0580_w24_qp

Question 1

Topic – C1.1

Write the number half a million in figures.

▶️ Answer/Explanation

Solution

Ans: 500 000

Half a million means 1,000,000 ÷ 2.

1,000,000 ÷ 2 = 500,000.

We can write this without the comma as 500 000.

Question 2

Topic – C9.4

Anton records the colour of each car in a car park. His results are shown in the table.

On the grid, draw a bar chart to show this information.

▶️ Answer/Explanation

Solution

Ans: Bar chart with correct heights (12, 9, 11, 4)

1. Draw equal width bars for each color.

2. Make Black bar reach 12, Grey to 9, White to 11, Blue to 4.

3. Label the x-axis with colors and y-axis with frequency.

4. Ensure bars are either touching or have equal gaps.

Question 3

Topic – C2.5

(a) Solve: 5x = 14

(b) Solve: x + 6 = 25

▶️ Answer/Explanation

Solution

(a) Ans: 2.8

5x = 14

Divide both sides by 5: x = 14 ÷ 5 = 2.8

(b) Ans: 19

x + 6 = 25

Subtract 6 from both sides: x = 25 – 6 = 19

Question 4

Topic – C4.1

The diagram shows a regular polygon.

(a) Write down the mathematical name for this polygon.

(b) On the diagram, draw all the lines of symmetry.

▶️ Answer/Explanation

Solution

(a) Ans: Pentagon

A regular 5-sided polygon is called a pentagon.

(b) Ans: 5 lines of symmetry

Draw lines from each vertex to the midpoint of the opposite side.

(c) Ans: 5

The pentagon looks identical 5 times during a full rotation.

Question 5

Topic – C1.10

Write 53 683.588 correct to:

(a) the nearest hundred

(b) 1 decimal place

▶️ Answer/Explanation

Solution

(a) Ans: 53 700

Look at the tens digit (8):

Since 8 ≥ 5, we round the hundreds digit (6) up to 7

53 683.588 → 53 700

(b) Ans: 53 683.6

Look at the second decimal place (8):

Since 8 ≥ 5, we round the first decimal place (5) up to 6

53 683.588 → 53 683.6

Question 6

Topic – C4.2

Triangle ABC has sides AC = 4.2 cm and CB = 5.6 cm.

Using a ruler and compasses only, construct triangle ABC.
Leave in your construction arcs.
The side AB has been drawn for you.

▶️ Answer/Explanation

Solution

Ans: Correct triangle with construction arcs

1. Use compass to mark 4.2 cm arc from point A

2. Use compass to mark 5.6 cm arc from point B

3. The intersection point is C

4. Draw lines AC and BC

5. Leave construction arcs visible

Question 7

Topic – C1.6

Put one pair of brackets in each calculation to make it correct.

(a) 15 + 12 – 3 × 4 = 51

(b) 15 + 12 – 3 × 4 = 96

▶️ Answer/Explanation

Solution

Ans (a): 15 + (12 – 3) × 4 = 51

First operation in brackets: 12 – 3 = 9

Then multiply: 9 × 4 = 36

Finally add: 15 + 36 = 51

Ans (b): (15 + 12 – 3) × 4 = 96

First operations in brackets: 15 + 12 – 3 = 24

Then multiply: 24 × 4 = 96

Question 8

Topic – C2.2

Simplify: 8c – d – 3c + 3d

▶️ Answer/Explanation

Solution

Ans: 5c + 2d

Combine like terms:

8c – 3c = 5c

-d + 3d = 2d

Final expression: 5c + 2d

Question 9

Topic – C4.6

The diagram shows an isosceles triangle.

Find the value of x.

▶️ Answer/Explanation

Solution

Ans: 94

In an isosceles triangle, base angles are equal (both 43°)

Sum of angles in triangle = 180°

x + 43° + 43° = 180°

x = 180° – 86° = 94°

Question 10

Topic – C1.1

Complete each statement with a number from the list.

…… is a natural number.

…… is an irrational number.

…… is the reciprocal of 4.

▶️ Answer/Explanation

Solution

Ans:

24 is a natural number (positive integer)

√3 is an irrational number (cannot be expressed as a simple fraction)

0.25 is the reciprocal of 4 (¼ = 0.25)

Question 11

Topic – C1.6

The temperature in town A is -8°C and the temperature in town B is 16°C.

(a) Find the difference in these two temperatures.

(b) The temperature in town A rises by 12°C. Find the temperature in town A now.

▶️ Answer/Explanation

Solution

Ans:

(a) 24°C (16 – (-8) = 24)

(b) 4°C (-8 + 12 = 4)

Question 12

Topic – C4.3

The scale drawing shows the positions of two ships, A and B. The scale is 1 cm represents 6 km.

(a) Measure the bearing of ship B from ship A.

(b) Find the actual distance between the two ships.

▶️ Answer/Explanation

Solution

Ans:

(a) 143° (measured from North clockwise to line AB)

(b) 39 km (6.5 cm × 6 km/cm = 39 km)

Question 13

Topic – C9.5

The scatter diagram shows the number of rooms and the number of people in each of eight buildings.

(a) One building has 67 rooms. Write down the number of people in this building.

(b) In another building there are 42 people and 33 rooms. On the scatter diagram, plot this point.

(c)(i) On the scatter diagram, draw a line of best fit.
(ii) There are 45 people in a different building. Find an estimate for the number of rooms in this building.

(d) What type of correlation is shown in the scatter diagram?

▶️ Answer/Explanation

Solution

Ans:

(a) 76 people

(b) Point at (42,33)

(d) Positive correlation

Question 14

Topic – C5.2

The diagram shows a trapezium.

The area of the trapezium is 42 cm²

Calculate the value of x.

▶️ Answer/Explanation

Solution

Ans: 4.5 cm

Area = ½ × (sum of parallel sides) × height

42 = ½ × (9.5 + x) × 6

14 = 9.5 + x

x = 4.5 cm

Question 15

Topic – C2.1

In a league, teams gain 4 points for each win, 2 points for each draw and bonus points.
A team has x wins, y draws and b bonus points.

Write down an expression, in terms of x, y and b, for the total number of points the team has.

▶️ Answer/Explanation

Solution

Ans: 4x + 2y + b

Points from wins: 4 × x = 4x

Points from draws: 2 × y = 2y

Bonus points: b

Total = 4x + 2y + b

Question 16

Topic – C1.13

Dana invests $3600 at a rate of 3.8% per year compound interest.

Calculate the value of her investment at the end of 5 years.

▶️ Answer/Explanation

Solution

Ans: 4340 or 4338 or 4337.99

Using compound interest formula: A = P(1 + r/100)ⁿ

A = 3600(1 + 0.038)⁵

First calculate 1.038⁵ ≈ 1.205

Then multiply by principal: 3600 × 1.205 ≈ 4338

Final value after 5 years is approximately $4338

Question 17

Topic – C4.6

The diagram shows a parallelogram.

Work out the size of the smallest interior angle of the parallelogram.

▶️ Answer/Explanation

Solution

Ans: 70°

Adjacent angles in parallelogram add to 180°

132 – 2x + 15 + 5x = 180

Combine terms: 147 + 3x = 180

Solve for x: 3x = 33 → x = 11

Calculate angles: 15+5(11)=70° and 132-2(11)=110°

Smallest angle is 70°

Question 18

Topic – C2.4

Simplify.

$\frac{18x^6}{3x^2}$

▶️ Answer/Explanation

Solution

Ans: 6x⁴

Divide coefficients: 18 ÷ 3 = 6

Subtract exponents: x^6-2 = x⁴

Combine results: 6x⁴

Question 19

Topic – C3.1

$ \overrightarrow{AB} = \begin{pmatrix}
3 \\
-2
\end{pmatrix}$

Mark point A on the grid.

▶️ Answer/Explanation

Solution

Ans: (1,4)

Vector AB = B – A

So A = B – AB

Coordinates of A: (4-3, 2-(-2))

Calculate: (1,4)

Question 20

Topic – C5.3

Points A and B lie on a circle, center O and radius r.

The area of the circle is 120 cm².

Find the area of the right-angled triangle AOB.

▶️ Answer/Explanation

Solution

Ans: 19.1 cm²

First find radius: πr² = 120 → r = √(120/π) ≈ 6.18 cm

Triangle AOB is right-angled at O with OA = OB = r

Area = ½ × base × height = ½ × r × r

Calculate: ½ × (6.18)² ≈ 19.1 cm²

Question 21

Topic – C1.7

Without using a calculator, work out $ 2\frac{3}{4} \times 1\frac{1}{2} $.

You must show all your working and give your answer as a mixed number in its simplest form.

▶️ Answer/Explanation

Solution

Ans: $ 4\frac{1}{8} $

Convert to improper fractions: $ \frac{11}{4} \times \frac{3}{2} $

Multiply numerators and denominators: $ \frac{33}{8} $

Convert back to mixed number: $ 4\frac{1}{8} $

Question 22

Topic – C2.5

Solve the simultaneous equations.

You must show all your working.

$ 2x + 7y = 34 $

$ 3x + 5y = 18 $

▶️ Answer/Explanation

Solution

Ans: $ x = -4, y = 6 $

Multiply first equation by 3: $ 6x + 21y = 102 $

Multiply second equation by 2: $ 6x + 10y = 36 $

Subtract to eliminate x: $ 11y = 66 $ → $ y = 6 $

Substitute y into first equation: $ 2x + 42 = 34 $ → $ x = -4 $

Resources

Members

Company