Algebra worksheet — GCSE Foundation

1.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

2.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.

3.Solve 4x² − 9 = 0.

4.a = 2 and b = 5. Work out the value of ab².

5.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

6.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

7.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

8.Solve 2x + 7 = x + 13

9.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

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

11.Solve 4(x − 3) = 2x + 6.

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

13.Expand 2(x + 12)

14.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

15.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?