Algebra worksheet — GCSE Higher

1.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

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

3.The solution set of a quadratic inequality is {x : x ≤ −3} ∪ {x : x ≥ 5}. Which of these inequalities has this solution set?

4.The graph of y = f(x) has a minimum turning point at (3, −5), crosses the x-axis at x = 1, and crosses the y-axis at (0, −2). Exactly one of these statements about the graph of y = −f(x + 2) is true. Which statement is true?

5.The area under a speed-time graph between t = 0 and t = 6 seconds is estimated using three strips of equal width, using the speeds, in m/s, at t = 0, 2, 4 and 6: 0, 5, 9 and 12. Using the trapezium rule with these three trapezia, estimate the distance travelled.

6.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

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

8.The point (20, 21) lies on the circle x² + y² = 841, which has centre O(0, 0). The tangent to the circle at (20, 21) crosses the x-axis at P and the y-axis at Q. Work out the area of triangle OPQ, correct to 1 decimal place.

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

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

11.The iterative formula xₙ₊₁ = xₙ³ − 2 is used repeatedly, starting from x₀ = 2. Which of these describes what happens to the sequence of values as n increases?

12.The equation x³ − 5x − 3 = 0 can be rearranged to give an iterative formula of the form xₙ₊₁ = ∛(…). Work out which one of these is a correct rearrangement.

13.A van's value depreciates by 18% each year. After 2 years it is worth £5,379.20. Work out its value when it was new, correct to the nearest pound.

14.Work out the value of 2(x + 2) when x = −5

15.Work out the value of 3a − 2b when a = 5 and b = 4