Edexcel IGCSE Math A 1 numbers and the number system

Use this number-system set to practise integer skills, fraction work, decimals, powers, percentages, ratio, standard form and accuracy bounds.

Covered syllabus points

1.1 Integers 1.2 Fractions 1.3 Decimals 1.4 Powers and roots 1.5 Set language and notation 1.6 Percentages 1.7 Ratio and proportion 1.8 Degree of accuracy 1.9 Standard form 1.10 Applying number 1.11 Electronic calculators

[Maximum number: 5]

$7 \mathscr{E}=\{23,24,25,26,27,28,29,30,31,32,33,34\}$ $A=\{$ even numbers $\}$ $B=\{23,29,31\}$ $C=\{$ multiples of 3 $\}$

(a)

List the members of the set

[ 2 ]

(i)

$B \cup C$

[ 1 ]

(ii)

$A^{\prime} \cap C$

[ 1 ]

(b)

Is it true that $B \cap C=\varnothing$ ?

Tick ( ✓ ) one of the boxes below.

Figure for Question (b) — Edexcel IGCSE Math A Higher

Give a reason for your answer.

The set D has 4 members and is such that $D \cap(A \cup C)=\varnothing$

[ 1 ]

(c)

List the members of set D

[ 2 ]

[Maximum number: 5]

$9 \quad N=480 \times 10^{9}$

(a)

Write N as a number in standard form.

[ 1 ]

Final answer:
$4.8\times10^{11}$

B1.

(b)

Write N as a product of powers of its prime factors. Show your working clearly.

[ 3 ]

$N=2^{14}\times3\times5^{10}$

Final answer:
$2^{14}\times3\times5^{10}$

B3.
B2 for an answer in the form $2^m\times3\times5^n$ , where m and n are positive integers.

(c)

Find the largest factor of N that is an odd number.

[ 1 ]

Final answer:
29296875

Accept:
$3\times5^{10},\qquad 2.9296875\times10^{7}$

B1.

[Maximum number: 3]

$14 \mathscr{E}=\{$ positive integers less than 20 $\}$ $A=\{x: x<12\}$ $B=\{x: 7 \leqslant x<16\}$

(a)

List the members of $A \cap B$
C is a set such that $C \subset A$ and n(C)=3
Given that all members of C are even numbers,

[ 2 ]

(b)

list the members of one possible set C.

[ 1 ]

[Maximum number: 6]

Gladys buys a table for $ 465 to sell in her shop.
She sells the table for $ 520

(a)

Work out the percentage profit that Gladys makes from the sale of the table. Give your answer correct to 3 significant figures.

Gladys has a sale in her shop.
She decreases all the normal prices by 12%
The normal price of an armchair was $ 550

[ 3 ]

520-465=55 $\frac{55}{465}\times100=11.827956\ldots$

Final answer:
$11.8\%$

A1 for 11.8 or better.

(b)

Work out the sale price of the armchair.
$

[ 3 ]

$0.12\times550=66$ 550-66=484

Final answer:
484

Alternative method:
$0.88\times550=484$

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Covered syllabus points

1 Numbers and the number system question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

1 Numbers and the number system question 2

Question (a)

Question (b)

Question (c)

1 Numbers and the number system question 3

Question (a)

Question (b)

1 Numbers and the number system question 4

Question (a)

Question (b)