Algebra worksheet — GCSE Higher

1.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.

2.Subtract, giving your answer as a single fraction in its simplest form: 4/(x − 1) − 2/(x + 3)

3.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

4.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

5.f(x) = x + 3 and g(x) = 2x. Work out fg(x).

6.n is an integer. Which of these expressions is always an even number?

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

8.Solve 6x − 5 = 3x + 13.

9.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

10.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.

11.Make x the subject of the formula y = x/2 − 5.

12.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

13.Write down the expression that means 5 more than half of n.

14.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

15.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).