Algebra worksheet — GCSE Higher

1.Write down the expression that means the same as (x + 7) ÷ 4.

2.By completing the square, find the turning point of the curve y = 2x² − 8x + 3.

3.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

4.A student attempts to prove that the sum of any three consecutive integers is a multiple of 3. Line 1: Let the three consecutive integers be n, n + 1 and n + 2. Line 2: Their sum is n + (n + 1) + (n + 2) = 3n + 2. Line 3: 3n + 2 leaves a remainder of 2 when divided by 3, so it is not a multiple of 3. Line 4: So the sum of three consecutive integers is not always a multiple of 3. Which line contains the FIRST error?

5.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

6.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

7.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

8.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

9.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

10.Write down the expression that means 5 more than half of n.

11.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

12.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

13.Factorise 3x² + 10x − 8.

14.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

15.The graph of y = f(x) has x-intercepts at x = −2 and x = 6 and crosses the y-axis at (0, −12). Work out the x-intercepts and the y-intercept of y = −f(x).