Algebra worksheet — GCSE Foundation

1.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

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

3.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.

4.Work out the gradient of the straight line with equation 3y = 12 − 6x.

5.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

6.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

7.Make a the subject of the formula b = 20 − a.

8.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

9.Solve x − 4 = −9

10.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.

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

12.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

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

14.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

15.Which of these is a term, rather than a whole expression, an equation, or a formula?