Algebra worksheet — GCSE Foundation

1.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

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

3.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

4.Which of these statements is an identity?

5.Solve (2x + 1)/3 = 5

6.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

7.Work out the value of 4p² − 3 when p = 2.5

8.Work out the value of 5y + 9 when y = 0

9.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

10.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

11.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

12.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

13.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

14.x = 5. Work out the value of 3x² − 4.

15.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?