GCSE: Math Practice Test! Trivia Quiz

1. What is the Lowest Common Multiple (LCM) of 4 and 7?

14

47

2

28

The LCM (Lowest Common Multiple) is the smallest multiple that two or more numbers have in common. In this case, we need to find the LCM of 4 and 7. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and so on. The multiples of 7 are 7, 14, 21, 28, and so on. The smallest multiple that both 4 and 7 have in common is 28, so the answer is 28.

Explanation

The LCM (Lowest Common Multiple) is the smallest multiple that two or more numbers have in common. In this case, we need to find the LCM of 4 and 7. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and so on. The multiples of 7 are 7, 14, 21, 28, and so on. The smallest multiple that both 4 and 7 have in common is 28, so the answer is 28.

2. Share £220 in the ratio 4 : 7

80 and 140

40 and 140

70 and 150

55 and 165

The given ratio is 4:7, which means that for every 4 parts, there are 7 parts. To divide £220 in this ratio, we need to find the value of each part.

To find the value of one part, we divide £220 by the sum of the parts in the ratio, which is 4+7=11.

£220 divided by 11 is £20.

Now, we multiply this value by the number of parts in each ratio to find the amount for each part:

4 parts x £20 = £80
7 parts x £20 = £140

Therefore, the correct answer is 80 and 140.

Explanation

The given ratio is 4:7, which means that for every 4 parts, there are 7 parts. To divide £220 in this ratio, we need to find the value of each part.

To find the value of one part, we divide £220 by the sum of the parts in the ratio, which is 4+7=11.

£220 divided by 11 is £20.

Now, we multiply this value by the number of parts in each ratio to find the amount for each part:

4 parts x £20 = £80
7 parts x £20 = £140

Therefore, the correct answer is 80 and 140.

3. What is 16% of £345?

£55.20

£57.80

£34.50

£552

To find 16% of £345, we can multiply £345 by 0.16. This gives us £55.20, which is the correct answer.

Explanation

To find 16% of £345, we can multiply £345 by 0.16. This gives us £55.20, which is the correct answer.

4. What is ²/₃ - ⁵/₁₂

7/12

9/3

10/12

3/12

The correct answer is 3/12 because when subtracting fractions, we need to have a common denominator. In this case, the common denominator is 12. So, we convert 2/3 to 8/12 by multiplying the numerator and denominator by 4. Then, we subtract 5/12 from 8/12, which gives us 3/12.

Explanation

The correct answer is 3/12 because when subtracting fractions, we need to have a common denominator. In this case, the common denominator is 12. So, we convert 2/3 to 8/12 by multiplying the numerator and denominator by 4. Then, we subtract 5/12 from 8/12, which gives us 3/12.

5. Write 28 as a product of prime factors.

4 x 7

1 x 2 x 14

2 x 2 x 7

2 x 7 x 7

28 = 2 x 14 14 = 2 x 7 2 and 7 are prime Therefore 28 = 2 x 2 x 7

Explanation

28 = 2 x 14 14 = 2 x 7 2 and 7 are prime Therefore 28 = 2 x 2 x 7

6. Estimate the answer to 5 x 0.05.

2.5

0.025

0.25

2.05

To estimate the answer to 5 x 0.05, we can round 0.05 to the nearest whole number, which is 0.1. Then, we multiply 5 by 0.1 to get 0.5. However, since we rounded 0.05 up, the actual answer will be slightly less than 0.5. The closest option to 0.5 is 0.25, which is the correct answer.

Explanation

To estimate the answer to 5 x 0.05, we can round 0.05 to the nearest whole number, which is 0.1. Then, we multiply 5 by 0.1 to get 0.5. However, since we rounded 0.05 up, the actual answer will be slightly less than 0.5. The closest option to 0.5 is 0.25, which is the correct answer.

7. Estimate the answer to 30 x 0.2.

60

0.6

0.03

6

The given question asks to estimate the answer to 30 multiplied by 0.2. When we multiply 30 by 0.2, we get 6. Therefore, the correct answer is 6.

Explanation

The given question asks to estimate the answer to 30 multiplied by 0.2. When we multiply 30 by 0.2, we get 6. Therefore, the correct answer is 6.

8. What is 2³ x 2⁵in index form?

256

2 to the power of 2

2 to the power 15

2 to the power of 8

The correct answer is 2 to the power of 8. In index form, 23 x 25 can be written as 2^3 x 2^5. When you multiply two numbers with the same base, you add their exponents. Therefore, 2^3 x 2^5 = 2^(3+5) = 2^8.

Explanation

The correct answer is 2 to the power of 8. In index form, 23 x 25 can be written as 2^3 x 2^5. When you multiply two numbers with the same base, you add their exponents. Therefore, 2^3 x 2^5 = 2^(3+5) = 2^8.

9. What is ¹/₃ + ³/₆

4/6

5/6

3/18

4/9

The given expression is asking for the sum of 1/3 and 3/6. To add these fractions, we need to find a common denominator, which in this case is 6. We can convert 1/3 to 2/6 by multiplying the numerator and denominator by 2. Now we have 2/6 + 3/6, which equals 5/6. Therefore, the correct answer is 5/6.

Explanation

The given expression is asking for the sum of 1/3 and 3/6. To add these fractions, we need to find a common denominator, which in this case is 6. We can convert 1/3 to 2/6 by multiplying the numerator and denominator by 2. Now we have 2/6 + 3/6, which equals 5/6. Therefore, the correct answer is 5/6.

10. What is 36: 108 in the simplest form?

2 : 54

1 : 3

1 : 4

4 : 12

The given ratio 36:108 can be simplified by dividing both numbers by their greatest common divisor, which is 36. This simplifies the ratio to 1:3.

Explanation

The given ratio 36:108 can be simplified by dividing both numbers by their greatest common divisor, which is 36. This simplifies the ratio to 1:3.

11. What is the Highest Common Factor (HCF) of 28 and 70?

14

7

140

2

The highest common factor (HCF) of two numbers is the largest number that divides both numbers evenly. To find the HCF of 28 and 70, we can list the factors of each number and find the largest common factor. The factors of 28 are 1, 2, 4, 7, 14, and 28. The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The largest common factor is 14, so the HCF of 28 and 70 is 14.

Explanation

The highest common factor (HCF) of two numbers is the largest number that divides both numbers evenly. To find the HCF of 28 and 70, we can list the factors of each number and find the largest common factor. The factors of 28 are 1, 2, 4, 7, 14, and 28. The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The largest common factor is 14, so the HCF of 28 and 70 is 14.

12. What is 3²/₅ + 6¹/₃

9 3/15

10 1/3

9 3/8

9 11/15

To find the sum of fractions, we need to have a common denominator. In this case, the common denominator is 15. So, we convert 32/5 to an equivalent fraction with a denominator of 15, which is 96/15. Similarly, we convert 61/3 to an equivalent fraction with a denominator of 15, which is 305/15. Now, we add these fractions together, which gives us 401/15. To simplify this fraction, we divide the numerator by the denominator, resulting in a whole number of 26 and a remainder of 11. Therefore, the answer is 9 11/15.

Explanation

To find the sum of fractions, we need to have a common denominator. In this case, the common denominator is 15. So, we convert 32/5 to an equivalent fraction with a denominator of 15, which is 96/15. Similarly, we convert 61/3 to an equivalent fraction with a denominator of 15, which is 305/15. Now, we add these fractions together, which gives us 401/15. To simplify this fraction, we divide the numerator by the denominator, resulting in a whole number of 26 and a remainder of 11. Therefore, the answer is 9 11/15.

13. Guildford is 27 miles from Petersfield. How long will a journey take at an average speed of 45 mph?

30 minutes

28 minutes

36 minutes

12 minutes

At an average speed of 45 mph, the journey from Guildford to Petersfield, which is 27 miles away, will take approximately 36 minutes. This can be calculated by dividing the distance (27 miles) by the speed (45 mph), which gives us 0.6 hours. Multiplying 0.6 by 60 minutes (since there are 60 minutes in an hour) gives us 36 minutes. Therefore, the correct answer is 36 minutes.

Explanation

At an average speed of 45 mph, the journey from Guildford to Petersfield, which is 27 miles away, will take approximately 36 minutes. This can be calculated by dividing the distance (27 miles) by the speed (45 mph), which gives us 0.6 hours. Multiplying 0.6 by 60 minutes (since there are 60 minutes in an hour) gives us 36 minutes. Therefore, the correct answer is 36 minutes.

14. Round 8327.4578 to 3 significant figures.

8327

8300

8327.458

8330

To round a number to 3 significant figures, we start from the leftmost non-zero digit and count three digits, including any zeros. In this case, the leftmost non-zero digit is 8. Counting three digits from the left, we have 832. The next digit, 7, is greater than or equal to 5, so we round up. Therefore, the rounded number is 8330.

Explanation

To round a number to 3 significant figures, we start from the leftmost non-zero digit and count three digits, including any zeros. In this case, the leftmost non-zero digit is 8. Counting three digits from the left, we have 832. The next digit, 7, is greater than or equal to 5, so we round up. Therefore, the rounded number is 8330.

15. I am buying some washing powder and there are four different offers. Which one is the best value?

200g @ £1.25

2 Kg @ £6.50

500g @ £1.55

1 Kg @ £3.59

To find the best value, we need to calculate the cost per gram for each offer:

200g @ £1.25: £1.25 / 200g = £0.00625 per gram

2 Kg @ £6.50: £6.50 / 2000g = £0.00325 per gram

500g @ £1.55: £1.55 / 500g = £0.0031 per gram

1 Kg @ £3.59: £3.59 / 1000g = £0.00359 per gram

So, the best value is the one with the lowest cost per gram, which is the 500g @ £1.55 offer.

Explanation

To find the best value, we need to calculate the cost per gram for each offer:

200g @ £1.25: £1.25 / 200g = £0.00625 per gram

2 Kg @ £6.50: £6.50 / 2000g = £0.00325 per gram

500g @ £1.55: £1.55 / 500g = £0.0031 per gram

1 Kg @ £3.59: £3.59 / 1000g = £0.00359 per gram

So, the best value is the one with the lowest cost per gram, which is the 500g @ £1.55 offer.

16. Estimate 16 x 0.001.

0.16

0.016

16

1.6

Explanation

17. What is ⁸/₁₁ x ⁵/₇

56/55

3/4

40/77

13/18

The given question asks for the product of two fractions, 8/11 and 5/7. To find the product of two fractions, we multiply the numerators (8 x 5 = 40) and the denominators (11 x 7 = 77). Therefore, the product of 8/11 and 5/7 is 40/77.

Explanation

The given question asks for the product of two fractions, 8/11 and 5/7. To find the product of two fractions, we multiply the numerators (8 x 5 = 40) and the denominators (11 x 7 = 77). Therefore, the product of 8/11 and 5/7 is 40/77.

18. What is ²/₉ ÷ ¹/₃

2/3

6/27

5/7

9/6

The given expression is a division of fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we have (2/9) divided by (1/3), which is the same as (2/9) multiplied by (3/1). Multiplying the numerators and denominators gives us (2*3)/(9*1), which simplifies to 6/9. This further simplifies to 2/3.

Explanation

The given expression is a division of fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we have (2/9) divided by (1/3), which is the same as (2/9) multiplied by (3/1). Multiplying the numerators and denominators gives us (2*3)/(9*1), which simplifies to 6/9. This further simplifies to 2/3.

19. £2,000 is invested for 3 years at 5%. If the money is left in the bank how much will there be after 3 years in Compound interest.

£300

£2431.01

£2313.25

£2300

If £2,000 is invested for 3 years at a 5% interest rate, the amount of money in the bank after 3 years can be calculated using the formula for compound interest: A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is £2,000, the interest rate is 5%, the number of times interest is compounded per year is 1, and the number of years is 3. Plugging these values into the formula, the final amount is calculated to be £2,313.25.

Explanation

If £2,000 is invested for 3 years at a 5% interest rate, the amount of money in the bank after 3 years can be calculated using the formula for compound interest: A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is £2,000, the interest rate is 5%, the number of times interest is compounded per year is 1, and the number of years is 3. Plugging these values into the formula, the final amount is calculated to be £2,313.25.