0580_w23_qp

Question 1

Topic – C4.6

Write down the mathematical name for this type of angle.

▶️ Answer/Explanation

Solution

Ans: Obtuse

An angle between 90° and 180° is called an obtuse angle. Since the given angle falls in this range, its mathematical name is “obtuse”.

Question 2

Topic – C1.1

Write down the value of the 8 in the number 58 317.

▶️ Answer/Explanation

Solution

Ans: 8000

In the number 58,317, the digit 8 is in the thousands place. Therefore, its value is 8 × 1000 = 8000.

Question 3

Topic – C2.5

Complete these statements.

(a) When $ x = \ldots, x + 3 = 8 $.

(b) When $ 7y = 63, 10y = \ldots $.

▶️ Answer/Explanation

Solution

Ans: (a) 5 (b) 90

(a) Subtract 3 from both sides: $ x = 8 – 3 = 5 $.

(b) First solve for y: $ y = 63 ÷ 7 = 9 $. Then multiply by 10: $ 10y = 10 × 9 = 90 $.

Question 4

Topic – C1.3

Find the value of $ \sqrt[3]{5832} $.

▶️ Answer/Explanation

Solution

Ans: 18

We need to find a number that when multiplied by itself three times equals 5832. Testing 18: $ 18 × 18 × 18 = 5832 $, so the cube root is 18.

Question 5

Topic – C1.13

A watch costs $12,400.
In a sale there is a discount of 16%.

Calculate the amount of the discount.

▶️ Answer/Explanation

Solution

Ans: $1984

Calculate 16% of $$12,400$: $ 0.16 × 12400 = 1984 $. The discount amount is $$1984$.

Question 6

Topic – C9.3

(a) Mei writes down five integers:

The lowest integer is 8
The range is 9
The median is 15
The total of the five integers is 66
There is no mode

Write down the five integers.

(b) Huan writes down four numbers.
The mean of these four numbers is 17.

He writes down a fifth number.
The mean of these five numbers is 20.

Find the fifth number.

▶️ Answer/Explanation

Solution

Ans: (a) 8, 10, 15, 16, 17 (b) 32

(a) Range = 9 ⇒ highest = 8+9 = 17. Median is 15 (third number). Total 66 ⇒ middle numbers sum to 66-8-17=41. No mode ⇒ all numbers distinct.

(b) Original total = 4×17 = 68. New total = 5×20 = 100. Fifth number = 100-68 = 32.

Question 7

Topic – C1.15

Arjun lives in Delhi and Haru lives in Tokyo.
They play a computer game online at the same time.

They start at 14 45 Tokyo local time.
The game lasts 3 hours 50 minutes.
The local time in Delhi is 3 hours 30 minutes behind the local time in Tokyo.

Find the local time in Delhi when the game finishes.

▶️ Answer/Explanation

Solution

Ans: 15:05 or 3:05 pm

Tokyo finish time: 14:45 + 3h50m = 18:35. Delhi is 3h30m behind ⇒ 18:35 – 3h30m = 15:05.

Question 8

Topic – C4.6

The diagram shows an isosceles triangle.

Find the value of x.

▶️ Answer/Explanation

Solution

Ans: 98

In an isosceles triangle, two angles are equal (41° each). Total angles = 180° ⇒ x = 180 – 41 – 41 = 98°.

Question 9

Topic – C9.4

The stem-and-leaf diagram shows the time, in minutes, it takes each of 15 people to complete a race.

Find:

(a) the mode

(b) the range

▶️ Answer/Explanation

Solution

Ans: (a) 27 (b) 15 (c) 25

(a) Mode = most frequent = 27 (appears 3 times)

(b) Range = 31 – 16 = 15 minutes

Question 10

Topic – C4.6

AB and CD are parallel lines.

Find the value of x.

▶️ Answer/Explanation

Solution

Ans: 83

Using parallel line properties: x + 52° = 135° ⇒ x = 135° – 52° = 83°.

Question 11

Topic – C1.9

Write 0.03682 correct to 2 significant figures.

▶️ Answer/Explanation

Solution

Ans: 0.037

The third digit (6) after the first two significant figures (3 and 6) is 5 or greater, so we round up the second significant figure from 6 to 7.

Question 12

Topic – C1.16

The table shows some information about Amir’s shopping.

Fruit	Cost per kilogram	Number of kilograms Amir buys	Cost
Oranges	$2.35	3.2	$……
Bananas	$……	2.8	$……
Total			$13.54

Complete the table.

▶️ Answer/Explanation

Solution

Ans:

Oranges cost: 3.2 × $2.35 = $7.52

Bananas cost: $13.54 – $7.52 = $6.02

Bananas cost per kg: $6.02 ÷ 2.8 = $2.15

Question 13

Topic – C9.5

For each of 10 people working in an office, the scatter diagram shows their salary and the value of their car.

(a) One of these people has a salary of $28,000. Find the value of their car.

(b) Another person starts to work in the office. Their salary is $54,000 and the value of their car is $6,100. Plot this information on the scatter diagram.

▶️ Answer/Explanation

Solution

Ans:

(a) $4,800 (estimated from the scatter plot)

(b) Point should be plotted at (54,000, 6,100)

Question 14

Topic – C2.2

Factorise completely.

42mk – 35m

▶️ Answer/Explanation

Solution

Ans: 7m(6k – 5)

First find the common factor of both terms: 7m

Divide each term by 7m: 42mk ÷ 7m = 6k, -35m ÷ 7m = -5

Write as product: 7m × (6k – 5)

Question 15

Topic – C1.1

Find the highest common factor (HCF) of 140 and 126.

▶️ Answer/Explanation

Solution

Ans: 14

Prime factors of 140: 2 × 2 × 5 × 7

Prime factors of 126: 2 × 3 × 3 × 7

Common factors are 2 and 7

HCF = 2 × 7 = 14

Question 16

Topic – C2.4

Simplify.

(a) $ n^5 \times n $

(b) $ 8x^6 \div 2x^2 $

▶️ Answer/Explanation

Solution

(a) Ans: $ n^6 $

When multiplying with the same base, add the exponents: $ n^5 \times n^1 = n^{5+1} = n^6 $

(b) Ans: $ 4x^4 $

Divide coefficients (8÷2=4) and subtract exponents (6-2=4): $ 4x^{6-2} = 4x^4 $

Question 17

Topic – C5.3

The circumference of a circle is 59 cm. Calculate the radius of the circle.

▶️ Answer/Explanation

Solution

Ans: 9.39 cm

Using circumference formula $ C = 2\pi r $

Rearrange to find radius: $ r = \frac{C}{2\pi} = \frac{59}{2 \times 3.142} $

Calculate: $ \frac{59}{6.284} ≈ 9.39 $ cm

Question 18

Topic – C1.9

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of:

$ \frac{36.9 + 24.2}{3.8 – 1.2} $

▶️ Answer/Explanation

Solution

Ans: 20

Round numbers: 36.9→40, 24.2→20, 3.8→4, 1.2→1

Numerator: 40 + 20 = 60

Denominator: 4 – 1 = 3

Estimate: $ \frac{60}{3} = 20 $

Question 19

Topic – C1.13

Indira invests $6000 at a rate of r% per year simple interest.
At the end of 4 years the value of her investment is $6840.

Find the value of r.

▶️ Answer/Explanation

Solution

Ans: 3.5

Interest earned = $6840 – $6000 = $840

Simple interest formula: $ I = \frac{P \times r \times t}{100} $

Substitute values: $ 840 = \frac{6000 \times r \times 4}{100} $

Solve for r: $ r = \frac{840 \times 100}{6000 \times 4} = 3.5 $%

Question 20

Topic – C5.2

Find the area of this trapezium.

▶️ Answer/Explanation

Solution

Ans: 66 cm²

Trapezium area formula: $ \frac{1}{2} \times (a + b) \times h $

Substitute values: $ \frac{1}{2} \times (8 + 14) \times 6 $

Calculate: $ \frac{1}{2} \times 22 \times 6 = 66 $ cm²

Question 21

Topic – C1.8

(a) Write these numbers in standard form.

(i) 45 000

(ii) 0.0063

(b) Calculate 8.2 × 10^-1 × 150000. Give your answer in standard form.

▶️ Answer/Explanation

Solution

Ans:

(a)(i) 4.5 × 10⁴

(a)(ii) 6.3 × 10^-3

(b) 1.23 × 10⁵

For (a), move decimal point to get a number between 1-10 and count places moved.

For (b), multiply 8.2 × 150000 = 1,230,000, then adjust to standard form.

Question 22

Topic – C1.10

The length, s metres, of a ship is 287 m, correct to the nearest metre.

Complete this statement about the value of s.

…… ≤ s < ……

▶️ Answer/Explanation

Solution

Ans: 286.5 ≤ s < 287.5

When rounding to nearest metre, any value from 286.5 up to but not including 287.5 would round to 287.

The lower bound is 287 – 0.5 = 286.5

The upper bound is 287 + 0.5 = 287.5

Question 23

Topic – C8.1

The table shows the number of people in a town who are left-handed and the number who are right-handed.

	Left-handed	Right-handed	Total
Number of people	8 400	48 600	57 000

Write down the probability that a person, chosen at random, is left-handed.

▶️ Answer/Explanation

Solution

Ans: 8400/57000 or equivalent simplified fraction

Probability = Number of left-handed people / Total number of people

8400 ÷ 57000 = 0.147 (3sf) or 14/95 when simplified

This represents about 14.7% chance.

Question 24

Topic – C5.1

(a) Change 1.2 m² into mm².

(b) The speed limit on a road is 80 km/h.
Sophie drives at a speed of 1200 m/min.

Show that Sophie drives at a speed lower than the speed limit.

▶️ Answer/Explanation

Solution

Ans:

(a) 1,200,000 mm²

(b) Sophie’s speed is 72 km/h which is less than 80 km/h

For (a): 1 m = 1000 mm, so 1 m² = 1,000,000 mm². 1.2 × 1,000,000 = 1,200,000

For (b): 1200 m/min × 60 = 72,000 m/h = 72 km/h. Since 72 < 80, she’s under limit.

Question 25

Topic – C5.3

Calculate the area of a semicircle with radius 10 cm.

▶️ Answer/Explanation

Solution

Ans: 157 cm² (to 3sf)

Area of full circle = π × r² = π × 10² = 100π

Area of semicircle = ½ × 100π = 50π

Using π ≈ 3.142: 50 × 3.142 ≈ 157.1 cm²

Rounded to 3 significant figures: 157 cm²

Resources

Members

Company