Algebra worksheet — GCSE Higher

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

2.Solve 2x + 7 = x + 13

3.A Fibonacci-type sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₁ = 5 and a₃ = 17, work out a₂.

4.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

5.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

6.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

7.Describe the single transformation that maps the graph of y = f(x) onto the graph of y = f(−x).

8.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

9.p = 4. Work out the value of 2p³.

10.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

11.Expand and simplify (x + 1)(x + 2)(x + 3).

12.A cyclist's speed rises from rest to a maximum — quickly at first, then more and more slowly — so her speed-time graph is a curve that is concave down (its gradient decreases as time goes on). A trapezium estimate is made for the distance travelled during this phase, using two points on the curve. Is the trapezium estimate an overestimate or an underestimate of the true distance, and why?

13.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

14.Simplify fully: (x + 2)/(3x) × 6x²/(x² − 4)

15.Write down the expression that means the same as (x + 7) ÷ 4.