Algebra worksheet — GCSE Higher

1.Solve 2x² − 32 = 0.

2.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

3.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

4.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

5.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

6.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

7.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

8.The equation x³ + 4x − 9 = 0 is to be solved by iteration. Work out which one of these iterative formulas comes from a correct rearrangement of that equation.

9.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

10.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

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

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

13.Solve 2x + 7 = x + 13

14.The equation x² = 5x − 3 is to be solved using iteration. Work out which of these iterative formulas comes from a correct rearrangement of the equation.

15.The nth term of a sequence is n² + 4n. Work out the term number, n, for which the term equals 45.