Algebra worksheet — GCSE Higher

1.Which of these rules generates the sequence 6, 11, 16, 21, …?

2.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

3.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.

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

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

6.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

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

8.A region S consists of every point that lies on or above the line y = 2, on or below the line y = x, and on or to the left of the line x = 6. Which of these is the system of inequalities that defines S?

9.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

10.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.

11.Using the table of values of f(x) (x = 0, 1, 2, 3 gives f(x) = 5, 8, 4, 1), work out the value of −f(x) when x = 1.

12.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

13.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

15.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.