Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 7
107 practice questions
Topics covered
Practice questions
101–107 of 107
Question 101
5 marks · Normal
Answer and see the solution →The decimal number has a repeating pattern. A group of students were surveyed about participating in maths (M) and science (S) clubs. The data, shown in a Venn diagram, relates to a total of 50 students:
(a)[2 marks]Write as a fraction in its simplest form.
(b)[3 marks]Venn diagram showing club membership for part b. The Venn diagram represents:
- 18 students belong only to the maths club (region M only)
- 7 students belong to both clubs (region M S)
- 10 students belong only to the science club (region S only)
- The rest do not belong to either club
A student is picked at random.
Using set notation, write an expression for the probability that the student belongs to exactly one club, and work out its value as a fraction in its simplest form.
Question 102
5 marks · Normal
Answer and see the solution →A class takes a survey about owning pets. Each student answers whether they have a cat, a dog, or both. The results are shown in the Venn diagram.
(a)[3 marks]The decimal has a recurring digit. Convert to a fraction in its simplest form. Show your working.
(b)[2 marks]A Venn diagram for students owning pets. In the Venn diagram: - 12 students have only a cat - 10 students have only a dog - 6 students have both a cat and a dog A student is selected at random. Find the probability that this student has a pet corresponding to the fraction from part (a), i.e. is in exactly as many sets as the denominator of your fraction from part (a). Give your answer as a fraction in its simplest form.
Question 103
5 marks · Normal
Answer and see the solution →(a)[2 marks]Write the decimal 0.1\dot{7} as a fraction in its simplest form.
(b)[2 marks]A bag contains 12 discs, each labelled with a different integer from 1 to 12. A disc is selected at random.
Let D be the event ‘the disc number is a divisor of the denominator of your answer to part (a)’. Let E be the event ‘the disc number is even’.
Represent this information using a Venn diagram.
Draw the Venn diagram with the universal set consisting of the numbers 1 to 12. Clearly label each set and shade the region representing D \cap E.
(c)[1 mark]Find the probability that a randomly chosen disc shows a number that is both a divisor of the denominator of your answer to part (a) and even.
Question 104
5 marks · Normal
Answer and see the solution →A maths club has 36 members. Every member is given a membership number which is a recurring decimal less than 1. For a club quiz, these numbers are put into two lists:
List A: Members whose membership numbers are 0.3\dot{7} or 0.2\dot{5}.
List B: Members whose membership numbers are 0.2\dot{5} or 0.6\dot{2}.
Let S = {members of the club}, A = {members with numbers 0.3\dot{7} or 0.2\dot{5}}, B = {members with numbers 0.2\dot{5} or 0.6\dot{2}}.
(a)[2 marks]Write each recurring decimal above as a fraction in its simplest form.
(b)[3 marks]In the club, 6 members are in both lists A and B. 11 members are only in list A. 14 members are only in list B. The rest are in neither list.
A member is chosen at random.
Calculate the probability that the member is in exactly one of the lists. Give your answer as a fraction in its simplest form.
Question 105
5 marks · Normal
Answer and see the solution →Let .
The universal set .
Let .
Let .
A number is chosen at random from .
(a)[2 marks]Show that can be written as a fraction in its simplest form, and state the recurring digit.
(b)[1 mark]List the elements of set and set .
(c)[2 marks]Calculate the probability that a randomly chosen number from is in . Give your answer as a fraction in its lowest terms.
Question 106
11 marks · Hard
Answer and see the solution →A circular garden has a radius of metres. A path of uniform width metres is built all around the edge of the garden, forming a larger circle.
The combined area of the garden and the path is . The area of just the garden is .
(a)[4 marks]Write down an expression for the area of the ring-shaped path in terms of and , and hence form a quadratic equation in .
(b)[2 marks]Find the value of , giving your answer to 3 significant figures.
(c)[3 marks]Using your value for , solve the quadratic equation you formed in part (a) to find the width of the path. Give your answer to 2 decimal places.
(d)[2 marks]Calculate the perimeter of the outer edge of the path. Give your answer to 1 decimal place and state the unit.
Question 107
11 marks · Hard
Answer and see the solution →Two rectangles, A and B, are similar. The length of rectangle A is cm and its width is cm. The length of rectangle B is 12 cm and its width is 8 cm.
(a)[3 marks]Show that the ratio of lengths to widths for both rectangles is equal. Write a quadratic equation for .
(b)[3 marks]Solve the quadratic equation you have formed in part (a). Give both solutions for .
(c)[2 marks]Explain which value of is valid for the dimensions of rectangle A, and justify your answer.
(d)[3 marks]One side of a third rectangle C is cm, and this rectangle is similar to rectangles A and B. Find the width of rectangle C.