Algebra worksheet — GCSE Higher

1.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

2.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

3.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

4.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.

5.The graph of y = f(x) has a minimum turning point at (3, −5), crosses the x-axis at x = 1, and crosses the y-axis at (0, −2). Exactly one of these statements about the graph of y = −f(x + 2) is true. Which statement is true?

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

7.How many turning points does the graph of y = x² − 7x + 10 have?

8.The solution set of an inequality is described as: x is less than −3, or x is greater than or equal to 1. Write this solution set using set notation.

9.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

10.The point (5, −12) lies on the circle x² + y² = 169, which has centre (0, 0). Work out the equation of the tangent to the circle at (5, −12), giving your answer in the form y = mx + c.

11.A circle has centre (0, 0) and passes through the point (7, 24). Work out the equation of the circle.

12.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

13.Write down the gradient of the line with equation y = −x + 3.

14.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

15.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.