Algebra worksheet — GCSE Foundation

1.Solve 4x + 3 = 19

2.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

3.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

4.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

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

6.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

7.Make x the subject of the formula y = x + 7.

8.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

9.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

10.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

11.Work out the value of 3a − 2b when a = 5 and b = 4

12.Solve x² − 6x = 0.

13.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

14.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

15.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.