Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 5
104 practice questions
Topics covered
Practice questions
91–100 of 104
Question 91
4 marks · Easy
Answer and see the solution →A box contains balls with masses that have been measured to the nearest gram. The total mass of all the balls is 230 g. The number of balls in the box is given by n, which satisfies the equation n^2 - 15n + 54 = 0.
(a)[1 mark]Write down the lower bound and upper bound for the total mass of the balls.
(b)[2 marks]Solve the equation n^2 - 15n + 54 = 0 to find the number of balls in the box.
(c)[1 mark]If each ball has approximately the same mass, estimate the average mass of one ball, using the lower bound for the total mass and the larger value of n. Give your answer to the nearest gram.
Question 92
4 marks · Easy
Answer and see the solution →A function is defined as f(x) = x^2. The function is transformed by a translation of (−2, 0). The number x has been measured to the nearest integer and is given as 5.
(a)[1 mark]Write down the equation of the transformed function.
(b)[1 mark]What is the image of the point (5, 25) after this translation?
(c)[1 mark]Write down the lower and upper bounds of x.
(d)[1 mark]Calculate the lower bound of f(x) using your answer to part (c).
Question 93
4 marks · Easy
Answer and see the solution →A triangle is reflected in the y-axis and then translated by the vector (4, -1) on a grid. One vertex of the triangle is at (2, 3). A table shows the number of students in four classes who completed a geometry exercise: 12, 15, 13, 20.
(a)[1 mark]Write down the coordinates of the vertex after reflection in the y-axis.
(b)[1 mark]Write the new coordinates after the translation.
(c)[1 mark]Calculate the mean number of students who completed the exercise.
(d)[1 mark]If one more student completes the exercise in the first class, how does the mean change? Work out the new mean.
Question 94
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 95
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 96
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 97
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 98
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 99
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 100
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.