Algebra worksheet — GCSE Higher

1.Work out the value of 2x² when x = −3

2.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

3.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

4.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

5.A car's speed, in m/s, during a journey is: 0 at t = 0 s, 8 at t = 4 s, and 8 (constant) from t = 4 s to t = 10 s, increasing at a constant rate between t = 0 and t = 4. Estimate the total distance the car travels, using the areas of a triangle and a rectangle.

6.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

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

8.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.

9.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

10.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

11.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

12.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?

13.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.

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

15.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.