Algebra worksheet — GCSE Foundation

1.Work out the coordinates of the reflection of (6, −3) in the y-axis.

2.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

3.Work out the gradient of the straight line with equation 2x + y = 8.

4.Write down the first four terms of the sequence with nth term 6n − 5.

5.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

6.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

7.Write down the coefficient of p in the expression 7 − 4p + 9q.

8.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

9.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.

10.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

11.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

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

13.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

14.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

15.Simplify 2a + 3b − a + 2b − b