Algebra worksheet — GCSE Foundation

1.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

2.x = 5. Work out the value of 3x² − 4.

3.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

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

5.Make c the subject of the formula k = 6c.

6.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

7.Which of these values of x is a solution of x² + 2x − 15 = 0?

8.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.

9.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.

10.Which of these statements is an equation with exactly one solution?

11.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

12.Solve x² + 7x = 0.

13.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

14.Write down 0.2x with its coefficient written as a fraction in its simplest form.

15.Solve the inequality x − 10 < −3.