Algebra worksheet — GCSE Higher

1.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.

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

3.Work out the value of m² + 3m when m = −2

4.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

5.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

6.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

7.The graph of y = f(x) has a maximum turning point at (−1, 6). Write down the coordinates of the maximum turning point of the graph of y = f(x − 3).

8.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.

9.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.

10.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

11.The curve y = 2x² − 12x + 7 has a minimum point. By completing the square, find the value of x at which the minimum occurs.

12.The 2nd term of a geometric sequence is 6 and the 4th term is 24. Given that all the terms of the sequence are positive, work out the common ratio.

13.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.

14.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

15.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.