Home / iGCSE Mathematics (0580) – C6.1 Pythagoras’ theorem- Exam Style Questions Paper 3

iGCSE Mathematics (0580) - C6.1 Pythagoras’ theorem- Exam Style Questions Paper 3- New Syllabus

IGCSE Mathematics(0580) Practice Questions Paper 3 - All Chapters

Question

The diagram shows a right-angled triangle ABC.

Calculate BC.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

• C6.1 Pythagoras’ theorem
▶️ Answer/Explanation
Since this is a right-angled triangle, we can use Pythagoras’ theorem: $a^2 + b^2 = c^2$
Substitute the known hypotenuse and side into the formula to find the missing side $BC$:
$BC^2 + 52.5^2 = 59.5^2$
$BC^2 = 59.5^2 – 52.5^2 = 3540.25 – 2756.25 = 784$
Take the square root to find the length of $BC$:
$BC = \sqrt{784} = 28 \text{ cm}$
✅ Answer: $28 \text{ cm}$
Question

The diagram shows a plan, $ABCDE$, of the floor of a room in Jo’s house.
$F$ is a point inside the room.

(a)
(i) Show that $EF=1.9$m
(ii) Work out $AF$

(b) Calculate the area of the floor.

(c) A cupboard in the room is in the shape of a cuboid.
The area of the base of the cupboard is $1.2$ m² and the height of the cupboard is $2.3$ m.
Calculate the volume of the cupboard.
Give the units of your answer.

(d) Jo buys $275$ floor tiles which cost \$1.64 each.
Calculate the total cost of the floor tiles.

(e) Jo builds a patio in the shape of a semicircle with radius $2.3$ m.
Calculate the area of the patio.

▶️ Answer/Explanation
Solution

(a)(i) Proof:

$EF = DC – AB = 5.5\,m – 3.6\,m = 1.9\,m$

(a)(ii) Ans: 3 m

$AF = BC – ED = 4.7\,m – 1.7\,m = 3\,m$

(b) Ans: 23 m²

Total area calculation:

  1. Rectangle ABMC: $3.6 \times 4.7 = 16.92\,m²$
  2. Rectangle DEFM: $1.9 \times 1.7 = 3.23\,m²$
  3. Triangle AFE: $\frac{1}{2} \times 1.9 \times 3 = 2.85\,m²$

Total = $16.92 + 3.23 + 2.85 = 23\,m²$

(c) Ans: 2.76 m³

Volume = Base area × Height = $1.2 \times 2.3 = 2.76\,m³$

(d) Ans: \$451

Total cost = $275 \times 1.64 = \$451$

(e) Ans: 8.31 m²

Semicircle area = $\frac{1}{2} \times \pi \times (2.3)^2 = \frac{1}{2} \times \pi \times 5.29 ≈ 8.31\,m²$

Key Notes:

  • For part (b), the floor area is calculated by dividing the shape into simple rectangles and a triangle
  • All linear measurements are in meters (m), areas in square meters (m²), and volumes in cubic meters (m³)
  • The semicircle area calculation uses exact value of π for precision
  • Monetary values are rounded to the nearest dollar
More IGCSE Mathematics(0580) Practice Questions Paper 3 ........
Scroll to Top