Algebra worksheet — GCSE Higher

1.Expand and simplify 2(a + 6) − 2(a − 7)

2.Factorise 3x² + 10x − 8.

3.A car's speed, in m/s, during a journey is: 0 at t = 0 s, 8 at t = 4 s, and 8 (constant) from t = 4 s to t = 10 s, increasing at a constant rate between t = 0 and t = 4. Estimate the total distance the car travels, using the areas of a triangle and a rectangle.

4.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

5.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

6.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

7.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.

8.A car's journey is represented by a velocity-time graph. The total distance travelled, found from the area under the graph, is 350 metres, and the total time for the journey is 25 seconds. Work out the car's average speed for the whole journey, in m/s.

9.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

10.A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₃ = 11 and a₅ = 29, work out a₁.

11.Make x the subject of the formula y = 3(x + 2).

12.The graph of y = 60 × (0.5)ˣ is sketched for x ≥ 0. Which statement correctly describes what happens to the curve as x increases?

13.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

14.Which expression is equivalent to 7x − 3(2x − 6)?

15.Which of these quadratic graphs does NOT cross the x-axis at all?