Algebra worksheet — GCSE Higher

1.Work out the gradient of the straight line with equation 2x + y = 8.

2.Factorise fully 5x + 5y − 5

3.Which expression is equivalent to 0.5(4x + 6) − x?

4.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

5.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

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

7.Solve the inequality x² ≥ 16, giving your answer using set notation.

8.A company's weekly profit, in £, is modelled by y = f(x), where x is the number of weeks since launch. The graph of y = f(x) has a maximum at (10, 45000). A rival company uses the same marketing strategy but starts trading 6 weeks later and has fixed costs £8000 higher every week, so its profit is modelled by y = f(x − 6) − 8000. In which week does the rival's maximum weekly profit occur, and what is it?

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

10.Solve the simultaneous equations y = 3 − x and x² + y² = 9, giving both pairs of solutions.

11.The graph of y = 2x² + 6x − 1 is translated by the vector (−2, 0). Work out the equation of the image, giving your answer in the form y = 2x² + bx + c.

12.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

13.Solve 3x + 14 = 8x − 6

14.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

15.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.