Edexcel IGCSE Math B 1 number

Use this Number hub to move from exact arithmetic and surds into indices, percentages, ratio, compound interest and rounding accuracy.

Covered syllabus points

1.A Ordinary number operations 1.B Prime numbers, factors and multiples 1.C Indices, powers and roots 1.D Surds 1.E Rationalising denominators 1.F Number sets 1.G Units, measures and money 1.H Fractions, decimals, ratio and percentage 1.I Accuracy 1.J Upper and lower bounds 1.K Standard form

[Maximum number: 1]

Figure for Question 1 Number question 1 — Edexcel IGCSE Math B

Ahmed and Hani play a game with 20 numbered balls.
The 20 balls are numbered from 1 to 20.
The balls are put in a bag.
Ahmed takes at random a ball from the bag, makes a note of its number and puts the ball back into the bag.
If the number is a multiple of 5, Ahmed wins.
If Ahmed does not win, Hani takes a ball, replaces it, and wins if the number is a multiple of 3.
If Hani does not win, Ahmed takes a ball, replaces it, and wins if the number is a multiple of 6.
If Ahmed does not win, Hani takes a ball, replaces it, and wins if the number is a multiple of 4.
If Hani does not win, the game stops and the result is a draw.

Write down all the multiples of 3 lying between 1 and 20.

[Maximum number: 5]

(a)

Calculate $3.6\times10^{103}\times7.5\times10^{101}$ .
Give your answer in standard form.

[ 2 ]

$27\times10^{204}$

Final answer: $2.7\times10^{205}$ .

M1 for a correct answer in the form $a\times10^n$ , or $3.6\times7.5\times10^{103+101}$ , or $27\times10^{103+101}$ .
A1 cao for $2.7\times10^{205}$ .

(b)

$c=4\times10^{-8n}$ , where n is an integer.
Find an expression for $c^{-\frac12}$ in terms of n.
Give your answer in standard form.

[ 3 ]

$\frac{1}{(4\times10^{-8n})^{1/2}}=\frac{1}{2\times10^{-4n}}$

Equivalent form: $\frac12\times10^{4n}$ .

Final answer: $5\times10^{4n-1}$ .

M1 for a correct power/root method.
A1 for a correct form involving $10^{4n}$ .
A1 for $5\times10^{4n-1}$ .

[Maximum number: 5]

Answer parts (a) and (b).

(a)

Express $\sqrt{50}+\sqrt{242}$ in the form $a\sqrt a$ , where a is an integer.

[ 2 ]

$\sqrt{50}+\sqrt{242} =5\sqrt2+11\sqrt2 =16\sqrt2 =8\sqrt8$

Final answer:
$8\sqrt8$

M1 for writing the surds in the form $c\sqrt2$ and adding, or equivalent.
A1 cao; allow a=8.

(b)

Express $\frac{12}{\sqrt5-1}$ in the form $y\sqrt x+y$ , where x and y are integers.
Show each stage of your working.

[ 3 ]

$\frac{12}{\sqrt5-1}\times\frac{\sqrt5+1}{\sqrt5+1} =\frac{12(\sqrt5+1)}{5-1}$ $=\frac{12\sqrt5+12}{4} =3\sqrt5+3$

Final answer:
$3\sqrt5+3$

M1 for multiplying by the conjugate. M1 for correct denominator/numerator simplification. A1; allow $3+3\sqrt5$ , but not $3(\sqrt5+1)$ .

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Covered syllabus points

1 Number question 1

1 Number question 2

Question (a)

Question (b)

1 Number question 3

Question (a)

Question (b)