Algebra worksheet — GCSE Higher

1.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

2.Work out the value of (x − 4)/2 + 3 when x = 10

3.Solve the inequality x² − 5x + 6 < 0.

4.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

5.A circle has centre (0, 0) and passes through the point (12, 35). Work out the equation of the circle.

6.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.

7.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

8.The diagram shows the graph of a function. Which equation could it represent?

9.Solve 4x − (2x − 6) = 18

10.A student attempts to prove that the product of two consecutive integers is always even: (i) Let the two consecutive integers be n and n + 1. (ii) Since n(n + 1) is even, one of n and n + 1 must be an even number. (iii) Therefore, n(n + 1) is even. At which statement does the proof first assume the very fact it is trying to prove?

11.A cyclist accelerates uniformly from rest to 6 m/s in 4 seconds, travels at a constant 6 m/s for 10 seconds, then decelerates uniformly to rest in 3 seconds. Work out the total distance the cyclist travels.

12.A student claims: 'For every positive integer n, n² + n + 1 is a prime number.' Which value of n shows that this claim is false?

13.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

14.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

15.Which of these rules generates the sequence 6, 11, 16, 21, …?