Algebra worksheet — GCSE Higher

1.Work out the gradient of the straight line with equation 3y = 12 − 6x.

2.A Fibonacci-type sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₁ = 5 and a₃ = 17, work out a₂.

3.A cyclist's velocity increases from 3 m/s to 11 m/s over 5 seconds, at a constant rate. Work out the cyclist's acceleration, in m/s².

4.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

5.Solve 6x − 5 = 3x + 13.

6.The numbers x and y satisfy x + y = 10 and xy = 21. Work out the pair of values.

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

8.A student attempts to prove that the product of two consecutive integers is always even: (i) Let the two consecutive integers be n and n + 1. (ii) Since n(n + 1) is even, one of n and n + 1 must be an even number. (iii) Therefore, n(n + 1) is even. At which statement does the proof first assume the very fact it is trying to prove?

9.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.

10.A car accelerates uniformly from rest at 2.5 m/s² until it reaches a speed of 20 m/s, then travels at this constant speed for a further 30 seconds. Work out the total distance travelled.

11.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

12.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

13.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

14.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

15.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.