Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 1
108 practice questions
Topics covered
Practice questions
41–50 of 51 · Normal
Question 41
2 marks · Normal
Answer and see the solution →State whether the following statement is true or false: If is an element of both sets and , then .
Question 42
4 marks · Normal
Answer and see the solution →Let the universal set . Set and set .
(a)[1 mark]List the elements of .
(b)[1 mark]List the elements of .
(c)[1 mark]Write down , the complement of set in .
(d)[1 mark]Describe, using set notation, the set of elements in that belong to but not to .
Question 43
3 marks · Normal
Answer and see the solution →Write down the meaning of these three symbols as used in set notation: (a) (b) (c) (the prime symbol as in )
Question 44
4 marks · Normal
Answer and see the solution →The Venn diagram below represents sets and in the universal set .
Venn diagram showing sets X and Y within U. Each region labelled with numbers. (a)[1 mark]List the elements of set .
(b)[1 mark]List the elements of set .
(c)[1 mark]Write down the elements of .
(d)[1 mark]List the elements in that are not in or .
Question 45
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 46
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?
Question 47
4 marks · Normal
Answer and see the solution →Consider the sets and .
Let represent the number of elements in set .
(a)[1 mark]List the elements in .
(b)[1 mark]Write down , the number of elements in set .
(c)[2 marks]If one element is chosen at random from set , write the probability that it is an even number.
Question 48
4 marks · Normal
Answer and see the solution →Let , , and .
Consider the algebraic expression .
(a)[2 marks]Evaluate the expression using the given values.
(b)[2 marks]Simplify the fraction to its lowest terms.
Question 49
5 marks · Normal
Answer and see the solution →On a graph, point P has coordinates ().
Let set S = {positive even numbers less than 10}.
(a)[1 mark]Write down the coordinates of P after reflecting it in the y-axis.
(b)[2 marks]List all elements of set S.
(c)[2 marks]Point Q is (3, 1). Find the gradient of the straight line joining P to Q.
Question 50
4 marks · Normal
Answer and see the solution →Let be a number such that .
Consider the set , a subset of even numbers.
(a)[2 marks]Find the value of .
(b)[2 marks]Write in set notation, using the element symbol and curly brackets.