Algebra worksheet — GCSE Foundation

1.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

2.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

3.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

4.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

5.Which of these equations describes a vertical line?

6.Work out the value of n² − n when n = −3

7.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

8.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

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

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

11.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

12.Which of these equations is equivalent to 5x − 2 = 3x + 8?

13.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.

14.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

15.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.