Algebra worksheet — GCSE Higher

1.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.

2.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

3.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

4.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

5.The nth term of a geometric sequence is given by aₙ = 3 × 2ⁿ⁻¹. Work out the position of the first term that is greater than 1,000.

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

7.A coastguard radar at the origin covers a circular region modelled by x² + y² = 400, where each unit represents 1 kilometre. A boat travels along the straight line that touches the boundary of the region at the point (12, 16). Work out the equation of the line the boat travels along.

8.A circle has centre O(0, 0) and equation x² + y² = 169. The point Q has coordinates (10, 11). Work out which of these gives the correct position of Q together with correct working.

9.A tap's flow rate, in litres per minute, is plotted against time, in minutes, on a graph. What are the units of the area under this graph?

10.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

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

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

13.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).

14.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

15.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.