Algebra worksheet — GCSE Higher

1.Work out the gradient of the straight line with equation 3y = 12 − 6x.

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

3.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

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

5.The curve y = x² − 1 and the line y = 3x − 3 meet at two points. Work out the x-coordinates of those two points.

6.The point (−4, 3) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the equation of the tangent to the circle at (−4, 3), giving your answer in the form y = mx + c.

7.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

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

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

10.Work out the value of a² − 2b when a = −3 and b = 4.

11.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

12.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

13.The curve y = 2x² − 12x + 7 has a minimum point. By completing the square, find the value of x at which the minimum occurs.

14.A student attempts to prove that the sum of any three consecutive integers is a multiple of 3. Line 1: Let the three consecutive integers be n, n + 1 and n + 2. Line 2: Their sum is n + (n + 1) + (n + 2) = 3n + 2. Line 3: 3n + 2 leaves a remainder of 2 when divided by 3, so it is not a multiple of 3. Line 4: So the sum of three consecutive integers is not always a multiple of 3. Which line contains the FIRST error?

15.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).