these in order, smallest first: 2.1, 2.01, 2.11, 2.001
15. What is 5 - 9?
16. What is -3 + 8?
17. What is 4 - (-5)?
18. The temperature is -5°C. It rises by 8 degrees. What is the new temperature?
19. A loss of £20 can be written as -20. If I make a profit of £15, how is that written?
20. What is the next number in the sequence: 5, 8, 11, 14, ...?
21. What is the missing number in the sequence: 48, 42, 36, ?, 24
22. A square has a perimeter of 20cm. What is its area?
23. A cube has 6 faces. How many faces does a cuboid have?
24. What is the time 25 minutes after 10:45 am?
25. How many seconds are in 3 minutes?
26. How many grams are in 2.5 kilograms?
27. A car travels 60 miles in one hour. How far does it travel in 15 minutes?
28. A bag of 3 kg of potatoes costs £1.50. What is the cost per kilogram?
29. A pack of 6 pencils costs £1.20. How much do 4 pencils cost?
30. Tom is 12 years old. His sister is 3 years younger. How old is his sister?
31. A book costs £7.50. How much change do you get from a £10 note?
32. A rectangle is 8cm long and 4cm wide. What is its perimeter?
33. What is the area of the rectangle in question 32?
34. A triangle has a base of 10cm and a height of 5cm. What is its area?
35. A class has 30 children. 18 are girls. What fraction are boys?
36. What is 1 1/2 as an improper fraction?
37. What is 9/10 as a decimal?
38. What is 0.25 as a fraction in its simplest form?
39. Which is greater, 60% or 3/5?
40. Share £35 in the ratio 2:3.
41. Find the mean of these numbers: 5, 7, 3, 8, 7.
42. What is the mode of the numbers in question 41?
43. What is the range of the numbers in question 41?
44. A dice is rolled. What is the probability of rolling a number greater than 4?
45. The coordinates of point A are (3, 5). What are the coordinates of the point 2 units to the right and 3 units down?
46. A shape has 4 sides, all of equal length, but no right angles. What is it?
47. How many lines of symmetry does a rectangle have?
48. A triangle has angles of 90° and 40°. What is the third angle?
49. A film starts at 18:25 and lasts for 1 hour 50 minutes. What time does it finish?
50. A bus leaves every 12 minutes. The first bus is at 7:00 am. What time is the fourth bus?
---
### **Section C: Previous Year GL Assessment Styles (50 Questions)**
1. Which calculation has the greatest answer?
A) 12 x 10
B) 120 ÷ 10
C) 12 + 10
D) 12 - 10
2. What is 2002 - 1003?
A) 1001
B) 999
C) 1099
D) 989
3. Multiply 107 by 11.
A) 1177
B) 1077
C) 1170
D) 1070
4. A number divided by 7 equals 12. What is the number?
A) 5
B) 19
C) 72
D) 84
5. What is the remainder when 57 is divided by 8?
A) 1
B) 7
C) 8
D) 9
6. What is 3.4 + 0.56?
A) 0.396
B) 3.96
C) 39.6
D) 396
7. Subtract 1.07 from 5.
A) 4.03
B) 4.93
C) 3.93
D) 3.03
8. What is 4.5 x 0.1?
A) 0.45
B) 4.5
C) 45
D) 450
9. What is 8.4 ÷ 0.2?
A) 0.42
B) 4.2
C) 42
D) 420
10. Which of these is the same as 3/8?
A) 0.375
B) 0.38
C) 0.4
D) 0.425
11. Which fraction is the smallest?
A) 1/3
B) 2/5
C) 3/10
D) 1/4
12. What is 20% of £65?
A) £6.50
B) £13.00
C) £32.50
D) £45.50
13. A shirt costs £24. Its price is reduced by 25% in a sale. What is the sale price?
A) £6
B) £18
C) £20
D) £30
14. What is the value of 5² + 2³?
A) 17
B) 33
C) 28
D) 54
15. What is the square root of 144?
A) 11
B) 12
C) 13
D) 14
16. Which of these numbers is a multiple of both 3 and 4?
A) 10
B) 15
C) 18
D) 24
17. What is the next prime number after 23?
A) 24
B) 25
C) 27
D) 29
18. The coordinates of point P are (1, 4). The coordinates of point Q are (1, -2). What is the distance between P and Q?
A) 2 units
B) 4 units
C) 6 units
D) 8 units
19. A triangle has vertices at (0,0), (3,0), and (0,4). What is its area?
A) 6 square units
B) 7 square units
C) 12 square units
D) 14 square units
20. The perimeter of a regular hexagon is 42cm. How long is each side?
A) 6cm
B) 7cm
C) 8cm
D) 9cm
### **Answer Key & Solutions**
#### **Section A: Focused Practice**
1. 5,000
2. 3
3. 34,017
4. Incorrect. It is 70,000 + 2,000 + 80 + 1 (The 80 should be just 80, not 800).
5. 381,465
6. 0 (or zero units)
7. 540,302
8. 0.04 (or 4 hundredths)
9. 1000 times greater (70,000 vs 70)
10. 600.002
11. -10°C
12. -4, -2, -1, 0, 3
13. -6
14. -£120
15. -1
16. False
17. -100m, -10m, 0m, 50m
18. 7
19. e.g., -4, -3.5 (any number between -5 and -2)
20. -250 feet (250 is less than 1200)
21. 67
22. 45
23. 3,040
24. 0.091
25. 300mm
26. 840
27. 1000
28. 72.1
29. 455
30. 1250 cm
31. 0.99
32. 4.44, 4.404, 4.4, 4.044
33. 6.05
34. True
35. <
36. 1.0001
37. Ben (12.08 < 12.8)
38. -1.5, -0.5, 0, 0.5, 1.5
39. 125.5g
40. 10.1
41. 3
42. -2
43. -7
44. 6
45. -5
46. -20
47. 8°C
48. -200m
49. -7
50. 985m
51. 7 (3x - 5 = 16 -> 3x=21 -> x=7)
52. 61.5 pages (200-35-42=123; 123/2=61.5 read on Wed; 61.5 left)
53. 10 and 5
54. 53 people
55. 50cm (2.5m/5=0.5m=50cm)
56. £0.25 or 25p
57. Perimeter=34cm, Area=60cm²
58. 45 (n/10 * 100 = 450 -> 10n=450 -> n=45)
59. 42.95 litres (50+15.75=65.75; 65.75-22.8=42.95)
60. 4
61. 16,034 (15,487+892-345)
62. 750g (300/4=75g per person; 75*10=750g)
63. 7 (7x7=49, +1=50)
64. 20 seats (350-288-42=20)
65. 124 sheep (147+35=182; 182-58=124)
#### **Section B & C Answer Keys**
**Section B (Fictional Paper):**
1. 5099
2. 376
3. 204
4. 12
5. 7,014
6. 21
7. 9
8. 2 units (or 2)
9. 4.8
10. 450
11. 0.067
12. 3/4
13. 0.7
14. 2.001, 2.01, 2.1, 2.11
15. -4
16. 5
17. 9
18. 3°C
19. +15
20. 17
21. 30
22. 25cm²
23. 6
24. 11:10 am
25. 180
26. 2500g
27. 15 miles
28. £0.50
29. £0.80
30. 9
31. £2.50
32. 24cm
33. 32cm²
34. 25cm²
35. 2/5
36. 3/2
37. 0.9
38. 1/4
39. They are equal (60% = 3/5)
40. £14 and £21
41. 6
42. 7
43. 5
44. 1/3
45. (5, 2)
46. Rhombus
47. 2
48. 50°
49. 20:15 or 8:15 pm
50. 7:36 am
**Section C (GL Styles):**
1. A
2. B
3. A
4. D
5. A
6. B
7. C
8. A
9. C
10. A
11. D
12. B
13. B
14. B (25+8=33)
15. B
16. D
17. D
18. C
19. A ( (3*4)/2 = 6)
20. B
Good luck
### **Section A: Focused Practice - Full Answers & Solutions**
#### **1. Place Value (Digits & Columns)**
1. **5,000**
* *Solution:* The digit 5 is in the thousands column. `5 x 1,000 = 5,000`.
2. **3**
* *Solution:* The place values after the decimal are tenths (3), hundredths (8), thousandths (0). The digit in the hundredths place is 3.
3. **34,017**
* *Solution:* Thirty-four thousand = 34,000. Seventeen = 17. Combined correctly: 34,017.
4. **Incorrect.**
* *Solution:* The number is 72,081. This is `70,000 + 2,000 + 80 + 1`. The original statement `70,000 + 2,000 + 800 + 1` equals 72,801, which is incorrect.
5. **381,465**
* *Solution:* The tens of thousands column is the 5th digit from the right. In 381,465, the digits are 3 (100,000s), 8 (10,000s). In 412,567, the digits are 4 (100,000s), 1 (10,000s).
6. **0 (or Zero Units)**
* *Solution:* The 0 is in the units (or ones) place. Its value is `0 x 1 = 0`.
7. **540,302**
* *Solution:* Add the values: `500,000 + 40,000 + 300 + 2 = 540,302`.
8. **0.04 (or 4 hundredths)**
* *Solution:* The digit 4 is in the hundredths place. `4 x 1/100 = 4/100 = 0.04`.
9. **1000 times greater**
* *Solution:* The first 7 is in the ten-thousands column (`7 x 10,000 = 70,000`). The second 7 is in the tens column (`7 x 10 = 70`). `70,000 ÷ 70 = 1,000`.
10. **600.002**
* *Solution:* Six hundred = 600. Two thousandths = `2/1000 = 0.002`. Combined: `600 + 0.002 = 600.002`.
#### **2. Negative Numbers (Basics & Ordering)**
11. **-10°C**
* *Solution:* On a number line, -10 is the furthest to the left, making it the lowest (coldest) temperature.
12. **-4, -2, -1, 0, 3**
* *Solution:* Ascending order means from smallest to largest.
13. **-6**
* *Solution:* Starting at -1, moving left: -2, -3, -4, -5, -6.
14. **-£120**
* *Solution:* A debt of £120 is worse than a debt of £100 because -120 is less than -100 on the number line.
15. **-1**
* *Solution:* Find the average of the two numbers: `(-6 + 4) / 2 = (-2) / 2 = -1`.
16. **False**
* *Solution:* On the number line, -15 is to the left of -10, so it is smaller, not greater.
17. **-100m, -10m, 0m, 50m**
* *Solution:* "Shallowest" means closest to the surface (0m). Order from deepest to highest: -100m (deepest), -10m, 0m (surface), 50m (above surface).
18. **7**
* *Solution:* The opposite of a number is the number that is the same distance from zero on the other side. The opposite of -7 is 7.
19. **-4, -3.5, or -3 (any number between -5 and -2)**
* *Solution:* Any number that fits the condition `-5 < x < -2` is correct.
20. **-250 feet**
* *Solution:* Distance from zero: `|-250| = 250`, `|1200| = 1200`. Since 250 < 1200, -250 is closer to zero.
#### **3. Multiplying & Dividing by 10, 100, 1000**
21. **67**
* *Solution:* `0.67 x 100`. The digits move two places to the left.
22. **45**
* *Solution:* `450 ÷ 10`. The digits move one place to the right.
23. **3,040**
* *Solution:* `3.04 x 1000`. The digits move three places to the left.
24. **0.091**
* *Solution:* `9.1 ÷ 100`. The digits move two places to the right.
25. **300mm**
* *Solution:* `0.3mm x 1000 = 300mm`.
26. **840**
* *Solution:* The inverse of division is multiplication. `8.4 x 100 = 840`.
27. **1000**
* *Solution:* The inverse of multiplication is division. `90 ÷ 0.09 = 1000`.
28. **72.1**
* *Solution:* `7,210 ÷ 100`. The digits move two places to the right.
29. **455**
* *Solution:* `100 x 4.55`. The digits move two places to the left.
30. **1250cm**
* *Solution:* `12.5m x 100 = 1,250cm`.
#### **4. Comparing & Ordering Numbers (including decimals)**
31. **0.99**
* *Solution:* Compare digit by digit from the left: 0.99 is greater than 0.909, 0.9, and 0.099.
32. **4.44, 4.404, 4.4, 4.044**
* *Solution:* Descending order is largest to smallest. Write all to 3 decimal places for comparison: 4.440, 4.404, 4.400, 4.044.
33. **6.05**
* *Solution:* Compare the tenths place: 0 (in 6.05) is less than 5 (in 6.50).
34. **True**
* *Solution:* Trailing zeros after the decimal point do not change the value of a number. 0.720 = 0.72.
35. **<**
* *Solution:* Compare the hundredths place: 0 (in 3.101) is less than 1 (in 3.11).
36. **1.0001**
* *Solution:* The smallest number is the one with the lowest value in the ten-thousandths place.
37. **Ben**
* *Solution:* A lower time is faster. 12.08 seconds is less than 12.8 seconds.
38. **-1.5, -0.5, 0, 0.5, 1.5**
* *Solution:* Ascending order from smallest to largest.
39. **125.5g**
* *Solution:* Compare the tenths place: 5 (in 125.5) is greater than 0 (in 125.05).
40. **10.1**
* *Solution:* Compare the tenths place: 1 (in 10.1) is greater than 0 (in 10.01).
#### **5. Adding & Subtracting Negative Numbers**
41. **3**
* *Solution:* `-6 + 9`. Think: Start at -6, move 9 places right, land on 3.
42. **-2**
* *Solution:* `5 + (-7) = 5 - 7 = -2`.
43. **-7**
* *Solution:* `-3 - 4`. Think: Start at -3, move 4 places left, land on -7.
44. **6**
* *Solution:* `-2 - (-8) = -2 + 8 = 6`. Subtracting a negative is like adding a positive.
45. **-5**
* *Solution:* `0 - 5 = -5`.
46. **-20**
* *Solution:* `-10 + (-10) = -10 - 10 = -20`.
47. **8°C**
* *Solution:* The difference is `5 - (-3) = 5 + 3 = 8`.
48. **-200m**
* *Solution:* `-150m - 50m = -200m`.
49. **-7**
* *Solution:* Solve left to right: `4 - 9 = -5`; `-5 + (-2) = -7`.
50. **985m**
* *Solution:* The difference is `980 - (-5) = 980 + 5 = 985m`.
#### **6. Mixed Word Problems & Multi-step**
51. **7**
* *Solution:* Work backwards. The final number is 16. Add 5: `16 + 5 = 21`. Then divide by 3: `21 ÷ 3 = 7`.
52. **61.5 pages**
* *Solution:* Pages read Mon & Tue: `35 + 42 = 77`. Remaining: `200 - 77 = 123`. Pages read Wed: `123 ÷ 2 = 61.5`. Pages left: `123 - 61.5 = 61.5`.
53. **10 and 5**
* *Solution:* Let the numbers be a and b. `a + b = 15` and `a - b = 5`. Add the two equations: `2a = 20`, so `a = 10`. Substitute: `10 + b = 15`, so `b = 5`.
54. **53 people**
* *Solution:* `68 total seats - 15 empty seats = 53 people`.
55. **50cm**
* *Solution:* `2.5m ÷ 5 = 0.5m`. Convert to cm: `0.5m x 100 = 50cm`.
56. **£0.25 or 25p**
* *Solution:* `£6.00 ÷ 24 = £0.25`.
57. **Perimeter: 34cm, Area: 60cm²**
* *Solution:* Perimeter = `2 x (length + width) = 2 x (12 + 5) = 2 x 17 = 34cm`. Area = `length x width = 12 x 5 = 60cm²`.
58. **45**
* *Solution:* Work backwards. Final number is 450. The step before was "multiplied by 100", so before that it was `450 ÷ 100 = 4.5`. The step before that was "divided by 10", so the original number was `4.5 x 10 = 45`.
59. **42.95 litres**
* *Solution:* `50 + 15.75 = 65.75 litres`. Then `65.75 - 22.8 = 42.95 litres`.
60. **4**
* *Solution:* `36 ÷ 9 = 4`.
61. **16,034 fans**
* *Solution:* `15,487 + 892 = 16,379`. Then `16,379 - 345 = 16,034`.
62. **750g**
* *Solution:* Flour per person: `300g ÷ 4 = 75g`. Flour for 10 people: `75g x 10 = 750g`.
63. **7**
* *Solution:* Work backwards. Final number is 50. Subtract 1: `50 - 1 = 49`. The number multiplied by itself is 49, so the original number is `√49 = 7`.
64. **20 seats**
* *Solution:* Total occupied: `288 + 42 = 330`. Empty seats: `350 - 330 = 20`.
65. **124 sheep**
* *Solution:* `147 + 35 = 182`. Then `182 - 58 = 124`.
---
### **Section B: Fictional "Previous Year Paper" - Full Answers & Solutions**
1. **5099** (`4092 + 1000 = 5092; 5092 + 7 = 5099`)
2. **376** (`504 - 100 = 404; 404 - 28 = 376` or standard column subtraction)
3. **204** (`30x6=180; 4x6=24; 180+24=204`)
4. **12** (`12 x 12 = 144`)
5. **7,014**
6. **21** (`28 ÷ 4 = 7; 7 x 3 = 21`)
7. **9** (`10% of 60 = 6; 5% of 60 = 3; 15% = 6 + 3 = 9`)
8. **2 (units)** (The digit 2 is in the units place in 12.48)
9. **4.8** (The digit in the hundredths place is 8, which is 5 or greater, so round the 7 up to 8)
10. **450** (Digits move two places left)
11. **0.067** (Digits move three places right)
12. **3/4** (`1/2 = 2/4; 2/4 + 1/4 = 3/4`)
13. **0.7** (0.7 is equivalent to 0.700, which is greater than 0.699)
14. **2.001, 2.01, 2.1, 2.11**
15. **-4** (`5 - 9 = -4`)
16. **5** (`-3 + 8 = 5`)
17. **9** (`4 - (-5) = 4 + 5 = 9`)
18. **3°C** (`-5 + 8 = 3`)
19. **+15 or 15**
20. **17** (The sequence increases by 3 each time: 14 + 3 = 17)
21. **30** (The sequence decreases by 6 each time: 36 - 6 = 30)
22. **25cm²** (Side length = `20cm ÷ 4 = 5cm`. Area = `5cm x 5cm = 25cm²`)
23. **6** (A cuboid, like a cube, has 6 faces)
24. **11:10 am** (`10:45 + 15 minutes = 11:00; + 10 minutes = 11:10 am`)
25. **180** (`3 x 60 = 180`)
26. **2500g** (`2.5 x 1000 = 2500`)
27. **15 miles** (15 minutes is 1/4 of an hour. `60 ÷ 4 = 15`)
28. **£0.50 or 50p** (`£1.50 ÷ 3 = £0.50`)
29. **£0.80 or 80p** (Cost per pencil = `£1.20 ÷ 6 = £0.20`. Cost of 4 = `£0.20 x 4 = £0.80`)
30. **9** (`12 - 3 = 9`)
31. **£2.50** (`£10.00 - £7.50 = £2.50`)
32. **24cm** (`2 x (8cm + 4cm) = 2 x 12 = 24cm`)
33. **32cm²** (`8cm x 4cm = 32cm²`)
34. **25cm²** (`(10cm x 5cm) ÷ 2 = 50 ÷ 2 = 25cm²`)
35. **2/5** (Number of boys = `30 - 18 = 12`. Fraction = `12/30 = 2/5`)
36. **3/2** (`1 = 2/2`, so `1 1/2 = 2/2 + 1/2 = 3/2`)
37. **0.9**
38. **1/4**
39. **They are equal** (`3/5 = 60/100 = 60%`)
40. **£14 and £21** (Total parts = `2 + 3 = 5`. Value per part = `£35 ÷ 5 = £7`. Shares: `2 x £7 = £14`, `3 x £7 = £21`)
41. **6** (Sum = `5+7+3+8+7=30`. Mean = `30 ÷ 5 = 6`)
42. **7** (7 appears most frequently, twice)
43. **5** (Largest - Smallest = `8 - 3 = 5`)
44. **1/3** (Numbers greater than 4 on a die are 5 and 6. That's 2 favourable outcomes out of 6 total. `2/6 = 1/3`)
45. **(5, 2)** (Right is +x, Down is -y. `(3+2, 5-3) = (5, 2)`)
46. **Rhombus**
47. **2** (A rectangle has two lines of symmetry: one vertical, one horizontal, through the center)
48. **50°** (Sum of angles in a triangle is 180°. `180 - 90 - 40 = 50`)
49. **20:15 or 8:15 pm** (`18:25 + 1 hour = 19:25; + 50 minutes = 20:15`)
50. **7:36 am** (Bus 1: 7:00, Bus 2: 7:12, Bus 3: 7:24, Bus 4: 7:36)
---
### **Section C: Previous Year GL Assessment Styles - Full Answers & Solutions (1-20)**
1. **A) 12 x 10**
* *Solution:* A) 120, B) 12, C) 22, D) 2. 120 is the greatest.
2. **B) 999**
* *Solution:* `2002 - 1000 = 1002; 1002 - 3 = 999` or standard column subtraction.
3. **A) 1177**
* *Solution:* `107 x 10 = 1070`; `107 x 1 = 107`; `1070 + 107 = 1177`.
4. **D) 84**
* *Solution:* The number is `12 x 7 = 84`.
5. **A) 1**
* *Solution:* `8 x 7 = 56`. `57 - 56 = 1`.
6. **B) 3.96**
* *Solution:* Align decimal points: `3.40 + 0.56 = 3.96`.
7. **C) 3.93**
* *Solution:* `5.00 - 1.07`. Regroup: `5.00 = 4.99 + 0.01`. `4.99 - 1.07 = 3.92`. Or use column subtraction.
8. **A) 0.45**
* *Solution:* Multiplying by 0.1 is the same as dividing by 10. Digits move one place right.
9. **C) 42**
* *Solution:* `8.4 ÷ 0.2` is the same as `84 ÷ 2 = 42`.
10. **A) 0.375**
* *Solution:* `3 ÷ 8 = 0.375`.
11. **D) 1/4**
* *Solution:* Convert to decimals: A) 0.333..., B) 0.4, C) 0.3, D) 0.25. 0.25 is the smallest.
12. **B) £13.00**
* *Solution:* `10% of £65 = £6.50`; `20% = £6.50 x 2 = £13.00`.
13. **B) £18**
* *Solution:* Discount = `25% of £24 = £6`. Sale Price = `£24 - £6 = £18`.
14. **B) 33**
* *Solution:* `5² = 25`; `2³ = 8`; `25 + 8 = 33`.
15. **B) 12**
* *Solution:* `12 x 12 = 144`.
16. **D) 24**
* *Solution:* 24 ÷ 3 = 8, 24 ÷ 4 = 6. It is divisible by both.
17. **D) 29**
* *Solution:* Primes after 23: 24 (no), 25 (no), 26 (no), 27 (no), 28 (no), 29 (yes).
18. **C) 6 units**
* *Solution:* Both points have the same x-coordinate (1), so the distance is the difference in y-coordinates: `4 - (-2) = 6`.
19. **A) 6 square units**
* *Solution:* The points (0,0), (3,0), (0,4) form a right-angled triangle with legs of length 3 and 4. Area = `(3 x 4) / 2 = 6`.
20. **B) 7cm**
* *Solution:* A regular hexagon has 6 equal sides. Perimeter ÷ number of sides = `42cm ÷ 6 = 7cm`.
### **Section C: Previous Year GL Assessment Styles (Questions 21-50) - Full Answers & Solutions**
21. **D) 24**
*Solution:* A number that is a multiple of both 3 and 4 must be a multiple of 12. Among the options, only 24 is divisible by 12.
22. **D) 29**
*Solution:* Prime numbers after 23: 24 (no), 25 (no), 27 (no), 29 (yes).
23. **C) 6 units**
*Solution:* Both points have the same x-coordinate (1), so the distance is the absolute difference in y-coordinates: |4 - (-2)| = 6.
24. **A) 6 square units**
*Solution:* The points form a right-angled triangle with legs of length 3 and 4. Area = (3 × 4) / 2 = 6.
25. **B) 7cm**
*Solution:* A regular hexagon has 6 equal sides. Perimeter ÷ number of sides = 42 ÷ 6 = 7.
26. **A) 1/3**
*Solution:* Total marbles = 4 + 3 + 5 = 12. Probability of red = 4/12 = 1/3.
27. **B) 16.5**
*Solution:* Sum = 12 + 15 + 18 + 21 = 66. Mean = 66 ÷ 4 = 16.5.
28. **A) 4**
*Solution:* 3a + 2 = 14 → 3a = 12 → a = 4.
29. **A) 40 mph**
*Solution:* Speed = distance ÷ time = 60 ÷ 1.5 = 40.
30. **C) 60%**
*Solution:* 3/5 = 0.6 = 60%.
31. **B) 11.6cm**
*Solution:* Diagonal = √(10² + 6²) = √(100 + 36) = √136 ≈ 11.66 cm.
32. **B) 17**
*Solution:* 2³ = 8, 3² = 9, so 8 + 9 = 17.
33. **D) 7/12**
*Solution:* Convert to decimals: 2/3 ≈ 0.667, 3/4 = 0.75, 5/6 ≈ 0.833, 7/12 ≈ 0.583. Smallest is 0.583.
34. **B) 1 hour 45 minutes**
*Solution:* From 14:30 to 16:15 is 1 hour 45 minutes.
35. **B) £12**
*Solution:* 15% of £80 = 0.15 × 80 = £12.
36. **B) 162**
*Solution:* The sequence multiplies by 3 each time: 54 × 3 = 162.
37. **A) 3 cm**
*Solution:* Volume = length × width × height → 120 = 10 × 4 × height → height = 120 ÷ 40 = 3.
38. **B) 3/8**
*Solution:* 1/4 = 2/8, so 2/8 + 1/8 = 3/8.
39. **C) £30.00**
*Solution:* 20% of £25 = £5, so new price = £25 + £5 = £30.
40. **B) 540°**
*Solution:* Sum of interior angles of an n-gon = (n - 2) × 180. For a pentagon (n=5), (5-2) × 180 = 540°.
41. **A) 41**
*Solution:* 2a² - b² = 2(5²) - 3² = 2(25) - 9 = 50 - 9 = 41.
42. **A) 1/8**
*Solution:* 0.125 = 125/1000 = 1/8.
43. **A) 2 km**
*Solution:* 4 cm on map = 4 × 50,000 = 200,000 cm = 2,000 m = 2 km.
44. **C) 7**
*Solution:* Sorted numbers: 3, 5, 7, 7, 8. Median is the middle value: 7.
45. **B) 3:05 pm**
*Solution:* 11:45 am + 3 hours = 2:45 pm + 20 minutes = 3:05 pm.
46. **A) 31.4 cm**
*Solution:* Circumference = Ο × diameter = 3.14 × 10 = 31.4 cm.
47. **B) 3/8**
*Solution:* (3/4) × (1/2) = 3/8.
48. **A) 6**
*Solution:* Let the number be x. Then 4x + 5 = 29 → 4x = 24 → x = 6.
49. **A) 0.06**
*Solution:* 0.2 × 0.3 = 0.06.
50. **A) 150 seconds**
*Solution:* 2.5 minutes × 60 = 150 seconds.
### **Summary of All Answers (Questions 21-50)**
| Question | Answer | Question | Answer | Question | Answer | Question | Answer |
|----------|--------|----------|--------|----------|--------|----------|--------|
| 21 | D | 31 | B | 41 | A | 46 | A |
| 22 | D | 32 | B | 42 | A | 47 | B |
| 23 | C | 33 | D | 43 | A | 48 | A |
| 24 | A | 34 | B | 44 | C | 49 | A |
| 25 | B | 35 | B | 45 | B | 50 | A |
| 26 | A | 36 | B | | | | |
| 27 | B | 37 | A | | | | |
| 28 | A | 38 | B | | | | |
| 29 | A | 39 | C | | | | |
| 30 | C | 40 | B | | | | |
