Home / iGCSE Mathematics (0580) :C4.5 Symmetry iGCSE Style Questions Paper 3

iGCSE Mathematics (0580) :C4.5 Symmetry iGCSE Style Questions Paper 3

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

(a) 

A wedding invitation is in the shape of a rectangle. Draw the lines of symmetry on this rectangle.

(b) There are 98 adults and 56 children at the wedding.

Find the fraction of people who are children.
Give your fraction in its simplest form.

(c) The wedding meal starts at 13 15 and lasts for 2 hours 50 minutes.

Find the time the meal ends.

(d) The probability that it will rain at the wedding is 0.12.

Find the probability that it will not rain.

(e) (i) These are the ages of the staff at the wedding.

16   24   39   28   17   48   31   33   17   29   40   25

Complete the stem-and-leaf diagram.

(ii) Find the range.

▶️ Answer/Explanation
Solution

(a) A rectangle has two lines of symmetry – one horizontal and one vertical through the center.

(b) Total people = 98 + 56 = 154.
Fraction of children = 56/154 = 4/11 when simplified.

(c) 13:15 + 2 hours = 15:15, plus 50 minutes = 16:05.

(d) Probability of no rain = 1 – 0.12 = 0.88.

(e)(i) Stem-and-leaf diagram: 

(e)(ii) Range = 48 (highest) – 16 (lowest) = 32.

Question

(a) For each quadrilateral, draw any lines of symmetry and write down its mathematical name.

(b) The diagram shows three triangles A, B, and C, on a grid.

(i) Describe fully the single transformation that maps

(a) triangle A onto triangle B

(b) triangle A onto triangle C.

(ii) On the grid, reflect triangle A in the line x = -1.

▶️ Answer/Explanation
Solution

(a)(i) First quadrilateral:

• Two lines of symmetry (both diagonals)

• Mathematical name: Rhombus

(a)(ii) Second quadrilateral:

• One line of symmetry (main diagonal)

• Mathematical name: Kite

(b)(i)(a) Transformation A→B:

• Type: Enlargement

• Scale factor: 3 (each side of B is 3× larger than A)

• Centre: (4,6) (point where lines through corresponding vertices meet)

(b)(i)(b) Transformation A→C:

• Type: Rotation

• Angle: 90° clockwise

• Centre: (0,0) (origin)

(b)(ii) Reflection of A in x = -1:

Reflection formula for vertical line x = k: \[ (x,y) \rightarrow (2k – x, y) \] For x = -1 (k = -1): \[ (1,4) \rightarrow (-3,4) \\ (1,2) \rightarrow (-3,2) \\ (4,2) \rightarrow (-6,2) \]

Final Answers:

(a)(i) Rhombus with two diagonal lines of symmetry

(a)(ii) Kite with one diagonal line of symmetry

(b)(i)(a) Enlargement, scale factor 3, centre (4,6)

(b)(i)(b) Rotation 90° clockwise about (0,0)

(b)(ii) Reflected triangle vertices at (-3,4), (-3,2), (-6,2)

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