Algebra worksheet — GCSE Higher

1.The graph of y = 60 × (0.5)ˣ is sketched for x ≥ 0. Which statement correctly describes what happens to the curve as x increases?

2.Solve 4x − (2x − 6) = 18

3.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

4.The point (20, 21) lies on the circle x² + y² = 841, which has centre O(0, 0). The tangent to the circle at (20, 21) crosses the x-axis at P and the y-axis at Q. Work out the area of triangle OPQ, correct to 1 decimal place.

5.A circle has centre (0, 0) and equation x² + y² = 100. A straight line is drawn from the origin through the point P(8, 9). Work out whether P lies inside, on, or outside the circle.

6.Solve 5x² − 15x = 0.

7.When a number is added to its square the result is 30. Work out the possible values of the number.

8.f(x) = 2x − 1. Work out ff(x).

9.Describe a sequence of two transformations that maps the graph of y = x² onto the graph of y = −(x − 5)².

10.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

11.The tangent to a curve at the point where x = 4 passes through the points (2, 5) and (6, 21). Use these two points to estimate the gradient of the curve at x = 4.

12.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.

13.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.

14.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.

15.A car's journey is represented by a velocity-time graph. The total distance travelled, found from the area under the graph, is 350 metres, and the total time for the journey is 25 seconds. Work out the car's average speed for the whole journey, in m/s.