Algebra worksheet — GCSE Higher

1.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

2.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

3.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

4.Describe the single transformation that maps the graph of y = f(x) onto the graph of y = f(−x).

5.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

6.A market trader builds a display of oranges in a rectangular block. The block is n oranges wide and 4 oranges longer than it is wide. The number of oranges needed is 5 when n = 1, 12 when n = 2, 21 when n = 3, 32 when n = 4, and 45 when n = 5. Work out an expression, in terms of n, for the number of oranges needed for a display of width n.

7.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

8.A circle has centre (0, 0) and passes through the point (12, 35). Work out the equation of the circle.

9.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

10.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).

11.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

12.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

13.Which expression means 'triple c, then add double d'?

14.Make x the subject of the formula y = 4x − 3.

15.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.