Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 5
104 practice questions
Topics covered
Practice questions
31–39 of 39 · Easy
Question 31
1 mark · Easy
Answer and see the solution →In an experiment, a bag contains only red and blue counters. Out of 40 counters, 18 are red. A counter is picked at random. Describe, in one sentence, the chance of picking a blue counter.
Question 32
3 marks · Easy
Answer and see the solution →A die is thrown 12 times. The outcomes are recorded as follows:
Throw 1 2 3 4 5 6 7 8 9 10 11 12 Result 6 4 3 2 4 1 2 6 3 5 4 1 Use the results to answer the following questions:
(a)[1 mark]Work out the number of times the result was an even number.
(b)[2 marks]Calculate the experimental probability of throwing a '4'. Give your answer as a fraction in its simplest form.
Question 33
2 marks · Easy
Answer and see the solution →A class records the number of times it rains in London over 10 consecutive days. Rain is recorded on 4 of the days.
Estimate the probability that it rains in London on any given day during this period.
Question 34
1 mark · Easy
Answer and see the solution →A teacher says, "If I roll a fair six-sided die 60 times, I would expect each number to appear about 10 times." Explain why the teacher is correct.
Question 35
2 marks · Easy
Answer and see the solution →A spinner has five equal sections numbered 1 to 5. It is spun 30 times and lands on 1 eight times.
Work out the experimental probability of the spinner landing on 1.
Question 36
3 marks · Easy
Answer and see the solution →The curve y = x^2 - 9 cuts the x-axis at two points.
(a)[2 marks]Solve the equation x^2 - 9 = 0 to find the x-coordinates where the curve cuts the x-axis.
(b)[1 mark]On the grid below, sketch the graph and indicate the points where it crosses the x-axis.
Question 37
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 38
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 39
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.