Algebra worksheet — GCSE Foundation

1.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

2.Simplify 5a/6 − a/3

3.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

4.Which expression means the same as 3 × a × b?

5.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

6.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

7.Work out the y-intercept of the graph of y = x² + 3x − 10.

8.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

9.Expand 7(a + 8)

10.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

11.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

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

13.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

14.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

15.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.