Algebra worksheet — GCSE Higher

1.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

2.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

3.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

4.Factorise x² − 3x − 10.

5.Which of these rules generates the sequence 6, 11, 16, 21, …?

6.Which line of algebra shows that the sum of two consecutive odd numbers is always a multiple of 4?

7.The nth term of a geometric sequence is given by aₙ = 3 × 2ⁿ⁻¹. Work out the position of the first term that is greater than 1,000.

8.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).

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

10.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

11.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

12.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

13.The simultaneous equations kx + 2y = 4 and 3x + y = 5 have no solution. Work out the value of k.

14.Which expression means 'triple c, then add double d'?

15.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.