Algebra worksheet — GCSE Higher

1.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

2.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

3.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.

4.p = 4. Work out the value of 2p³.

5.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?

6.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

7.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

8.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

9.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?

10.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

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

12.A circle has centre (0, 0) and equation x² + y² = 3721. The point (11, 60) lies on the circle. One of these is the gradient of the tangent to the circle at (11, 60). Work out which one.

13.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

14.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

15.Work out the value of a² − 2b when a = −3 and b = 4.