Algebra worksheet — GCSE Higher

1.x = 5. Work out the value of 3x² − 4.

2.A region S consists of every point that lies on or above the line y = 2, on or below the line y = x, and on or to the left of the line x = 6. Which of these is the system of inequalities that defines S?

3.How many turning points does the graph of y = x² − 7x + 10 have?

4.Write down the expression that means the same as m² × m × 3.

5.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

6.Solve 5(x + 3) = 40

7.Make x the subject of the formula y = 5x + 3.

8.Which expression means 'triple c, then add double d'?

9.When a number is added to its square the result is 30. Work out the possible values of the number.

10.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

11.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

12.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

13.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.

14.A cyclist's speed-time graph is described as follows: speed increases steadily from 0 m/s to 8 m/s over the first 4 seconds, stays constant at 8 m/s for the next 6 seconds, then decreases steadily to 0 m/s over the final 2 seconds. Work out the total distance travelled.

15.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.