Section A
Number
Topics: Prime factorisation · HCF · LCM · Sequences · nth term · Fractions
M1
Find the HCF of 100 and 120.
100 = 2² × 5² · 120 = 2³ × 3 × 5
100 = 2² × 5² · 120 = 2³ × 3 × 5
2 marks
M2
Find the LCM of 100 and 120.
2 marks
M3
Amina has ribbon lengths of 32 cm and 44 cm. She wants to cut both into equal shorter pieces with no leftover. What is the longest possible piece length?
2 marks
cm
M4
Look at this sequence: 25, 28, 31, 34, 37, …
Write the next three terms.
Write the next three terms.
1 mark
M5
For the sequence 25, 28, 31, 34, 37, … — write an expression for the nth term.
2 marks
M6
Using your nth term formula, find the 75th term of the sequence.
1 mark
M7
Work out: 8⁴⁄₇ × 10
2 marks
M8
Work out: 5 ÷ ⁸⁄₁₁
2 marks
Section A score
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Section B
Algebra & Formulae
Topics: Expanding brackets · Factorising · Substitution · Rearranging formulae · Word equations
M9
Expand and simplify: 5(3p − 2q) − 2(3p − 2q)
2 marks
M10
Factorise your answer to M9: 9p − 6q
1 mark
M11
Use the formula a = 15b + 8c to find a when b = 1.2 and c = 1.5.
2 marks
M12
Rearrange a = 15b + 8c to make c the subject.
2 marks
M13
Expand and simplify: 5(3x − 2) − 5(2 + x)
2 marks
M14
Factorise: 10x − 20
1 mark
M15 ⭐
Challenge: Object A is 5 kg heavier than Object B. The mass of Object C is twice the mass of Object B. The total mass of all three is 165 kg. Find the mass of Object C.
3 marks
kg
M16
Triangle CDB: the exterior angle at A = 120°, angle DCB = 15x + 5°, angle DBC = 22x + 4°. Find x.
3 marks
Section B score
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Section C
Geometry & Measures
Topics: Bearings · Angles (parallel lines, triangles) · Circumference · Midpoint · Quadrilateral properties
M17
The bearing of Bangkok from Jakarta is 070°. Find the bearing of Jakarta from Bangkok.
2 marks
°
M18
The circumference of a circular coin is 88 mm. Find its diameter. (Use π = ²²⁄₇)
2 marks
mm
M19
The circumference of a circle is 220 cm. (Use π = ²²⁄₇) Find its diameter.
1 mark
cm
M20
Find the radius of the circle in M19.
1 mark
cm
M21
Find the midpoint of (−5, 7) and (9, −1). Enter the x-coordinate.
1 mark
M22
Find the midpoint of (−5, 7) and (9, −1). Enter the y-coordinate.
1 mark
M23
AB is parallel to CD. A transversal PQRS crosses both lines. Angle BQR = 113°. Find angle x° = CRS.
2 marks
°
M24
A rectangle has which set of properties?
1 mark
Section C score
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Section D
Data & Statistics
Histogram (Q20): Ages of karaoke contestants — frequencies: Age 10→4, 11→5, 12→3, 13→6, 14→7, 15→5
M25
From the histogram above: which age has the fewest contestants?
1 mark
M26
Find the total number of contestants in the karaoke contest.
1 mark
M27
Find the percentage of contestants over 13 years old in the karaoke contest.
2 marks
%
Pie chart (Q21): Gill's garden time — sector angles: cutting the grass = 40°, planting = 80°, digging = 100°, weeding = 140°. Total time = 36 hours.
M28
What fraction of the time did Gill spend cutting the grass? (Give your answer in simplest form)
1 mark
M29
Gill spent 36 hours total in her garden. How many hours did she spend planting?
2 marks
hours
M30
A jacket increases in price from $300 to $390. Find the percentage increase.
2 marks
%
Section D score
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Section E
Area, Volume & Ratio
Topics: Area (rectangle, trapezium, parallelogram) · Volume & surface area of prism · Ratio · Word problems
M31
Ghina buys carpet for a rectangular floor: length 8¾ m, width 5 m. The carpet costs $10 per m². How much does Ghina spend?
3 marks
$
M32
In a figure, square EFGH has area 36 cm² (so its side = 6 cm, which is also the height between the parallel lines). Trapezium IJKL has parallel sides IL = 10 cm and JK = 5 cm. Find the area of trapezium IJKL.
2 marks
cm²
M33
In the same figure, parallelogram ABCD has base BC = 12 cm and the same height (6 cm). Find the ratio of area ABCD : area IJKL in its simplest form.
2 marks
M34
Molly, Paige and Demi share 42 sweets in the ratio 3 : 2 : 1. How many sweets does Molly receive?
1 mark
sweets
M35
How many sweets does Demi receive (ratio 3:2:1, total 42)?
1 mark
sweets
M36 ⭐
Challenge: A triangular prism has right-angle triangle cross-section with AC = 3 cm, BC = 4 cm, AB = 5 cm (hypotenuse). Length of prism BE = 20 cm. Find the volume.
2 marks
cm³
M37 ⭐
Challenge: Find the total surface area of the same triangular prism (AC=3, BC=4, AB=5, BE=20 cm).
3 marks
cm²
Section E score
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Section F
Functions & Graphs
Function: y = 2x − 4. Complete the table, then identify key features of the straight-line graph.
M38
For y = 2x − 4: find y when x = −1.
1 mark
M39
For y = 2x − 4: find y when x = 1.
1 mark
M40
For the line y = 2x − 4: what is the gradient?
1 mark
M41
For the line y = 2x − 4: what is the y-intercept?
1 mark
M42
For the line y = 2x − 4: what is the x-intercept (where y = 0)?
1 mark
📝 Drawing task (Q22b): Use your table values (x: −1, 0, 1, 2 → y: −6, −4, −2, 0) to plot the graph of y = 2x − 4 on paper or in your exercise book. Draw this on graph paper before your exam.
Section F score
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