Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 8
106 practice questions
Topics covered
Practice questions
91–100 of 106
Question 91
4 marks · Hard
Answer and see the solution →Maria chooses a marble from bag X and a marble from bag Y. In bag X there are 4 red and 6 blue marbles. In bag Y there are 3 red and 5 blue marbles.
She claims: 'Picking a blue marble from bag X and a red marble from bag Y is independent from picking a red marble from bag X and a blue marble from bag Y.' Is Maria correct? Give reasons for your answer.
Question 92
7 marks · Easy
Answer and see the solution →This question is about using a graph to solve a quadratic equation and expressing a vector as a column vector.
(a)The sketch below shows the graph of for .
Graph of \( y = x^2 - 4x + 3 \) (sketch) (i)[1 mark]Write down the values of where the graph crosses the -axis.
(ii)[2 marks]By drawing a suitable horizontal line on the graph, explain how you would use it to solve .
(b)[1 mark]A triangle has vertices at and .
Write down the vector as a column vector.
(c)[1 mark]The vector is given by .
What are the components of ?
(d)[2 marks]The vector .
Write down the magnitude of .
Question 93
9 marks · Easy
Answer and see the solution →This question is about graphs and vectors. Answer each part, showing your methods.
(a)[2 marks]Draw the graph of the curve for .
(b)[2 marks]Use your graph to solve the equation . Write down the values of correct to 1 decimal place.
(c)[2 marks]Let vector and vector .
Calculate the column vector .
(d)[1 mark]The point has coordinates . The vector represents the movement from to point .
Write down the coordinates of point .
(e)[2 marks]Find the magnitude of the vector from part (c). Give your answer to 2 decimal places.
Question 94
8 marks · Easy
Answer and see the solution →Answer the questions about quadratic equations and vector geometry below.
(a)[2 marks]The graph below shows for .
Graph of \( y = x^2 - 5x + 4 \) for \( 0 \le x \le 5 \) (b)[2 marks]Use the graph to estimate the solutions to . Give your answers correct to 1 decimal place.
(c)[2 marks]In the diagram below, vector and vector .
Write as a column vector.
(d)[2 marks]Find the magnitude of . Give your answer to 2 decimal places.
Question 95
8 marks · Easy
Answer and see the solution →A point P moves so that its coordinates (x, y) satisfy the quadratic equation .
(a)[2 marks]Draw the graph of for .
(b)[1 mark]Write down the coordinates of the points where the graph crosses the x-axis.
(c)[1 mark]Let A be the point where on your graph. Write the vector , from the origin O(0,0) to A, as a column vector.
(d)[2 marks]On the same grid, draw the vector , starting from the origin O(0,0).
You may estimate the y-value using the graph if needed.
(e)[1 mark]Write down as a column vector.
(f)[1 mark]What is the magnitude of ? Give your answer to 2 decimal places.
Question 96
8 marks · Easy
Answer and see the solution →The graph of the equation is shown below.
y = x^2 - 2x - 3 Point A is at and point B is at on this graph.
(a)[2 marks]Write down the solution(s) to the equation using the graph.
(b)[2 marks]Express the vector as a column vector.
(c)[2 marks]Find the magnitude of the vector , giving your answer to 1 decimal place.
(d)[2 marks]Point C has coordinates . Write vector as a column vector and calculate its magnitude to 1 decimal place.
Question 97
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 98
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 99
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 100
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?