Algebra worksheet — GCSE Foundation

1.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

2.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.

3.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

4.Write down the gradient of the line with equation y = 7x − 2.

5.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

6.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

7.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

8.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

9.Factorise fully 5x + 5y − 5

10.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

11.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

12.Solve 2x² = 18.

13.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

14.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

15.A curve has equation y = x² − 9. Which statement about its graph is correct?