Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 6
104 practice questions
Topics covered
Practice questions
11–19 of 19 · Hard
Question 11
2 marks · Hard
Answer and see the solution →A tangent touches a circle at point T. The chord AB passes through T. Given that angle ATB = 37°, write down the size of the angle in the alternate segment which is subtended by AB, and state which theorem you used.
Question 12
4 marks · Hard
Answer and see the solution →Circle with centre O, points Q, R, S and T. In the diagram, O is the centre of the circle. QR and ST are two chords which intersect at right angles at point P inside the circle. If OP = 3 cm, QR = 6 cm, and ST = 8 cm, find the radius of the circle.
Question 13
4 marks · Hard
Answer and see the solution →Explain how the alternate segment theorem can be used to find an unknown angle in a circle. Give a clear step-by-step example, including both the reasoning and the calculation.
Question 14
2 marks · Hard
Answer and see the solution →Express the set of all positive integers greater than 4 and less than or equal to 15 in set-builder notation.
Question 15
4 marks · Hard
Answer and see the solution →Let .
Write the following sets using set-builder notation:
(a)[1 mark]The set of all negative elements of .
(b)[1 mark]The set of all in such that .
(c)[1 mark]The set of elements of that are not odd numbers.
(d)[1 mark]The set of all elements in such that .
Question 16
4 marks · Hard
Answer and see the solution →Consider the set .
A student claims the set can also be written in the form .
Explain whether the student's claim is correct. Justify your answer, referring to set-builder notation.
Question 17
2 marks · Hard
Answer and see the solution →The universal set is .
Let , .
List the elements belonging to .
Question 18
6 marks · Hard
Answer and see the solution →The sequence is defined by , for .
(a)[2 marks]Write an explicit expression for the sum $S_m$ of the first $m$ terms of the sequence.
(b)[2 marks]For which value of $m$ is $S_m = 0$?
(c)[2 marks]Let $A = \{n\,|\, a_n > 0,\ n\in \mathbb{N}\}$ and $B = \{x \in \mathbb{Z} \mid x = 2y+1,\ y \in \mathbb{N}, x < 7\}$. List all the elements of $A \cap B$.
Question 19
7 marks · Hard
Answer and see the solution →In the diagram, $O$ is the centre of the circle. $AD$ and $BC$ are chords that intersect at $E$. $AB$ is parallel to $CD$. $\angle BAD = 30^\circ$, $\angle DCA = 52^\circ$.
Circle with chords intersecting, labelled A, B, C, D, E, centre O. AB parallel to CD, angles as described. (a)[2 marks]Find $\angle EAB$ and justify your answer using a circle theorem.
(b)[2 marks]Find $\angle BCD$ and give a reason for your answer.
(c)[3 marks]Let set $S = \{x \mid x$ is an integer angle less than $70^\circ$ occurring at vertex $C$ or $A$ in this diagram $\}$. Describe $S$ using set-builder notation.