Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 6
104 practice questions
Topics covered
Practice questions
101–104 of 104
Question 101
5 marks · Normal
Answer and see the solution →7. A father shares some money between his two children, Amira and Bilal, in the ratio x:2x.
(a)[2 marks]If the total amount shared is £120 and Bilal receives £48, find the value of x.
(b)[1 mark]Write an equation relating the amount Bilal receives (B) to the total shared (T) and x.
(c)[2 marks]Suppose instead each amount (for Amira and Bilal) is directly proportional to x. For x = 5, find the amounts each receives.
Question 102
4 marks · Normal
Answer and see the solution →8. The sequence {T_n} has nth term T_n = 2n - 1, for n = 1, 2, 3, …
Let A = {T_n | n ∈ N, n ≤ 6}.
(a)[1 mark]List all elements of set A.
(b)[2 marks]Find the sum of all elements of A.
(c)[1 mark]Let S be the set of all odd numbers less than 12. Express S using set-builder notation.
Question 103
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 104
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.