iGCSE Mathematics (0580) :C1.2 Understand notation of Venn diagrams. Definition of sets. iGCSE Style Questions Paper 3

Question

 (a) 8  15  18  33  39  41  51  57  60  81
From this list, write down
(i) a factor of 54,
………………………………………….
(ii) a multiple of 19,
………………………………………….
(iii) a prime number.
………………………………………….
(b) Write down the reciprocal of 64.
………………………………………….
(c) (i) Write 4.81\times \(10^{-3}\) as an ordinary number.
………………………………………….
(ii) Write 75000 in standard form.
………………………………………….
(iii) Calculate \(\frac{6.3\times 10^{2}}{7\times 10^{-3}}.\)
Write your answer in standard form.
………………………………………….
(d) (i)
E = {2, 4, 8, 16, 32, 64}
A = {square numbers}
B = {cube numbers}
Use this information to complete the Venn diagram.


(ii) On this Venn diagram, shade the region \(P\cup Q\).

Answer/Explanation

(a)(i) 18
(ii) 57
(iii) 41
(b)\frac{1}{64}
(c)(i) [0].00481
(ii) \(7.5 ×10^{4}\)
(iii)\(9\times 10^{4}\)
(d)(i)
(ii)

Question

(a) Use set notation to describe the shaded region in each Venn diagram.


(b) E= {x : x is a natural number G15}
F = {x : x is a factor of 12}
O = {x : x is an odd number}
(i) Complete the Venn diagram to show the elements of these sets.
(ii) Write down one number that is in set O, but not in set F.
…………………………………………. [1]
(iii) Find \(n(F\cup O) .\)
…………………………………………. [1]
(iv) A number is chosen at random from E.


Work out the probability that this number is in set O.
………………………………………….

Answer/Explanation

(a)\(A\cup B A\cap B\)
(b)(i)
(ii)One of 5, 7, 9, 11, 13, 15
(iii) 12
(iv)\(\frac{8}{15}\)

Question

 (a) E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
F = {x: x is a factor of 14}
P = {x: x is a prime number less than 14}
(i) Write down the elements in set F.
F = { ………………………………………… }
(ii) Write down the elements in set P.
P = { ………………………………………… }
(iii)
(a) Complete the Venn diagram.
(b) Write down \(n(F\cap P ) .\)
………………………………………….
(c) A number is chosen at random from the universal set E.
Write down the probability that the number is in the set \(F\cup P, \)
………………………………………….
(b) Write 195 as a product of its prime factors.
………………………………………….

Answer/Explanation

(a)(i) 1, 2, 7, 14
(ii) 2, 3, 5, 7, 11, 13
(iii)(a) 1, 14 2, 7 3, 5, 11, 13
4, 6, 8, 9, 10, 12
(b) 2
(c) \(\frac{4}{7}\)
(b) 3 × 5 × 13

Question

(a) A baker puts some cakes in the oven at 5.50 pm.
The cakes take 20 minutes to bake.


Complete the clock diagram to show the time when the cakes are baked.
(b) A recipe uses 550 g of flour to make 8 cakes.

(c)
Work out the amount of flour needed to make 360 cakes.
Give your answer in kilograms.
……………………………………… kg
Work out which bag of flour is the best value.
Show all your working.
Bag …………………………………………
d) One cake costs 24 cents to make.
The baker sells each cake for 65 cents.
Calculate the percentage profit the baker makes on each cake.
……………………………………….%
(e) The baker asks some customers if they like lemon cake (L) and if they like chocolate cake (C).
The Venn diagram shows the results.


(i) Complete the statement.
n(E) = ……………..
(ii) Work out the fraction of the customers who like lemon cake or chocolate cake but not both.
………………………………………….
(iii) Use set notation to complete the statement.
{Jai, Nera} = …………………..
(iv) What does the Venn diagram show about Taj?
……………………………………………………………………………………………………………………………

Answer/Explanation

(a) 10 past 6 shown on clock face diagram
(b) 24.75
(c) B
With correct comparisons made of
the 3 bags with suitable accuracy
shown
(d) 171 or 170.8…
(e)(i) 12
(ii)\( \frac{3}{4}\) or equivalent fraction.
(iii) L ∩C
(iv) Correct statement

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