Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 8
106 practice questions
Topics covered
Practice questions
41–47 of 47 · Normal
Question 41
9 marks · Normal
Answer and see the solution →This question connects compound measures (speed) and analysis of function domains.
(a)[2 marks]Anna cycles 18 km in 1 hour 12 minutes. Calculate her average speed in km/h.
(b)[2 marks]Express Anna's speed from part (a) in metres per second (m/s). Give your answer correct to 2 decimal places.
(c)[2 marks]Consider the function , where is the number of hours cycled.
i) Write down a suitable domain for in this context, explaining your reasoning.
(d)[3 marks]Give the value of and interpret your answer in the context of the problem.
Question 42
9 marks · Normal
Answer and see the solution →This question tests your skill in converting metric units and finding the inverse of functions.
(a)[2 marks]A field has an area of 24000 cm². Convert this area to m².
(b)Let , where is a positive real number.
i) Calculate .
(ii)[3 marks]Find the inverse of , , expressing your answer in terms of .
(c)[4 marks]A patch of land has an area of 27 m². Using your answer from part (b), find the value of such that .
Question 43
9 marks · Normal
Answer and see the solution →This question connects the definition of a function (Algebra 8) and basic probability with tree diagrams (Handling Data 5).
(a)Consider the following mapping diagrams:
Mappings M, N and P. Input M Output N Output P Output 1 2 3 3 2 3 2 2 3 4 1 1 4 5 1 1 (i)[2 marks]Which of the mappings M, N, P are functions? Write down all that are functions, giving a reason for each choice.
(ii)[1 mark]For one mapping that is not a function, explain why.
(b)In a probability experiment, a spinner shows either 1, 2, 3 or 4 with equal probability. The outcome is used as the input for mapping N above.
If you spin the spinner twice, each time applying the mapping N to the number spun, let A be the event 'both outputs are the same'. Draw a probability tree diagram to represent this experiment and calculate the probability of event A.
(i)[2 marks]Draw or describe a probability tree diagram for this experiment, labelling all outcomes with both spinner result and mapped output.
(ii)[4 marks]Work out the probability that both mapped outputs are the same, showing your steps.
Question 44
9 marks · Normal
Answer and see the solution →A study collected the number of books read by each member of a club last month. The numbers are shown in the table:
(a)[1 mark]Number of books read in March Number of books (x) Frequency (f) 2 3 3 5 4 6 5 2 6 4 Work out the modal number of books in the table above.
(b)[2 marks]Write a function such that gives the total number of books for a given number of members, where each member reads exactly books in a month. Express in terms of and .
(c)[2 marks]In April, a club member read twice as many books as in March every day. Let the number of books the member read each day in March be . Write a composite function that gives the number of books read each day in April, using your function from (b) and the rule .
Write explicitly.
(d)[2 marks]Suppose the probability that a member is selected at random and has read more than 4 books in March is . Work out using the frequency data from the table.
(e)[2 marks]If two members are selected at random, with replacement, what is the probability that both of them read more than 4 books in March?
Question 45
9 marks · Normal
Answer and see the solution →Let the function be defined as , for all real values of . In a probability experiment, the results are summarised in the table:
(a)[2 marks]State the domain and range of .
(b)[3 marks]Possible scores and their frequencies Score (x) Frequency (f) 1 6 2 4 3 5 4 2 5 3 A score is chosen at random. Work out the probability that the score is in the domain of and that .
(c)[2 marks]A score is selected at random. Another score is selected at random without replacement. Find the probability that both scores are greater than 3. Give your answer as a fraction in its lowest terms.
(d)[2 marks]The function is now restricted to the domain . For this domain, is one-to-one or many-to-one? Explain your answer.
Question 46
8 marks · Normal
Answer and see the solution →This question involves composite functions and probability tree diagrams.
(a)Let the function be defined by and the function by .
(i)[2 marks]Write down an expression for the composite function and simplify your answer.
(ii)[1 mark]Calculate the value of .
(b)A bag contains 5 red and 3 blue balls. A ball is chosen at random, noted, and replaced. A second ball is chosen. Tree diagrams are to be used for this part.
(i)[2 marks]Draw a tree diagram showing all possibile outcomes and label the probabilities on each branch.
(ii)[1 mark]Work out the probability that both balls chosen are red.
(iii)[2 marks]Work out the probability that one ball is red and one is blue (in any order).
Question 47
9 marks · Normal
Answer and see the solution →This question is about functions and probability. Answer each part, using reasoning and showing your methods.
(a)A function is defined by .
(i)[2 marks]Explain why is a function.
(ii)[2 marks]What is the domain and range of if can be any real number?
(b)A bag contains 2 red, 1 blue, and 1 green ball. A ball is selected at random, noted, replaced, and then a second ball is selected at random.
(i)[2 marks]Draw a probability tree diagram to show the outcomes for both selections.
(ii)[1 mark]Calculate the probability that both balls selected are red.
(iii)[2 marks]Calculate the probability that at least one of the balls selected is green.