Algebra worksheet — GCSE Higher

1.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.

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

3.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

4.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

5.f(x) = 3x − 2. Find f⁻¹(x).

6.Work out the coordinates of the reflection of (6, −3) in the y-axis.

7.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

8.Work out the value of (x − 4)/2 + 3 when x = 10

9.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

10.Which of these quadratic graphs does NOT cross the x-axis at all?

11.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.

12.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

13.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

14.Work out the gradient of the straight line with equation y = (2x/5) − 3.

15.A square patio of side length n slabs is surrounded by a single border of square paving slabs of the same size. For a patio with side length n, the total number of slabs used for the patio and its border together is 9 when n = 1, 16 when n = 2, 25 when n = 3, and 36 when n = 4. Work out an expression, in terms of n, for the total number of slabs.