Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 1
108 practice questions
Topics covered
Practice questions
101–108 of 108
Question 101
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 102
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 103
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 104
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.
Question 105
4 marks · Normal
Answer and see the solution →Simplify the algebraic expression .
The following numbers are given: 0.5 and .
(a)[2 marks]Simplify the expression as much as possible.
(b)[1 mark]Express 0.5 as a fraction in its lowest terms.
(c)[1 mark]Which is greater, 0.5 or ? Write your answer as a sentence.
Question 106
5 marks · Hard
Answer and see the solution →Let the set . Consider the algebraic expression .
(a)[2 marks]List the elements of set in order of increasing size.
(b)[1 mark]If , evaluate .
(c)[2 marks]Write the smallest element of set as a simplified fraction.
Question 107
5 marks · Hard
Answer and see the solution →On a Cartesian plane, the points M(0, 3) and N(4, 3) are marked.
Consider the set Q = { square, pentagon, hexagon, triangle }.
(a)[1 mark]Write down the coordinates of point M and point N.
(b)[2 marks]Find the distance between M and N.
(c)[2 marks]Write the set Q in set notation.
Question 108
6 marks · Hard
Answer and see the solution →Consider the expression .
Given the set S = {}.
A point A has coordinates (1, 1) and is reflected in the x-axis.
(a)[2 marks]Simplify the expression as much as possible.
(b)[2 marks]List all the elements of set S in their lowest terms.
(c)[2 marks]Write the coordinates of the image of point A after the reflection.