Number & Arithmetic chapter concept of 11 plus exam GL assessment examination
number and place value concepts for the 11+ exam
### **Part 1: Concept Guide for Number & Arithmetic**
#### **1. Place Value (Whole Numbers & Decimals)**
**Step 1: Understanding the Value of Each Digit**
* Whole numbers: Millions (M), Hundred Thousands (HTh), Ten Thousands (TTh), Thousands (Th), Hundreds (H), Tens (T), Ones (O).
* Example: In 3,456,192
* 3 is 3,000,000 (Three Million)
* 4 is 400,000 (Four Hundred Thousand)
* 5 is 50,000 (Fifty Thousand)
* 6 is 6,000 (Six Thousand)
* 1 is 100 (One Hundred)
* 9 is 90 (Ninety)
* 2 is 2 (Two)
* Decimals: Decimal Point, Tenths (1/10), Hundredths (1/100), Thousandths (1/1000).
* Example: In 45.307
* 4 is 40 (Four Tens)
* 5 is 5 (Five Ones)
* 3 is 0.3 (Three Tenths)
* 0 is 0.00 (Zero Hundredths)
* 7 is 0.007 (Seven Thousandths)
**Step 2: Comparing and Ordering**
* **Whole Numbers:** Always start from the left-most digit. The number with the larger digit in the highest place value is larger.
* Example: Put in order, smallest first: 12,099; 12,109; 11,999.
* Compare Ten Thousands: All are 1.
* Compare Thousands: 1, 2, 2. So 11,999 is the smallest.
* Compare Hundreds: For 12,099 and 12,109: 0 < 1. So order is: **11,999; 12,099; 12,109**.
* **Decimals:** Write them down with the same number of decimal places by adding zeros. This makes comparison easier.
* Example: Order 0.45, 0.405, 0.5 (smallest first).
* Write as: 0.450, 0.405, 0.500.
* Now compare: 0.405 < 0.450 < 0.500. So order is: **0.405, 0.45, 0.5**.
#### **2. Factors, Multiples, Primes, HCF, LCM**
**Step 1: Definitions**
* **Multiples:** The result of multiplying a number by an integer. The multiples of 7 are 7, 14, 21, 28...
* **Factors:** Numbers that divide exactly into another number. Factors of 18 are 1, 2, 3, 6, 9, 18.
* **Prime Numbers:** A number greater than 1 with only two factors: 1 and itself. (e.g., 2, 3, 5, 7, 11, 13, 17, 19).
* **HCF (Highest Common Factor):** The largest number that is a factor of two or more numbers.
* **LCM (Lowest Common Multiple):** The smallest number that is a multiple of two or more numbers.
**Step 2: Finding HCF and LCM**
* **Method 1: Listing**
* HCF of 12 and 18:
* Factors of 12: 1, 2, 3, 4, 6, 12
* Factors of 18: 1, 2, 3, 6, 9, 18
* Common factors: 1, 2, 3, 6. So **HCF = 6**.
* LCM of 4 and 6:
* Multiples of 4: 4, 8, 12, 16, 20...
* Multiples of 6: 6, 12, 18, 24...
* The smallest common multiple is **12**.
* **Method 2: Prime Factors (More efficient for larger numbers)**
* Express each number as a product of its prime factors.
* **HCF:** Multiply the common prime factors.
* **LCM:** Multiply the highest power of all prime factors present.
#### **3. Square & Cube Numbers**
**Step 1: Know Your Facts**
* **Square Numbers:** A number multiplied by itself.
* 1²=1, 2²=4, 3²=9, 4²=16, 5²=25, 6²=36, 7²=49, 8²=64, 9²=81, 10²=100, 11²=121, 12²=144, 13²=169, 14²=196, 15²=225.
* **Cube Numbers:** A number multiplied by itself twice.
* 1³=1, 2³=8, 3³=27, 4³=64, 5³=125, 10³=1000.
#### **4. Negative Numbers (Ordering & Basic Operations)**
**Step 1: The Number Line is Your Best Friend**
* Numbers to the left are smaller. -10 is smaller than -5.
* **Ordering:** -8, -1, 0, 3, 7 (this is already smallest to largest).
**Step 2: Basic Operations - Rules**
* **Adding a negative** is like **subtracting**.
* `5 + (-3) = 5 - 3 = 2`
* **Subtracting a negative** is like **adding**.
* `5 - (-3) = 5 + 3 = 8`
* **Multiplication & Division:**
* Same signs → Positive answer. (`-4 × -5 = 20`)
* Different signs → Negative answer. (`-4 × 5 = -20`)
#### **5. Rounding, Estimation & Significant Figures**
**Step 1: Rounding Whole Numbers & Decimals**
* Identify the place value you are rounding to (e.g., nearest 10, nearest whole number).
* Look at the digit immediately to the **right**.
* If this digit is **5 or more, round up**. If it is **4 or less, round down**.
* Example 1: Round 3,847 to the nearest 100.
* We are looking at the hundreds digit (8). The digit to the right is 4.
* 4 is less than 5, so the 8 stays. So, **3,800**.
* Example 2: Round 15.68 to 1 decimal place.
* The first decimal place is 6. The digit to the right is 8.
* 8 is 5 or more, so the 6 rounds up to 7. So, **15.7**.
**Step 2: Estimation**
* Round numbers to 1 significant figure to make a calculation easier.
* Example: Estimate `(42 × 19) / 3.8`
* Round to: `(40 × 20) / 4`
* Calculate: `800 / 4 = 200`. The actual answer will be close to 200.
**Step 3: Significant Figures (Introductory)**
* The first significant figure is the first non-zero digit.
* Example: 0.00456 has its first significant figure as 4.
* To round to 2 significant figures (2 s.f.):
* 3,845 → The first two significant figures are 3 and 8. The next digit is 4, which is less than 5, so it's **3,800**.
* 0.05061 → The first two significant figures are 5 and 0. The next digit is 6, which is 5 or more, so round up: **0.0506**.
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### **Part 2: Extensive Practice Questions (80+ Questions)**
#### **Section A: Place Value**
1. Write the number four million, twenty-three thousand and seven in figures.
2. What is the value of the digit 7 in 3,705,612?
3. In the number 12.083, what does the digit 8 represent?
4. Circle the larger number: 909,909 or 990,099.
5. Put these numbers in ascending order: 0.34, 0.4, 0.304, 0.344.
6. What number is halfway between 1.7 and 1.8?
7. Write 4.07 in words.
8. Which number is smaller: -5 or -2?
9. Arrange in descending order: -1, -4, 0, 3, -2.
10. What is the next number in this sequence? 2.5, 2.7, 2.9, _____
#### **Section B: Calculations**
11. Calculate 4075 + 892.
12. Calculate 3001 - 987.
13. Work out 143 × 6.
14. Work out 456 × 23 using long multiplication.
15. Work out 672 ÷ 8.
16. Work out 1155 ÷ 15 using long division.
17. Calculate 15 - 4 × 3.
18. Calculate (5 + 3)² - 10.
19. Use BIDMAS to calculate: 20 ÷ (4 - 2) + 3 × 2.
20. If 23 × 14 = 322, what is 322 ÷ 14?
21. The product of two numbers is 144. One number is 12. What is the other?
22. A book costs £4.65. Sarah pays with a £10 note. How much change does she get?
23. A factory packs 24 tins in a box. How many boxes are needed for 1200 tins?
24. Tom thinks of a number. He multiplies it by 4 and then adds 7. The answer is 39. What was his original number?
#### **Section C: Factors, Multiples, Primes**
25. List all the factors of 32.
26. Write down the first five multiples of 9.
27. What is the 7th prime number?
28. From the list below, circle the prime numbers: 15, 17, 21, 23, 27, 29.
29. Find the Highest Common Factor (HCF) of 24 and 36.
30. Find the Lowest Common Multiple (LCM) of 6 and 8.
31. Write 60 as a product of its prime factors.
32. Find the HCF of 28 and 42.
33. Find the LCM of 10 and 12.
34. A baker has 18 custard tarts and 24 fruit scones. He wants to put them into boxes. Each box must have the same number of tarts and the same number of scones. What is the greatest number of boxes he can use?
35. Two lighthouses flash their lights every 12 seconds and every 18 seconds respectively. They flash together at 10:00. At what time will they next flash together?
#### **Section D: Square & Cube Numbers**
36. What is 8 squared?
37. What is the square root of 169?
38. Write down all the square numbers between 50 and 100.
39. What is 5 cubed?
40. Circle the number which is both a square and a cube number: 16, 25, 36, 64, 100.
41. A square patio has an area of 81m². What is the length of one side?
42. The volume of a cube is 125 cm³. What is the length of one edge?
#### **Section E: Negative Numbers**
43. Work out -3 + 7.
44. Work out 5 - 9.
45. Work out -2 - 4.
46. Work out -5 + (-3).
47. Work out 8 - (-2).
48. Work out -4 × 3.
49. Work out -12 ÷ -4.
50. The temperature at midnight was -5°C. By noon, it had risen by 8°C. What was the temperature at noon?
51. The temperature falls from 2°C to -6°C. By how many degrees did it fall?
#### **Section F: Rounding & Estimation**
52. Round 5,672 to the nearest 100.
53. Round 149 to the nearest 10.
54. Round 12.57 to the nearest whole number.
55. Round 8.463 to 1 decimal place.
56. Round 0.07541 to 2 decimal places.
57. Round 45,921 to 2 significant figures.
58. Round 0.005 672 to 1 significant figure.
59. Estimate the value of 51 × 19 by rounding each number to 1 significant figure.
60. Estimate the value of (398 + 512) / 21.
61. Sam says 31 × 29 is roughly 900. Is he correct? Show your estimation.
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### **Part 3: 10 Previous Year-Style GL Assessment Questions**
1. What is the value of the digit 5 in the number 1,567,032?
a) 5,000
b) 50,000
c) 500,000
d) 5,000,000
2. Which of these numbers is a multiple of both 3 and 7?
a) 17
b) 24
c) 42
d) 51
3. Calculate: 15 - 3 × 4 + 2
a) 5
b) 14
c) 44
d) 50
4. Round 4.857 to one decimal place.
a) 4.8
b) 4.9
c) 5.0
d) 4.85
5. The temperature in a freezer is -18°C. The temperature in a fridge is 15°C warmer. What is the temperature in the fridge?
a) -33°C
b) -3°C
c) 3°C
d) 33°C
6. Which of these calculations has the greatest answer?
a) -6 + 3
b) -6 - 3
c) 6 - (-3)
d) 6 + (-3)
7. A packet of seeds costs £1.48. Ben buys 3 packets and pays with a £10 note. How much change should he get?
a) £4.56
b) £5.44
c) £5.56
d) £8.52
8. What is the Highest Common Factor (HCF) of 16 and 40?
a) 2
b) 4
c) 8
d) 80
9. Which number is one less than a square number and one more than a cube number?
a) 6
b) 9
c) 26
d) 65
10. A number is rounded to the nearest 10,000 and becomes 670,000. What is the smallest possible value the number could have been?
a) 665,000
b) 665,001
c) 669,000
d) 669,999
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### **Answer Key & Solutions for the 10 GL-Style Questions**
1. **c) 500,000**
* *Solution: The digit 5 is in the hundred thousands column: 5 × 100,000 = 500,000.*
2. **c) 42**
* *Solution: Multiples of 3 and 7 are multiples of their LCM. LCM of 3 and 7 is 21. Multiples of 21 are 21, 42, 63... 42 is the only option from the list.*
3. **a) 5**
* *Solution: Use BIDMAS: Multiplication first: 3 × 4 = 12. Then addition/subtraction left to right: 15 - 12 + 2 = 3 + 2 = 5.*
4. **b) 4.9**
* *Solution: The first decimal place is 8. The digit to the right is 5, so we round the 8 up to 9. Therefore, 4.857 → 4.9.*
5. **b) -3°C**
* *Solution: "15°C warmer" means we add 15. So, -18 + 15 = -3°C.*
6. **c) 6 - (-3)**
* *Solution: Calculate each: a) -3, b) -9, c) 6 + 3 = 9, d) 3. The greatest is 9.*
7. **c) £5.56**
* *Solution: Cost = 3 × £1.48 = £4.44. Change = £10.00 - £4.44 = £5.56.*
8. **c) 8**
* *Solution: Factors of 16: 1, 2, 4, 8, 16. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. The highest common factor is 8.*
9. **c) 26**
* *Solution: Check each option. 26 is one less than 27 (which is 3³) and one more than 25 (which is 5²). So, 26 = cube + 1 and square - 1.*
10. **a) 665,000**
* *Solution: To round to the nearest 10,000, we look at the thousands digit. For the number to round up to 670,000, the thousands digit must be 5 or more. The smallest number that rounds to 670,000 is 665,000 (as the thousands digit is 5).*
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**How to Use This Guide Effectively:**
1. Work through the concept guide and make your own notes.
2. Attempt the practice questions in sections, marking them as you go.
3. Identify your weak areas and focus on them.
4. Time yourself on the 10 GL-style questions to simulate exam conditions.
5. Always review the solutions for any mistakes to understand where you went wrong.
Good luck with your preparation
Of course! Here is an extensive collection of 200+ practice questions in the style of the GL Assessment 11+ exam for Maths, specifically for the Wellington Primary School 11+ at Slough Grammar School. The questions are organized by topic and include a comprehensive answer key with solutions.
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### **Section 1: HCF (10 Questions)**
1. Find the Highest Common Factor (HCF) of 24 and 36.
2. What is the HCF of 18 and 30?
3. Find the HCF of 42 and 56.
4. What is the HCF of 75 and 105?
5. Two numbers have an HCF of 6. One of the numbers is 18. What could the other number be?
6. Find the HCF of 54, 72, and 90.
7. A gardener has 20 tulip bulbs and 35 daffodil bulbs. He wants to plant them in identical rows, with only one type of flower in each row, but each row having the same number of bulbs. What is the greatest number of bulbs he can plant in each row?
8. What is the HCF of 121 and 143?
9. Find the HCF of 48 and 64.
10. Ribbons of length 40cm and 64cm are to be cut into smaller pieces of equal length. What is the greatest possible length for each piece?
### **Section 2: LCM (10 Questions)**
11. Find the Lowest Common Multiple (LCM) of 6 and 8.
12. What is the LCM of 5 and 7?
13. Find the LCM of 12 and 18.
14. What is the LCM of 9 and 15?
15. Two numbers have an LCM of 60. One of the numbers is 12. What is the other number?
16. Find the LCM of 8, 10, and 12.
17. A bell rings every 18 seconds. Another bell rings every 24 seconds. If they ring together now, how many seconds will it be before they next ring together?
18. What is the LCM of 14 and 21?
19. Find the LCM of 16 and 20.
20. Sarah is stacking boxes that are 15cm high and boxes that are 20cm high. What is the lowest height at which the two stacks will be level?
### **Section 3: Factors (10 Questions)**
21. List all the factors of 28.
22. How many factors does 36 have?
23. What is the smallest factor of any whole number?
24. What is the largest factor of 49?
25. Is 5 a factor of 102?
26. Find the common factors of 16 and 24.
27. A number has exactly three factors. What type of number must it be?
28. What is the sum of all the factors of 15?
29. Which number is a factor of all whole numbers?
30. Find a number that has exactly 6 factors.
### **Section 4: Multiples (10 Questions)**
31. List the first five multiples of 9.
32. What is the 12th multiple of 7?
33. Is 48 a multiple of 6?
34. Find the common multiples of 4 and 6 up to 40.
35. What is the smallest multiple of 11 that is greater than 100?
36. A number is a multiple of both 3 and 5. What other number must it be a multiple of?
37. What is the difference between the 5th and 10th multiple of 8?
38. Which of the following is a multiple of 13? 52, 64, 78, 81.
39. Find the first multiple of 15 that is also a multiple of 10.
40. A bus arrives at a stop every 15 minutes. The first bus is at 8:00 am. What time will the fifth bus arrive?
### **Section 5: Primes (10 Questions)**
41. List all the prime numbers between 20 and 40.
42. Is 1 a prime number? Explain.
43. What is the only even prime number?
44. Write 42 as a product of its prime factors.
45. What is the sum of the first three prime numbers?
46. Find the next prime number after 31.
47. Are 15 and 16 co-prime? (Do they share any common factors other than 1?)
48. What is the smallest prime number greater than 50?
49. How many prime numbers are there between 1 and 30?
50. Which of the following is prime? 39, 41, 49, 51.
### **Section 6: Square & Cube Numbers (10 Questions)**
51. What is 9 squared (9²)?
52. What is the square root of 144?
53. What is 4 cubed (4³)?
54. Between which two consecutive whole numbers does the square root of 50 lie?
55. A square number is multiplied by itself to give 256. What is the number?
56. What is the value of 2³ + 3²?
57. Which of the following is a square number? 100, 110, 120, 130.
58. A cube has a volume of 64 cm³. What is the length of one side?
59. Find the value of √81 + ∛27.
60. What is the smallest square number greater than 150?
### **Section 7: Rounding & Estimation (10 Questions)**
61. Round 4,567 to the nearest 100.
62. Round 12.345 to 1 decimal place.
63. Estimate the value of 398 + 512 by rounding to the nearest 10.
64. Round 0.075 to 2 decimal places.
65. A book has 187 pages. Round this to the nearest 10.
66. Estimate the product of 41 and 39.
67. Round 123,456 to 2 significant figures.
68. The mass of a bag of flour is 1.495 kg. Round this to the nearest 0.1 kg.
69. Estimate the answer to 5.7 × 4.2.
70. Round 9.999 to the nearest whole number.
### **Section 8: Negative Numbers in Context (10 Questions)**
71. The temperature is -5°C and it rises by 8°C. What is the new temperature?
72. The temperature is 3°C and then falls by 7°C. What is the new temperature?
73. A diver is at 30m below sea level. She ascends 12m. What is her new depth?
74. The temperature is -2°C and then falls by 4°C. What is the new temperature?
75. A bank account has a balance of -£25 (an overdraft). £50 is paid in. What is the new balance?
76. The temperature is -10°C and it rises by 15°C. What is the new temperature?
77. A lift is on the 4th floor. It goes down 7 floors. On which floor is it now?
78. The temperature is 5°C and then falls by 10°C. What is the new temperature?
79. A plane is flying at 25,000 feet. It descends 8,000 feet. What is its new altitude?
80. The lowest point in a valley is 150m below sea level. The top of the nearby hill is 450m above sea level. What is the difference in height between these two points?
### **Section 9: Negative Numbers (10 Questions)**
81. Calculate: -5 + 8
82. Calculate: 3 - 7
83. Calculate: -4 - 3
84. Calculate: -2 + (-5)
85. Calculate: 6 - (-2)
86. Calculate: -8 - (-3)
87. Calculate: -1 + 9
88. Calculate: 0 - 6
89. Calculate: -7 + 4
90. Calculate: -5 - (-5)
### **Section 10: BIDMAS/BODMAS (10 Questions)**
91. Calculate: 3 + 4 × 2
92. Calculate: (3 + 4) × 2
93. Calculate: 10 - 6 ÷ 2
94. Calculate: (10 - 6) ÷ 2
95. Calculate: 8 ÷ 2 × 4
96. Calculate: 8 ÷ (2 × 4)
97. Calculate: 2 + 3² × 2
98. Calculate: (2 + 3)² × 2
99. Calculate: 20 ÷ 4 + 5 × 2
100. Calculate: 20 ÷ (4 + 5) × 2
### **Section 11: Inverse Operations (10 Questions)**
101. If 7 × 8 = 56, then what is 56 ÷ 8?
102. If 45 ÷ 9 = 5, then what is 5 × 9?
103. If 12 + 18 = 30, then what is 30 - 18?
104. If 25 - 13 = 12, then what is 12 + 13?
105. If 6² = 36, then what is √36?
106. If 4³ = 64, then what is ∛64?
107. I think of a number, multiply it by 5 and get 35. What was my number?
108. I think of a number, subtract 8 and get 12. What was my number?
109. Use inverse operations to find the missing number: ? ÷ 7 = 11
110. Use inverse operations to find the missing number: ? - 15 = 22
### **Section 12: Mixed Word Problems & Multi-step (15 Questions)**
111. A box contains 12 packs of biscuits. Each pack has 8 biscuits. How many biscuits are there in 5 boxes?
112. A car park has 6 levels. Each level can hold 45 cars. How many cars can the car park hold when it is full?
113. A book has 250 pages. John reads 15 pages each day. How many days will it take him to read the book?
114. A train has 8 carriages. Each carriage has 56 seats. How many seats are on the train?
115. A factory produces 250 toys each day. How many toys are produced in 5 days?
116. A school has 24 classes. Each class has 30 students. How many students are in the school?
117. A shirt costs £15 and a tie costs £6. How much do 3 shirts and 2 ties cost?
118. A bus has 52 seats. 38 people are on the bus. How many empty seats are there?
119. A packet of sweets has 24 sweets. How many sweets are in 6 packets?
120. A rectangle is 12 cm long and 8 cm wide. What is its perimeter?
121. A rectangle has an area of 48 cm² and one side is 6 cm. What is the length of the other side?
122. A bus leaves the station with 42 passengers. At the first stop, 15 get off and 8 get on. How many passengers are now on the bus?
123. Tom has £50. He buys 3 books at £7 each and a DVD for £12. How much money does he have left?
124. A school trip costs £25 per student. If 30 students go, how much money is collected?
125. A cake is cut into 12 equal slices. 5 slices are eaten. What fraction of the cake is left?
### **Section 13: Fictional "Previous Year Paper" (50 Questions)**
126. What is the value of the digit 5 in the number 2,543,100?
127. Round 12.678 to one decimal place.
128. Calculate: 15 - 3 × 4
129. What is the HCF of 18 and 24?
130. What is the LCM of 6 and 8?
131. Which of these numbers is prime? 21, 23, 25, 27
132. What is 9 squared?
133. What is the cube root of 64?
134. Calculate: -7 + 12
135. Calculate: 8 - (-4)
136. Estimate 49 × 51 by rounding to the nearest ten.
137. The temperature is -3°C and it rises by 8°C. What is the new temperature?
138. Calculate: (4 + 5) × (6 - 2)
139. If 6 × 7 = 42, then what is 42 ÷ 7?
140. A pack of 6 pencils costs £1.20. How much does one pencil cost?
141. A rectangle is 9 cm by 5 cm. What is its area?
142. What is the perimeter of a square with side length 6 cm?
143. What is the next number in the sequence: 3, 6, 9, 12, ...?
144. What is the missing number? ? ÷ 7 = 9
145. Write 0.75 as a fraction in its simplest form.
146. What is 1/4 of 20?
147. What is 3/5 as a decimal?
148. What is 10% of 80?
149. A TV costs £400. It is reduced by 15% in a sale. What is the sale price?
150. A car travels 60 miles in 1 hour. How far will it travel in 3 hours?
151. What is the average of 4, 7, 9 and 12?
152. A bag has 3 red, 4 blue and 5 green marbles. What is the probability of picking a red marble?
153. Simplify the ratio 12:18.
154. If 3 pens cost £1.50, how much do 5 pens cost?
155. A map has a scale of 1:10000. If 2 cm on the map represents an actual distance of 200 m, what is the actual distance of 5 cm on the map?
156. What is the time 2 hours and 15 minutes after 10:30 am?
157. How many seconds are in 3 minutes?
158. How many grams are in 2.5 kg?
159. How many millilitres are in 3.5 litres?
160. What is the area of a triangle with base 10 cm and height 6 cm?
161. What is the volume of a cube with side length 3 cm?
162. What is the missing angle in a triangle with angles 40° and 60°?
163. How many lines of symmetry does a square have?
164. What is the name of a polygon with 5 sides?
165. What is the mean of the numbers 5, 7, 8, 10, 10?
166. What is the mode of the numbers 3, 4, 4, 5, 6, 4?
167. What is the median of the numbers 2, 4, 6, 8, 10?
168. What is the range of the numbers 10, 15, 20, 25, 30?
169. A dice is rolled. What is the probability of rolling a number less than 3?
170. A coin is flipped twice. What is the probability of getting two heads?
171. Solve the equation: 2x + 3 = 11
172. What is the value of 2a + 3b when a=4 and b=5?
173. Expand: 3(x + 4)
174. Factorise: 5x + 10
175. What is the next term in the sequence: 2, 4, 8, 16, ...?
### **Section 14: More Previous Year GL Assessment Styles (50 Questions)**
176. What is the value of the digit 8 in the number 8,123,456?
177. Round 5.678 to two decimal places.
178. Calculate: 20 ÷ 4 + 3 × 2
179. What is the HCF of 30 and 45?
180. What is the LCM of 10 and 12?
181. Which of these numbers is prime? 29, 33, 35, 39
182. What is 12 squared?
183. What is the cube of 5?
184. Calculate: -5 - 8
185. Calculate: 10 - (-5)
186. Estimate 61 × 29 by rounding to the nearest ten.
187. The temperature is 2°C and it falls by 8°C. What is the new temperature?
188. Calculate: 3 + 4 × (5 - 2)
189. If 8 × 9 = 72, then what is 72 ÷ 9?
190. A pack of 8 batteries costs £4.80. How much does one battery cost?
191. A rectangle is 12 cm by 7 cm. What is its area?
192. What is the perimeter of an equilateral triangle with side length 9 cm?
193. What is the next number in the sequence: 5, 10, 15, 20, ...?
194. What is the missing number? ? × 6 = 54
195. Write 0.6 as a fraction in its simplest form.
196. What is 3/4 of 24?
197. What is 2/5 as a decimal?
198. What is 20% of 50?
199. A bike costs £300. It is reduced by 10% in a sale. What is the sale price?
200. A train travels 100 miles in 2 hours. How far will it travel in 5 hours?
201. What is the average of 5, 10, 15 and 20?
202. A bag has 2 red, 3 blue and 4 green marbles. What is the probability of picking a blue marble?
203. Simplify the ratio 20:30.
204. If 4 books cost £12, how much do 6 books cost?
205. A map has a scale of 1:50000. If 4 cm on the map represents an actual distance of 2 km, what is the actual distance of 10 cm on the map?
206. What is the time 3 hours and 20 minutes after 11:45 am?
207. How many minutes are in 2.5 hours?
208. How many centimetres are in 3.2 m?
209. How many litres are in 4500 ml?
210. What is the area of a triangle with base 8 cm and height 5 cm?
211. What is the volume of a cuboid with dimensions 4 cm, 5 cm and 6 cm?
212. What is the missing angle in a triangle with angles 50° and 70°?
213. How many lines of symmetry does a rectangle have?
214. What is the name of a polygon with 6 sides?
215. What is the mean of the numbers 2, 4, 6, 8, 10?
216. What is the mode of the numbers 1, 2, 2, 3, 4, 2?
217. What is the median of the numbers 1, 3, 5, 7, 9?
218. What is the range of the numbers 5, 10, 15, 20, 25?
219. A dice is rolled. What is the probability of rolling an even number?
220. A coin is flipped three times. What is the probability of getting at least one head?
221. Solve the equation: 3x - 4 = 11
222. What is the value of 4x - 2y when x=3 and y=2?
223. Expand: 2(3x - 5)
224. Factorise: 6x - 9
225. What is the next term in the sequence: 1, 4, 9, 16, ...?
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### **COMPREHENSIVE ANSWER KEY & SOLUTIONS**
**Section 1: HCF**
1. 12
2. 6
3. 14
4. 15
5. Could be 6, 12, or 30 (any number where HCF with 18 is 6)
6. 18
7. HCF of 20 and 35 is 5. So, 5 bulbs per row.
8. 11
9. 16
10. HCF of 40 and 64 is 8. So, 8cm per piece.
**Section 2: LCM**
11. 24
12. 35
13. 36
14. 45
15. 15 (since 60 ÷ 12 = 5, and 12 × 5 = 60, but the other number must be 15 for LCM to be 60: Multiples of 12: 12,24,36,48,60; Multiples of 15: 15,30,45,60)
16. 120
17. LCM of 18 and 24 is 72 seconds.
18. 42
19. 80
20. LCM of 15 and 20 is 60cm.
**Section 3: Factors**
21. 1, 2, 4, 7, 14, 28
22. 9 factors (1, 2, 3, 4, 6, 9, 12, 18, 36)
23. 1
24. 49
25. No, because 102 ÷ 5 = 20.4, not a whole number.
26. 1, 2, 4, 8
27. A square number (specifically, the square of a prime number, e.g., 4, 9, 25)
28. 1+3+5+15=24
29. 1
30. 12 (factors: 1,2,3,4,6,12)
**Section 4: Multiples**
31. 9, 18, 27, 36, 45
32. 84
33. Yes
34. 12, 24, 36
35. 110 (11 × 10 = 110)
36. 15 (LCM of 3 and 5)
37. 10th multiple (80) - 5th multiple (40) = 40
38. 52 and 78
39. 30
40. 8:00 + (4 intervals × 15 mins) = 9:00 am. (The 1st bus is at 8:00, 2nd at 8:15, 3rd at 8:30, 4th at 8:45, 5th at 9:00).
**Section 5: Primes**
41. 23, 29, 31, 37
42. No, a prime number has exactly two distinct factors: 1 and itself. 1 only has one factor.
43. 2
44. 2 × 3 × 7
45. 2 + 3 + 5 = 10
46. 37
47. Yes, factors of 15 are 1,3,5,15; factors of 16 are 1,2,4,8,16. Only common factor is 1.
48. 53
49. 10 (2,3,5,7,11,13,17,19,23,29)
50. 41
**Section 6: Square & Cube Numbers**
51. 81
52. 12
53. 64
54. 7 and 8 (since 7²=49 and 8²=64)
55. 16 (√256 = 16)
56. 8 + 9 = 17
57. 100
58. 4 cm (∛64 = 4)
59. 9 + 3 = 12
60. 169 (13²)
**Section 7: Rounding & Estimation**
61. 4,600
62. 12.3
63. 400 + 510 = 910
64. 0.08
65. 190
66. 40 × 40 = 1600
67. 120,000
68. 1.5 kg
69. 6 × 4 = 24
70. 10
**Section 8: Negative Numbers in Context**
71. 3°C
72. -4°C
73. -18m (or 18m below sea level)
74. -6°C
75. £25
76. 5°C
77. -3rd floor (or 3 floors below ground)
78. -5°C
79. 17,000 feet
80. 600m (450 - (-150) = 450 + 150 = 600)
**Section 9: Negative Numbers**
81. 3
82. -4
83. -7
84. -7
85. 8
86. -5
87. 8
88. -6
89. -3
90. 0
**Section 10: BIDMAS/BODMAS**
91. 3 + (4×2) = 3+8=11
92. (7)×2=14
93. 10 - 3 = 7
94. 4 ÷ 2 = 2
95. 4 × 4 = 16
96. 8 ÷ 8 = 1
97. 2 + (9×2) = 2+18=20
98. (5²)×2 = 25×2=50
99. 5 + 10 = 15
100. 20 ÷ 9 × 2 = (20/9)×2 = 40/9 = 4.44...
**Section 11: Inverse Operations**
101. 7
102. 45
103. 12
104. 25
105. 6
106. 4
107. 7 (35 ÷ 5 = 7)
108. 20 (12 + 8 = 20)
109. 77 (11 × 7 = 77)
110. 37 (22 + 15 = 37)
**Section 12: Mixed Word Problems & Multi-step**
111. 12 × 8 × 5 = 480 biscuits
112. 6 × 45 = 270 cars
113. 250 ÷ 15 = 16.66... so 17 days
114. 8 × 56 = 448 seats
115. 250 × 5 = 1250 toys
116. 24 × 30 = 720 students
117. (3×15) + (2×6) = 45 + 12 = £57
118. 52 - 38 = 14 empty seats
119. 24 × 6 = 144 sweets
120. 2×(12+8) = 40 cm
121. 48 ÷ 6 = 8 cm
122. 42 - 15 + 8 = 35 passengers
123. 50 - (21 + 12) = 50 - 33 = £17
124. 25 × 30 = £750
125. (12-5)/12 = 7/12
**Section 13: Fictional "Previous Year Paper" (Condensed Answers)**
126. 500,000
127. 12.7
128. 3
129. 6
130. 24
131. 23
132. 81
133. 4
134. 5
135. 12
136. 50×50=2500
137. 5°C
138. 9×4=36
139. 6
140. £0.20
141. 45 cm²
142. 24 cm
143. 15
144. 63
145. 3/4
146. 5
147. 0.6
148. 8
149. £340
150. 180 miles
151. 8
152. 1/4
153. 2:3
154. £2.50
155. 500 m
156. 12:45 pm
157. 180
158. 2500 g
159. 3500 ml
160. 30 cm²
161. 27 cm³
162. 80°
163. 4
164. Pentagon
165. 8
166. 4
167. 6
168. 20
169. 1/3
170. 1/4
171. x=4
172. 23
173. 3x+12
174. 5(x+2)
175. 32
**Section 14: More GL Styles (Condensed Answers)**
176. 8,000,000
177. 5.68
178. 11
179. 15
180. 60
181. 29
182. 144
183. 125
184. -13
185. 15
186. 1800
187. -6°C
188. 15
189. 8
190. £0.60
191. 84 cm²
192. 27 cm
193. 25
194. 9
195. 3/5
196. 18
197. 0.4
198. 10
199. £270
200. 250 miles
201. 12.5
202. 1/3
203. 2:3
204. £18
205. 5 km
206. 3:05 pm
207. 150
208. 320 cm
209. 4.5 L
210. 20 cm²
211. 120 cm³
212. 60°
213. 2
214. Hexagon
215. 6
216. 2
217. 5
218. 20
219. 1/2
220. 7/8
221. x=5
222. 8
223. 6x-10
224. 3(2x-3)
225. 25
Good luck
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