Algebra worksheet — GCSE Higher

1.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

2.The diagram shows the graph of a function. Which equation could it represent?

3.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?

4.The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at (6, 8).

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

6.Which of these pairs of lines are perpendicular to each other?

7.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?

8.The table shows the height, in metres, of a firework rocket at various times, in seconds, during its flight: 40 at t = 2, 54 at t = 3, and 60 at t = 4. Use the chord between t = 2 and t = 4 to estimate the gradient of the height-time graph at t = 3, stating the correct units.

9.Solve 2x² − 32 = 0.

10.Write down the expression that means 5 more than half of n.

11.Solve the simultaneous equations y = 3 − x and x² + y² = 9, giving both pairs of solutions.

12.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

13.The nth term of a sequence is n² + 4n. Work out the term number, n, for which the term equals 45.

14.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

15.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?