Algebra worksheet — GCSE Higher

1.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

2.Which of these statements is an identity?

3.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.

4.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

5.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

6.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

7.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

8.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

9.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.

10.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

11.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

12.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.

13.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.

14.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.

15.Work out the gradient of the straight line with equation y = (2x/5) − 3.