Algebra worksheet — GCSE Higher

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

2.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

3.A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₃ = 11 and a₅ = 29, work out a₁.

4.Work out the value of 2(x + 2) when x = −5

5.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

6.The equation x³ − 2x − 7 = 0 has exactly one solution. It can be found using the iterative formula xₙ₊₁ = ∛(2xₙ + 7), with starting value x₀ = 2, so that x₁ is the value after the formula has been used once. Work out the solution correct to 2 decimal places, iterating until two consecutive values round to the same 2 decimal places.

7.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?

8.Make x the subject of the formula y = x/2 − 5.

9.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

10.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

11.Make x the subject of the formula y = 4x − 3.

12.The graph of y = f(x) has a root (an x-intercept) at x = 5. Work out the x-coordinate of the corresponding root on the graph of y = f(x + 2).

13.Which of these is an identity?

14.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

15.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.