Algebra worksheet — GCSE Higher

1.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

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

3.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

4.Which expression is equivalent to 0.5(4x + 6) − x?

5.Work out the gradient of the straight line with equation y = (2x/5) − 3.

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

7.Solve (2x + 1)/3 = 5

8.The tangent to a curve at the point where x = 4 passes through the points (2, 5) and (6, 21). Use these two points to estimate the gradient of the curve at x = 4.

9.Solve 2x² − 32 = 0.

10.A region R satisfies y ≤ x + 1, x + y ≤ 5 and y ≥ 0. Which of these correctly describes R in words?

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

12.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

13.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

14.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

15.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.