Algebra worksheet — GCSE Foundation

1.Which of these is a formula?

2.Simplify k + k + k + k + k.

3.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

4.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

5.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

6.A person's body mass index is given by the formula B = m ÷ h², where m is the mass in kg and h is the height in metres. Work out B, to 1 decimal place, when m = 68 and h = 1.6.

7.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

8.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

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

10.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

11.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

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

13.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

14.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

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