Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 1
108 practice questions
Topics covered
Practice questions
91–100 of 108
Question 91
4 marks · Hard
Answer and see the solution →In a class of 30 students, the universal set U consists of all the students. Let set M be the students who play music (18 students), set S be the students who play sports (15 students), and 8 students play both music and sports.
(a)[1 mark]How many students play only music?
(b)[2 marks]How many students play neither music nor sports?
(c)[1 mark]Represent this information in a Venn diagram. Clearly label all sets and indicate the number of students in each region.
Question 92
2 marks · Hard
Answer and see the solution →Describe, using set notation, the difference between the sets and . Give an example with sets A = \{apple, banana\} and B = \{banana, cherry\}.
Question 93
3 marks · Hard
Answer and see the solution →Let the universal set . Let , .
(a)[1 mark]List the elements of P and Q.
(b)[1 mark]Find .
(c)[1 mark]How many elements are in ?
Question 94
3 marks · Easy
Answer and see the solution →A rectangle has a length of 8 cm and a width of 3 cm. Consider the fraction .
(a)[1 mark]Write down the name of this shape.
(b)[1 mark]Calculate the perimeter of the rectangle.
(c)[1 mark]Simplify the fraction to its lowest terms.
Question 95
3 marks · Easy
Answer and see the solution →Consider the numbers: . Let set N = \{ 6, 18, 24 \}. Consider the fraction .
(a)[1 mark]Write down all the elements of set N.
(b)[1 mark]Simplify the fraction .
(c)[1 mark]Find the largest element of N.
Question 96
3 marks · Easy
Answer and see the solution →On the Cartesian plane, a point B has coordinates (1, 4). A set F contains the elements { triangle, rectangle, square, circle }.
(a)[1 mark]Write down the coordinates of point B.
(b)[2 marks]List any two elements from set F that have four sides.
Question 97
3 marks · Easy
Answer and see the solution →On the same axes, plot the points C (2, 2) and D (2, 5). Consider the expression 2y + 1.
(a)[1 mark]What is the vertical distance between points C and D?
(b)[1 mark]If y = 3, evaluate the expression 2y + 1.
(c)[1 mark]Write your answer to part (b) as a set containing one element.
Question 98
3 marks · Easy
Answer and see the solution →Look at the algebraic expression 5y - 4 + 2y. The fraction is given.
(a)[2 marks]Simplify the algebraic expression 5y - 4 + 2y.
(b)[1 mark]Write in its simplest form.
Question 99
5 marks · Normal
Answer and see the solution →A class collects data about their favourite fruit. The results are shown in the table below.
Fruits chosen by students Fruit Number of students Apple 12 Banana 8 Orange 6 Grape 4 (a)[2 marks]Write the fraction of students who chose banana as their favourite fruit. Give your answer in its simplest form.
(b)[1 mark]Let the number of students who chose orange be represented by the letter . Write down an algebraic expression for the total number of students who chose apple and orange, using .
(c)[2 marks]Using the values in the table, calculate the total number of students who took part in the survey.
Question 100
4 marks · Normal
Answer and see the solution →Here are three fractions: , , and .
A point A has coordinates (2, 3) on the Cartesian plane.
(a)[2 marks]Place these fractions in increasing order.
(b)[1 mark]Write down the coordinates of the point that is reflected across the x-axis from point A.
(c)[1 mark]What is the value of the numerator in the fraction that is equivalent to with denominator 12?