Algebra worksheet — GCSE Higher

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

2.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

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

4.Make x the subject of the formula y = 2x − 9.

5.The first five terms of a quadratic sequence are −1, 4, 13, 26, 43. Work out an expression, in terms of n, for the nth term.

6.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

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

8.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

9.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

10.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

11.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

12.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

13.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.

14.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.

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