Edexcel IGCSE Math B 1 Number

[Maximum number: 1]

Figure for 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 $3(\sqrt5+1)$ .

[Maximum number: 3]

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

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

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: 2]

Answer parts (a) and (b).

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

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

Final answer:
$8\sqrt8$

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

[Maximum number: 3]

Answer parts (a) and (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.

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

Final answer:
$3\sqrt5+3$

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

[Maximum number: 2]

From the list
$-3,\quad 4,\quad \frac32,\quad \sqrt3,$
write down a number that is

(a)

both a rational number and a natural number.

[ 1 ]

(b)

an irrational number.

[ 1 ]

[Maximum number: 5]

Chetan owns a fruit shop.
In January, Chetan sold 560 kg of citrus fruit.
In February, Chetan sold 518 kg of citrus fruit.

The table below shows the weight of citrus fruit, berries and tropical fruit Chetan sold in March.

Table for Question 8 — Edexcel IGCSE Math B

The table below gives information about the weight, in kg, of berries sold on each of the 30 days in April.

Chetan wants to buy 60 kg of apples for his shop from US traders or French traders.
US traders: 12 kg box of apples for $29.50, free delivery, buy 4 boxes and get a 5th box free.
French traders: 1.72 euros per kg of apples, total delivery cost of 22.80 euros, special offer of 15% off the cost of apples and delivery.
Exchange rate: $\$1=0.92$ euros.

Compare the cost, including delivery, of 60 kg of apples bought from US traders with the cost of 60 kg of apples bought from French traders.
State which of the traders is the cheaper when buying 60 kg of apples.
Show all your working.

US traders:
$4\times \$29.50=\$118$ $\$118\times0.92=108.56\text{ euros}$

French traders:
$1.72\times60+22.80=126\text{ euros}$ $0.85\times126=107.10\text{ euros}$

Since 107.10<108.56, the French traders are cheaper.

M1 for a method to find the US cost.
M1 for using the exchange rate.
M1 for a method to find the French total before discount.
M1 for applying the $15\%$ discount to the full French amount.
A1 for French traders with correct comparable figures.

[Maximum number: 2]

Chetan owns a fruit shop.
In January, Chetan sold 560 kg of citrus fruit.
In February, Chetan sold 518 kg of citrus fruit.

The table below shows the weight of citrus fruit, berries and tropical fruit Chetan sold in March.

Table for Question 9 — Edexcel IGCSE Math B

The table below gives information about the weight, in kg, of berries sold on each of the 30 days in April.

Chetan wants to buy 60 kg of apples for his shop from US traders or French traders.
US traders: 12 kg box of apples for $29.50, free delivery, buy 4 boxes and get a 5th box free.
French traders: 1.72 euros per kg of apples, total delivery cost of 22.80 euros, special offer of 15% off the cost of apples and delivery.
Exchange rate: $\$1=0.92$ euros.

Calculate the percentage decrease in the weight of citrus fruit sold.

$\frac{560-518}{560}\times100=7.5$

Final answer:
$7.5\%$

M1 for a method to find the percentage change.
A1 allow $-7.5\%$ .

[Maximum number: 1]

Give your answer to part (a) as a decimal to 3 significant figures.

[Maximum number: 6]

Each interior angle of a regular polygon is $172^{\circ}$

Calculate, in $\mathrm{cm}^2$ to 3 significant figures, the upper bound of the area of the polygon.

[Maximum number: 1]

Give your answer to part (b) in standard form.

$6.75\times10^{-1}\text{ or better}$

Edexcel IGCSE Math B 1 Number Questions

Covered syllabus points

Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question 3

Question (a)

Question (b)

Question 4

Question 5

Question 6

Question 7

Question (a)

Question (b)

Question 8

Question 9

Question 10

Question 11

Question 12