Algebra worksheet — GCSE Higher

1.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.

2.The numbers x and y satisfy x + y = 10 and xy = 21. Work out the pair of values.

3.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?

4.The table shows the height, in metres, of a firework rocket at various times, in seconds, during its flight: 40 at t = 2, 54 at t = 3, and 60 at t = 4. Use the chord between t = 2 and t = 4 to estimate the gradient of the height-time graph at t = 3, stating the correct units.

5.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.

6.Solve the inequality 3x − 1 ≤ 11.

7.A curve has equation y = x² − 9. Which statement about its graph is correct?

8.Factorise fully 12x² + 18x.

9.The nth term of a sequence is 3n² + 2n − 1. Work out the 10th term.

10.a = 2 and b = 5. Work out the value of a²b.

11.The equation x² − 7 = 0 has a positive root. Let f(x) = x² − 7. Given that x₁ = 2.6 and x₂ = 2.65, work out which of these is correct.

12.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

13.The point (3, 6) lies on the circle x² + y² = 45. The tangent to the circle at (3, 6) crosses the x-axis at the point P. Work out the coordinates of P.

14.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.

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