Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 1
108 practice questions
Topics covered
Practice questions
11–20 of 20 · Hard
Question 11
4 marks · Hard
Answer and see the solution →The diagram shows a quadrilateral PQRS with vertices at P(1,2), Q(5,2), R(4,6), and S(0,6).
Quadrilateral PQRS in the coordinate plane (a)[1 mark]Calculate the length of side PQ.
(b)[3 marks]Show that PQRS is a parallelogram.
Question 12
4 marks · Hard
Answer and see the solution →A regular polygon has an interior angle that is 165°. Calculate:
(a)[3 marks]The number of sides of the polygon.
(b)[1 mark]The sum of the interior angles of the polygon.
Question 13
3 marks · Hard
Answer and see the solution →A kite is a quadrilateral with two distinct pairs of adjacent sides equal. List all the lines of symmetry and describe the order of rotational symmetry for a typical kite.
Question 14
4 marks · Hard
Answer and see the solution →Triangle ABC has vertices at A(2,3), B(6,3), and C(2,8).
(a)[2 marks]Calculate the lengths of each side of the triangle.
(b)[2 marks]Determine the type of triangle (by its sides).
Question 15
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 16
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 17
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 18
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 19
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 20
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.