GCSE maths questions, with the working shown

1. The bottom numbers are 8 and 7. The smallest number they both go into is 56, so use 56 as the common bottom.
2. Change the fractions so they both have 56 on the bottom: 38 = 2156, and 17 = 856.
3. Subtract the tops and keep the bottom the same: 2156 − 856 = 1356.

Answer 1356

1. Find the digit in the 2nd decimal place. It is 0. Then look at the digit straight after it, which is 8.
2. 8 is 5 or more, so the 0 goes up by one (round up).
3. Drop the digits after it. 50.508 to 2 decimal places is 50.51.

Answer 50.51

1. The power is 6, so move the decimal point 6 places to the right.
2. Fill any empty places with zeros.
3. 8.55 × 10⁶ = 8,550,000.

Answer 8,550,000

1. Factors of 35: 1, 5, 7, 35.
2. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
3. The biggest number in both lists is 5.

Answer 5

1. Brackets first: 3 + 4 = 7.
2. Then multiply: 7 × 4 = 28.
3. Then subtract: 28 − 4 = 24.

Answer 24

1. Replace x with 2: 5 × 2 + 7.
2. Multiply first: 5 × 2 = 10.
3. Then add: 10 + 7 = 17.

Answer 17

1. Collect the x terms: 1 − 6 + 1 = −4, so −4x.
2. Collect the y terms: 6 + 3 = 9, so 9y.
3. Put the answer together: −4x + 9y.

Answer −4x + 9y

1. Multiply the numbers: 6 × 2 = 12.
2. Add the powers of t: 9 + 7 = 16.
3. Put them together: 12t¹⁶.

Answer 12t¹⁶

1. Multiply every term inside the bracket by -6.
2. (−6) × 2x = −12x
3. (−6) × 8 = −48
4. Put the results together: −12x − 48.

Answer −12x − 48

1. Find the biggest factor that goes into every term (a letter). Here it is x.
2. Write x outside a bracket. Inside, put what is left after dividing each term by x: 2x² ÷ x = 2x and 5x ÷ x = 5.
3. So 2x² + 5x = x(2x + 5).
4. Check by expanding: x(2x + 5) gives back 2x² + 5x.

Answer x(2x + 5)

1. Take 11 away from both sides: x ÷ 8 = 18 − 11 = 7.
2. Multiply both sides by 8: x = 7 × 8 = 56.

Answer x = 56

1. Replace n with 5: 3 × 5 + 4.
2. 3 × 5 = 15, then 15 + 4 = 19.

Answer 19

1. Call the equations (1) and (2). The y terms are y and y, so we can eliminate y.
2. The y terms have the same sign, so SUBTRACT (2) from (1): 2x = −2.
3. Divide by 2: x = −2 ÷ 2 = −1.
4. Put x = −1 into equation (1): 6 × (−1) + y = −11, so y = −5.
5. Check in equation (2): 4 × (−1) + 1 × (−5) = −9. It works.

Answer x = −1, y = −5

1. Two things multiplied together make 0, so one of them must be 0.
2. x+5 = 0 gives x = −5.
3. x+9 = 0 gives x = −9.
4. The answers are x = −5 and x = −9.

Answer x = −5, x = −9

1. Find the biggest number that goes into every number in the ratio: 3.
2. Divide each number by 3: 12 : 3 : 27 = 4 : 1 : 9.
3. One of the numbers is 1, so nothing else can go into all of them. That is the simplest form.

Answer 4 : 1 : 9

1. First find 5% of £400. Find 10% first: £400 ÷ 10 = £40.
2. 5% is half of 10%: £40 ÷ 2 = £20.
3. Take it off: £400 − £20 = £380.

Answer £380