Algebra worksheet — GCSE Higher

1.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

2.Solve 5(x + 3) = 40

3.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

4.A circle has centre (0, 0) and equation x² + y² = 50. Work out the radius of the circle, giving your answer as a surd in its simplest form.

5.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

6.f(x) = 3x − 2. Find f⁻¹(x).

7.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

8.Line L has equation y = 2x + 3. Work out the equation of the line perpendicular to L that passes through the point (4, 1), giving your answer in the form x + 2y = c.

9.The point (18, 24) lies on the circle x² + y² = 900, which has centre (0, 0). The tangent to the circle at (18, 24) crosses the y-axis at the point Q. Work out the y-coordinate of Q.

10.An exponential graph y = A × rˣ passes through the points (0, 8) and (2, 18). Work out the value of r, correct to 2 decimal places.

11.A circle has centre (0, 0) and equation x² + y² = 50. Work out the length of the diameter of the circle, correct to 1 decimal place.

12.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

13.A tram travels between two stops. Its velocity-time graph consists of straight line segments joining the points (0, 0), (5, 20), (12, 20), (16, 4) and (20, 4), where time is in seconds and velocity is in m/s. Work out the average speed of the tram over the whole 20 seconds. Give your answer to 1 decimal place.

14.A circle has centre (0, 0) and equation x² + y² = 36. Work out the coordinates of the two points where the circle crosses the y-axis.

15.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?