Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 5
104 practice questions
Topics covered
Practice questions
41–48 of 48 · Normal
Question 41
5 marks · Normal
Answer and see the solution →2. The cumulative frequency diagram shows the distribution of times (in minutes) taken by 100 students to finish a puzzle. The median time is read as 42 minutes.
A function representing the time to complete a puzzle is f(x) = (x - 40)^2 + 16.
(a)[1 mark]Explain how the cumulative frequency diagram can be used to estimate the 75th percentile.
(b)[2 marks]Calculate the value of the function f(x) for the median time.
(c)[2 marks]Describe the transformation of the graph y = x^2 to y = f(x).
Question 42
4 marks · Normal
Answer and see the solution →3. A rectangle has a length (x + 5) cm and a width (x − 2) cm. A square of side x cm is cut out from it.
A vector describes a translation of the square to another position with vector (4, −1).
(a)[2 marks]Find and simplify an expression for the area of the shaded part after the square is cut out.
(b)[2 marks]The shaded area is 54 cm². Form and solve a quadratic equation to find the value of x.
Question 43
4 marks · Normal
Answer and see the solution →4. The heights (h) of 30 saplings are grouped in a histogram. The table below shows the grouped data:
Height (cm) Frequency 0 < h ≤ 10 3 10 < h ≤ 20 8 20 < h ≤ 30 12 30 < h ≤ 40 7 The heights are said to be transformed using the function y = 2h + 5.
(a)[2 marks]Calculate an estimate for the mean height of the saplings.
(b)[1 mark]Find the value of y for a sapling at the midpoint of the tallest group (30 < h ≤ 40).
(c)[1 mark]Explain what the transformation y = 2h + 5 does to the distribution of heights.
Question 44
4 marks · Normal
Answer and see the solution →5. The quadratic graph y = x^2 − 4x + 3 is transformed by a translation to obtain y = (x − 2)^2 − 4x + 3.
The original and transformed quadratics The x-intercepts are shown as points A and B.
(a)[2 marks]Find the coordinates of A and B.
(b)[1 mark]Describe the translation that maps the original graph to the transformed graph.
(c)[1 mark]Write down the equation of the axis of symmetry of the original quadratic.
Question 45
4 marks · Normal
Answer and see the solution →6. A parallelogram has vertices at A(1,1), B(5,1), C(7,4), D(3,4).
It is mapped onto another parallelogram by an enlargement of scale factor 2, centre (1,1).
A tree diagram is used to calculate the probability of randomly selecting two red marbles from a bag containing 2 red and 3 blue marbles, without replacement.
(a)[1 mark]Write down the coordinates of the image of C after the enlargement.
(b)[1 mark]Describe fully the transformation that maps the original parallelogram onto its image.
(c)[2 marks]Calculate the probability that both marbles chosen are red.
Question 46
6 marks · Normal
Answer and see the solution →A rectangle has a length of cm (to the nearest cm) and a width of cm (to the nearest cm).
(a)[2 marks]Write down the upper and lower bounds of the length and width.
(b)[2 marks]Calculate the upper and lower bounds for the area of the rectangle. Give your answers with units.
(c)[2 marks]A quadratic function represents the relationship between two variables. Solve .
Question 47
6 marks · Normal
Answer and see the solution →The table below shows the masses (in g) of some apples, measured to the nearest gram:
Mass of apples (g) Mass (g) Frequency 85 – 89 2 90 – 94 5 95 – 99 8 100 – 104 6 (a)[2 marks]Estimate the mean mass of the apples.
(b)[2 marks]One apple's recorded mass is 100 g, correct to the nearest gram. Write down the lower and upper bounds of its actual mass.
(c)[2 marks]Let the mass of this apple be g with . The weight in newtons is given by . Find the lower and upper bounds for . Give your answers correct to 3 significant figures.
Question 48
7 marks · Normal
Answer and see the solution →The graph below shows the curve .
Quadratic curve y = x² - 4 (a)[1 mark]State the points where the curve cuts the x-axis.
(b)[2 marks]Use the graph or otherwise to write down the equation solved at the y-intercept. Find the y-intercept.
(c)[2 marks]Describe the transformation that maps the graph of to the graph of .
(d)[2 marks]Solve the inequality . Give the solution set for .