Algebra worksheet — GCSE Higher

1.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

2.Which of these is a formula, rather than an expression, an equation, or an identity?

3.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.

4.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

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

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

7.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).

8.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.

9.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

10.A Fibonacci-type sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₁ = 5 and a₃ = 17, work out a₂.

11.Write down the gradient of the line with equation y = −x + 3.

12.Work out the value of 2x² when x = −3

13.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

14.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.

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