Algebra worksheet — GCSE Higher

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

2.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.

3.The curve y = x² − 6 and the line y = 2x − 3 intersect at two points. Which pair of points is correct?

4.Work out the value of 3a − 2b when a = 5 and b = 4

5.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

6.The graph of y = f(x) passes through the point (2, 5). Write down the coordinates of the corresponding point on the graph of y = f(x − 4) + 1.

7.A square patio of side length n slabs is surrounded by a single border of square paving slabs of the same size. For a patio with side length n, the total number of slabs used for the patio and its border together is 9 when n = 1, 16 when n = 2, 25 when n = 3, and 36 when n = 4. Work out an expression, in terms of n, for the total number of slabs.

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

9.The solution set of an inequality is described as: x is less than −3, or x is greater than or equal to 1. Write this solution set using set notation.

10.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

11.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

12.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.

13.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

14.Factorise fully 12x² + 18x.

15.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.