iGCSE Mathematics (0580) :C1.4 Use directed numbers in practical situations. iGCSE Style Questions Paper 3

Question

(a) Write one hundred and twenty thousand and twenty in figures.
(b) Find the value of$ \sqrt{3481}.$
(c)
(i) Write down the fraction of the rectangle that is shaded.
(ii) Find the percentage of the rectangle that is not shaded.
(d) Write these numbers in order, starting with the smallest.
27% $ \frac{5}{17}$ 0.268 $\frac{7}{29}$
(e) Write 0.3728 correct to 1 decimal place.
(f) Write down the value of $19^{\circ}$
(g) The height, h metres, of a tower is 128m, correct to the nearest metre.
Complete the statement about the value of h.
$……………… \leq h< ………………$
(h) Find the highest common factor (HCF) of 126 and 180.
(i) Write down an irrational number with a value between 6 and 7.

▶️ Answer/Explanation

Answers:

(a) 120,020 – “One hundred twenty thousand” = 120,000; “and twenty” = +20

(b) 59 – Check 59×59=3,481 (60×60=3,600 → test 59)

(c)(i) 5/8 – 5 shaded parts out of 8 total

(ii) 37.5% – Unshaded = 3/8 → 0.375 → 37.5%

(d) 7/29 < 0.268 < 27% < 5/17 – Convert all to decimals: 0.241, 0.268, 0.270, 0.294

(e) 0.4 – Second decimal (7) rounds first decimal up (3→4)

(f) 1 – Assuming cos(0°)=1 (question likely missing “cos”)

(g) 127.5 ≤ h < 128.5 – Nearest meter includes ±0.5m range

(h) 18 – 126=2×3²×7; 180=2²×3²×5 → HCF=2×3²=18

(i) √37 or π+3 – √36=6, √49=7 → √37≈6.08 (irrational)

Question

(a) Burton City is a football team with 1732 supporters traveling to the next game.

(i) Work out the number of buses needed if each bus seats 52 supporters.

(ii) The cost of the buses ($198 per bus) is shared equally among supporters. Calculate the cost per supporter (nearest 10 cents).

(b) Adam and Mabel’s homes are shown on a scale drawing (1 cm = 500 m).

(i) Find the distance from A to M in km.

(ii) Mark the football ground’s position given bearings: 105° from A and 068° from M.

(c) Teams earn points: w for a win, d for a draw.

(i) Burton City has 24 points after 2 wins and 5 draws. Complete: 2w + 5d = ____.

(ii) Sowton Rovers has 29 points after 3 wins and 4 draws. Write the equation.

(iii) Solve the equations to find w and d.

(iv) Cranbrook United has 4 wins, 5 draws, and 3 losses in 12 games. Calculate their total points.

▶️ Answer/Explanation

Solution

(a) (i) Ans: 34 buses

Divide supporters by bus capacity: $1732 \div 52 = 33.307$. Round up to 34 buses since partial buses aren’t possible.

(ii) Ans: \$3.90

Total cost: $34 \times 198 = 6732$. Cost per supporter: $6732 \div 1732 \approx 3.887$. Round to \$3.90.

(b) (i) Ans: 3.9 km

Measure distance on scale drawing (e.g., 7.8 cm). Convert: $7.8 \times 500 = 3900$ m = 3.9 km.

(c) (i) Ans: 24

Direct substitution: $2w + 5d = 24$.

(ii) Ans: $3w + 4d = 29$

Equation from given data: 3 wins and 4 draws total 29 points.

(iii) Ans: $w = 7$, $d = 2$

Solve the system: $2w + 5d = 24$ and $3w + 4d = 29$. Multiply first by 3 and second by 2, subtract to find $d = 2$, then $w = 7$.

(iv) Ans: 38 points

Calculate: $4 \times 7 + 5 \times 2 = 28 + 10 = 38$.

iGCSE Mathematics (0580) :C1.4 Use directed numbers in practical situations. iGCSE Style Questions Paper 3

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