Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 7x − 3(2x − 6)?

2.Work out the distance of the point (−6, 4) from the x-axis.

3.A vertical line passes through the point (4, 7). Write down the equation of this line.

4.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

5.Write down the gradient of the line with equation y = −x + 3.

6.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

7.Expand and simplify (x − 3)²

8.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

9.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

10.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

11.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.

12.A number machine multiplies its input by 5. Work out the output when the input is −1.

13.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

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

15.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.