Algebra worksheet — GCSE Foundation

1.The graph of y = (x − 4)(x + 1) crosses the x-axis. Which pair gives the correct roots and reasoning?

2.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.

3.A number machine multiplies its input by 3. The output is 15. Work out the input.

4.Which of these is an identity?

5.Work out the value of a² − 2b when a = −3 and b = 4.

6.Write down the expression that means the same as (x + 7) ÷ 4.

7.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

8.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

9.The point B has coordinates (−2, −2). In which quadrant is B?

10.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

11.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

12.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

13.Make p the subject of the formula n = p/3.

14.Which expression is equivalent to 4(x − 2) + 10?

15.Which expression is equivalent to 3(2x − 5) + 4x?