0580_w21_qp

Question 1

Topic – C1.4

Complete the table.

▶️ Answer/Explanation

Solution

Fraction: $\frac{1}{4}$, Percentage: 25, Decimal: 0.2

1. 0.25 is equivalent to $\frac{1}{4}$ and 25%.

2. 20% is equivalent to $\frac{1}{5}$ and 0.2.

3. Complete the table by filling in the missing values.

Question 2

Topic – C5.2

This shape is drawn on a 1 cm² grid.
Find the perimeter of the shape.

▶️ Answer/Explanation

Solution

24 cm

1. Count the number of 1 cm sides around the shape.

2. The perimeter is the total length of all sides.

3. The correct answer is 24 cm.

Question 3

Topic – C4.5

Write down the order of rotational symmetry of this shape.

▶️ Answer/Explanation

Solution

1. Rotational symmetry is how many times a shape matches itself in a full rotation.

2. This shape matches itself twice (at 180° and 360°).

3. Therefore, the order of rotational symmetry is 2.

Question 4

Topic – C4.1

Write down the letter of the shape that is congruent to the shaded shape.

▶️ Answer/Explanation

Solution

1. Congruent shapes are identical in size and shape.

2. Compare each option to the shaded shape.

3. Shape E matches exactly in size and shape.

Question 5

Topic – C9.3

The number of items that each of 22 people buy in a supermarket is shown in the stem-and-leaf diagram.

(a) Find the mode.

(b) Find the median.

▶️ Answer/Explanation

Solution

(a) 22

(b) 30

1. (a) The mode is the most frequent value – 22 appears most often.

2. (b) For median with 22 data points, average the 11th and 12th values.

3. Counting the ordered data, both the 11th and 12th values are 30.

Question 6

Topic – C5.1

(a) Change 2.7 kilometres into metres.

(b) Find the number of hours in 5 days.

▶️ Answer/Explanation

Solution

(a) 2700 m (b) 120 h

(a) 1 km = 1000 m, so 2.7 km = 2.7 × 1000 = 2700 m

(b) 1 day = 24 hours, so 5 days = 5 × 24 = 120 hours

Question 7

Topic – C1.15

Hank flies from Los Angeles to Shanghai.

(a) The flight departs on Friday 22 July at 21:40.
The flight takes 13 hours 35 minutes.
The local time in Shanghai is 15 hours ahead of the local time in Los Angeles.

Find the day, date and time in Shanghai when Hank’s flight arrives.

(b) The cost of the flight is $920.
The exchange rate is $1 = 6.87 Chinese yuan.

Find the cost of the flight in yuan.

▶️ Answer/Explanation

Solution

(a) Sunday 24 July 0215 (b) 6320.40 yuan

(a) Flight time + time difference: 21:40 + 13h35m = 11:15 next day (LA time). Shanghai time: 11:15 + 15h = 02:15 on Sunday 24 July.

(b) 920 × 6.87 = 6320.40 yuan

Question 8

Topic – C2.5

$ P = 2n – 3t $

Find the value of $ n $ when $ P = 9 $ and $ t = 8 $.

▶️ Answer/Explanation

Solution

n = 16.5

1. Substitute values: $ 9 = 2n – 3(8) $

2. Simplify: $ 9 = 2n – 24 $

3. Add 24: $ 33 = 2n $

4. Divide by 2: $ n = 16.5 $

Question 9

Topic – C4.3

The scale drawing shows the positions of two towns, P and Q.
The scale is 1 cm represents 4 km.

(a) Find the actual distance between town P and town Q.

(b) Measure the bearing of town Q from town P.

▶️ Answer/Explanation

Solution

(a) 32.8 km (b) 065° (c) X marked 7 cm from P at 140°

(a) Measure PQ in cm (8.2 cm) and multiply by 4: 8.2 × 4 = 32.8 km

(b) Measure angle clockwise from north line to PQ: 065°

Question 10

Topic – C1.13

Chung invests $2460 at a rate of 3.5% per year simple interest.

Calculate the total amount of his investment at the end of 4 years.

▶️ Answer/Explanation

Solution

$2804.40

1. Calculate interest: 2460 × 0.035 × 4 = $344.40

2. Add to principal: 2460 + 344.40 = 2804.40

Or in one step: 2460 × (1 + 0.035 × 4) = 2804.40

Question 11

Topic – C9.3

125 people taste a new drink.
Each person gives a score out of 5.
The bar chart shows the results.

Calculate the mean score.

▶️ Answer/Explanation

Solution

Ans: 3.08

Multiply each score by its frequency: (0×4) + (1×15) + (2×23) + (3×36) + (4×19) + (5×28) = 385

Divide total by number of people: 385 ÷ 125 = 3.08

Question 12

Topic – C2.7

(a) 7, 13, 19, 25, …

Find the next term in this sequence.

(b) 30, 26, 22, 18, …

Write down the term to term rule for this sequence.

Find the nth term for this sequence.

▶️ Answer/Explanation

Solution

Ans:

(a) 31 (adding 6 each time: 25 + 6 = 31)

(b) Subtract 4 (each term is 4 less than the previous one)

Question 13

Topic – C5.3

A circular disc has circumference 250 cm.
Calculate the radius of the disc.

▶️ Answer/Explanation

Solution

Ans: 39.8 cm

Use circumference formula C = 2πr

Rearrange to find r: r = C ÷ (2π)

r = 250 ÷ (2 × 3.142) ≈ 39.8 cm

Question 14

Topic – C2.2

(a) Factorise completely.
18x² – 12x

(b) Expand and simplify.
(x + 5)(x – 3)

▶️ Answer/Explanation

Solution

Ans:

(a) 6x(3x – 2) (take out common factor 6x)

(b) x² + 2x – 15 (use FOIL method: x×x + x×(-3) + 5×x + 5×(-3))

Question 15

Topic – C1.9

Sophie buys 73 books for her school. Each book costs $21.95 .

(a) By rounding each number correct to 1 significant figure, estimate the total cost of these books.

(b) Write down whether this estimate is greater or less than the exact cost. Explain how you decide, without working out the exact cost.

▶️ Answer/Explanation

Solution

Ans:

(a) 70 × 20 = $1400 (73 → 70, 21.95 → 20)

(b) Less than because both numbers were rounded down (70 < 73 and 20 < 21.95)

Question 16

Topic – C4.6

Calculate the size of one interior angle of a regular octagon.

▶️ Answer/Explanation

Solution

Ans: 135°

For a regular octagon, each interior angle = (8-2)×180° ÷ 8 = 6×180° ÷ 8 = 1080° ÷ 8 = 135°.

Question 17

Topic – C8.2

The table shows the relative frequency of the games won by a football team.

Result of game	won	lost	drawn
Relative frequency	0.1

The number of games lost is twice the number of games drawn.

Complete the table.

▶️ Answer/Explanation

Solution

Ans: lost 0.6, drawn 0.3

Total probability = 1. Remaining probability = 1 – 0.1 = 0.9.

Let drawn = x, then lost = 2x. So x + 2x = 0.9 → 3x = 0.9 → x = 0.3.

Thus drawn = 0.3, lost = 0.6.

Question 18

Topic – C1.4

Without using a calculator, work out $1\frac{5}{6} + \frac{2}{5}$.
You must show all your working and give your answer as a mixed number in its simplest form.

▶️ Answer/Explanation

Solution

Ans: $2\frac{7}{30}$

Convert mixed number: $1\frac{5}{6} = \frac{11}{6}$.

Find common denominator (30): $\frac{11}{6} = \frac{55}{30}$, $\frac{2}{5} = \frac{12}{30}$.

Add: $\frac{55}{30} + \frac{12}{30} = \frac{67}{30}$.

Convert to mixed number: $2\frac{7}{30}$.

Question 19

Topic – C3.5

Find the equation of line L. Give your answer in the form y = mx + c.

▶️ Answer/Explanation

Solution

Ans: y = 3x + 2

From the graph, y-intercept (c) = 2.

Slope (m) = rise/run = (5-2)/(1-0) = 3/1 = 3.

Thus equation is y = 3x + 2.

Question 20

Topic – C1.2

There are 50 families in a village.

C = {families who own a car}
B = {families who own a bicycle}

23 families own a car.
10 families own a car and a bicycle.
6 families own no cars and no bicycles.

(a) Complete the Venn diagram.

(b) Find n(C∪B).

▶️ Answer/Explanation

Solution

Ans: (a) Venn diagram: Only car = 13, Both = 10, Only bicycle = 21, Neither = 6

(b) 44

(a) Only car = 23 – 10 = 13. Total accounted for = 13 + 10 + 6 = 29, so only bicycle = 50 – 29 = 21.

(b) n(C∪B) = Total – neither = 50 – 6 = 44, or 13 + 10 + 21 = 44.

Question 21

Topic – C5.3

The diagram shows a sector of a circle with radius 4.8 cm and sector angle 45°.

Calculate the area of the sector.

▶️ Answer/Explanation

Solution

Ans: 9.05 cm² (or 9.04-9.06)

Area of full circle = π × 4.8² ≈ 72.382 cm².

Sector area = (45/360) × 72.382 ≈ 9.048 cm².

Or directly: (π × 4.8² × 45)/360 ≈ 9.05 cm².

Resources

Members

Company