Algebra worksheet — GCSE Higher

1.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

2.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

3.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?

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

5.f(x) = x + 3 and g(x) = 2x. Work out fg(x).

6.The graph of y = f(x) has a maximum turning point at (−1, 6). Write down the coordinates of the maximum turning point of the graph of y = f(x − 3).

7.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

8.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

9.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

10.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

11.f(x) = 2x − 1. Work out ff(x).

12.Which expression is equivalent to 3(2x − 5) + 4x?

13.A car is decelerating. The tangent to its velocity-time graph at t = 12 seconds passes through the points (8, 22) and (16, 6), where velocity is in m/s and time is in seconds. Work out the gradient of this tangent, in m/s².

14.Make x the subject of the formula y = (x − 4)/5.

15.The trapezium rule is used to estimate the area under a curve between x = 2 and x = 6. The curve is concave up (it curves upwards, like the inside of a bowl) throughout this interval. Which statement about the estimate is correct?