Algebra worksheet — GCSE Higher

1.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?

2.The graph of y = 2x² + 6x − 1 is translated by the vector (−2, 0). Work out the equation of the image, giving your answer in the form y = 2x² + bx + c.

3.The graph of y = f(x) passes through the point (2, 5). Write down the coordinates of the corresponding point on the graph of y = f(x − 4) + 1.

4.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

5.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

6.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?

7.Write down the gradient of the line with equation y = −x + 3.

8.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

9.Work out the period of the graph of y = cos x, in degrees.

10.Solve 6x − 5 = 3x + 13.

11.Simplify (x² − 9) ÷ (x² + 5x + 6).

12.A geometric sequence has first term 3 and common ratio √2. Work out the 6th term of the sequence, giving your answer in the form a√2.

13.The graph of y = f(x) has a minimum turning point at (2, −3). The graph of y = −f(x) + a has a maximum turning point at (2, 9). Work out the value of a.

14.f(x) = 2x + 1. Work out the value of x for which f⁻¹(x) = 5.

15.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.