Algebra worksheet — GCSE Higher

1.A car is decelerating. The tangent to its velocity-time graph at t = 12 seconds passes through the points (8, 22) and (16, 6), where velocity is in m/s and time is in seconds. Work out the gradient of this tangent, in m/s².

2.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

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

4.The graph of y = f(x) has a minimum turning point at (4, −5). The graph of y = f(x) + a has a minimum turning point whose minimum VALUE is 2. Work out the value of a, and state the coordinates of the minimum turning point of y = f(x) + a.

5.Make x the subject of the formula y = 2x − 9.

6.The graph of y = cos x is transformed onto the graph of y = cos(x − 90°). State the direction of the translation and which standard graph the image is.

7.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?

8.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.

9.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.

10.Which expression is equivalent to 3(2x − 5) + 4x?

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

12.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

13.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

14.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

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