Algebra worksheet — GCSE Foundation

1.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.

2.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

3.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?

4.Which expression means 'add 3 to n, then multiply the result by 4'?

5.Solve 3x − 1 = 8

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

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

8.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

9.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

10.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

11.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

12.Work out the value of n² − n when n = −3

13.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

14.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

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