Algebra worksheet — GCSE Higher

1.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

2.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

3.Work out the value of the discriminant b² − 4ac for the equation 2x² + 3x − 2 = 0.

4.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

5.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

6.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

7.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

8.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

9.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

10.Describe a sequence of two transformations that maps the graph of y = cos x onto the graph of y = cos(x + 90°) − 2.

11.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

12.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

13.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.

14.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

15.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.