Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

2.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

3.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

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

5.Which of these equations describes a vertical line?

6.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

7.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

8.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

9.a = 3 and b = 5. Work out the value of a²b.

10.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

11.Make x the subject of the formula y = 5x + 3.

12.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

13.Factorise fully 12x² + 18x.

14.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

15.Solve 4x² − 9 = 0.