Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as m × m × m × n.

2.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

3.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

4.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

5.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

6.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

7.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.

8.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

9.Solve x² = 81.

10.Simplify 2a + 3b − a + 2b − b

11.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

12.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

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

14.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

15.Work out the value of m² + 3m when m = −2