Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 8
106 practice questions
Topics covered
Practice questions
1–10 of 19 · Hard
Question 1
2 marks · Hard
Answer and see the solution →A piece of string is 1.85 metres long. Write this length in millimetres, giving your answer in standard form.
Question 2
4 marks · Hard
Answer and see the solution →A block of plastic has a mass of 2.4 kg and occupies a volume of 1500 cm³.
(a)[1 mark]Convert the mass to grams (g).
(b)[2 marks]Work out the density of the plastic in g/cm³.
(c)[1 mark]Express your answer to part (b) in kg/m³.
Question 3
4 marks · Hard
Answer and see the solution →A swimming pool is 25 m long, 8 m wide, and has an average depth of 2 m. The pool is filled with water at a rate of 40 litres per minute.
(a)[1 mark]Calculate the total volume of the pool in cubic metres (m³).
(b)[1 mark]Work out how many litres of water are needed to fill the pool. (1 m³ = 1000 litres)
(c)[2 marks]Estimate how many hours it will take to fill the pool at the given rate. Show your reasoning.
Question 4
2 marks · Hard
Answer and see the solution →Let . Write down the equation of the inverse function .
Question 5
4 marks · Hard
Answer and see the solution →A function is defined by .
Let the function be defined by .
Calculate the value of the composite function . Show your working.
Question 6
4 marks · Hard
Answer and see the solution →Consider the function with domain .
Explain how you determine the range of . Then write down the range.
Question 7
2 marks · Hard
Answer and see the solution →The curve is drawn on a set of axes. Solve the equation by referring to the graph, and write down both solutions for .
Question 8
4 marks · Hard
Answer and see the solution →A student is asked to solve the equation by drawing suitable graphs.
Write down:
(a)[1 mark]Which two graphs the student must draw.
(b)[1 mark]Explain how the solutions can be found using these graphs.
(c)[2 marks]If the graphs intersect at one point only, estimate the solution for to one decimal place.
Question 9
4 marks · Hard
Answer and see the solution →Consider the simultaneous equations and .
Explain, step by step, how you would use graphs to solve these equations simultaneously, and write down the solution(s) for and .
Question 10
2 marks · Hard
Answer and see the solution →ABCD is a parallelogram. Given and , E is the point such that . Write the vector as a column vector.