Algebra worksheet — GCSE Higher

1.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

2.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?

3.Factorise x² − 3x − 10.

4.A student attempts to prove that the product of two consecutive integers is always even: (i) Let the two consecutive integers be n and n + 1. (ii) Since n(n + 1) is even, one of n and n + 1 must be an even number. (iii) Therefore, n(n + 1) is even. At which statement does the proof first assume the very fact it is trying to prove?

5.Which line of algebra shows that the sum of two consecutive odd numbers is always a multiple of 4?

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

7.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

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

9.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

10.A speed-time graph shows a constant speed of 15 m/s for 20 seconds. Work out the distance travelled, using the area under the graph.

11.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

12.Factorise fully 12x² + 18x.

13.Solve 2(x + 3) = 10

14.Factorise 6x² − 7x − 3.

15.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).