Algebra worksheet — GCSE Higher

1.Describe a sequence of two transformations that maps the graph of y = cos x onto the graph of y = cos(x + 90°) − 2.

2.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

3.A car's speed, in m/s, during a journey is: 0 at t = 0 s, 8 at t = 4 s, and 8 (constant) from t = 4 s to t = 10 s, increasing at a constant rate between t = 0 and t = 4. Estimate the total distance the car travels, using the areas of a triangle and a rectangle.

4.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

5.Solve the inequality 3x + 6 ≤ 0.

6.Solve x² + 7x = 0.

7.A circle has equation x² + y² = 49. Work out the coordinates of the point(s) on the circle where the tangent is horizontal.

8.Make x the subject of the formula y = x/2 − 5.

9.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

10.Solve x² − 6x = 0.

11.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

12.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

13.The graph of y = f(x) has a minimum turning point at (3, 2). Write down the coordinates of the minimum turning point of the graph of y = f(x) + 5.

14.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.

15.Write down the first four terms of the sequence with nth term 6n − 5.