AEIS Secondary 3 Placement Test — English & Math
Complete the introduction first, then answer Sections A–D; only Q1–Q12 will be auto-graded after you submit.
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Part 1 — Composition (20 marks)
Choose ONE of the topics below. Write between 300 and 400 words.
Which composition topic will you write about?
Topic 1: Some people believe that examinations are the best way to assess a student's ability, while others disagree. Discuss both views and give your own opinion.
Topic 2: Continue the story from this sentence, giving your own ending: 'The train screeched to a halt in the middle of nowhere, and the lights flickered once before going out completely.'
Write your composition here (300–400 words):
Part 2 — Multiple-Choice Questions (12 marks)
Section A: Grammar
Q1. "Rarely ___ such dedication among young athletes."
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A) do we see
B) we see
C) we do see
D) seeing we
Section B: Vocabulary
Q2. "Had she known about the traffic, she ___ earlier."
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A) would leave
B) left
C) will leave
D) would have left
Q3. "The report, along with the supporting documents, ___ submitted yesterday."
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A) were
B) are
C) was
D) have been
Section C: Cloze Passage
Q4. "The politician's speech was full of ___ promises that he had no intention of keeping."
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A) sincere
B) empty
C) heartfelt
D) modest
Q5. "Her ___ approach to problem-solving impressed the entire team."
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A) methodical
B) haphazard
C) careless
D) hesitant
Q6. "After hours of heated debate, the committee finally reached a ___ decision that everyone agreed with."
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A) divisive
B) premature
C) reluctant
D) unanimous
Section D: Comprehension Passage
Social media platforms have fundamentally (7) ___ the way people communicate and access information. While these platforms offer numerous benefits, such as connecting people across great distances, they have also been (8) ___ for spreading misinformation. As a result, many users are becoming increasingly (9) ___ of the content they encounter online.
Q7. "Choose the correct word for gap (7)."
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A) change
B) changing
C) changed
D) changes
Q8. "Choose the correct word for gap (8)."
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A) praised
B) criticised
C) ignored
D) rewarded
Q9. "Choose the correct word for gap (9)."
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A) skeptical
B) confident
C) unaware
D) supportive
In recent years, many cities around the world have invested heavily in creating more urban green spaces, from rooftop gardens to expansive public parks. Proponents argue that these spaces significantly improve residents' mental and physical wellbeing, citing studies that link access to nature with reduced stress levels and increased physical activity. Green spaces also play a practical role in mitigating the urban heat island effect, where concrete and asphalt absorb and radiate heat, making cities noticeably warmer than surrounding rural areas. Critics, however, point out that urban green spaces are expensive to maintain and often benefit wealthier neighbourhoods disproportionately, as parks and gardens tend to be developed in areas where property values — and thus tax revenues — are already high. This has led some urban planners to call for a more equitable distribution of green spaces, ensuring that lower-income communities are not left without access to nature within their neighbourhoods. As cities continue to grow, balancing the benefits of green spaces with the practical challenges of cost and equitable access remains an ongoing debate.
Q10. "According to the passage, what is one practical benefit of urban green spaces mentioned besides wellbeing?"
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A) They increase property taxes.
B) They eliminate the need for public transport.
C) They reduce the number of parks needed.
D) They help reduce the urban heat island effect.
Q11. "What criticism do some people have about urban green spaces?"
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A) They are not popular with residents.
B) They increase stress levels.
C) They often disproportionately benefit wealthier neighbourhoods.
D) They cause urban heat islands.
Q12. "What is the main purpose of this passage?"
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A) To argue that green spaces should be removed from cities.
B) To present both the benefits and challenges of urban green spaces.
C) To explain how to build a rooftop garden.
D) To criticise wealthy neighbourhoods.
SECTION B — MATH
Level: Secondary 2 syllabus | Time: about 28 minutes | Total: 28 marks. Calculators are not allowed.
Part 1 — Multiple Choice (8 marks)
Q1. A right-angled triangle has legs of 9 cm and 12 cm. Find the length of the hypotenuse.
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A) 13 cm
B) 14 cm
C) 16 cm
D) 15 cm
Q2. Expand: (x + 4)(x − 3).
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A) x²+x-12
B) x²+7x-12
C) x²-x-12
D) x²+x+12
Q3. Factorise: x² − 9.
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A) (x-3)(x-3)
B) (x+3)(x+3)
C) (x-3)(x+3)
D) (x-9)(x+1)
Q4. If x + y = 10 and x − y = 2, find the value of x.
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A) 4
B) 6
C) 5
D) 8
Q5. y is inversely proportional to x. When x = 4, y = 15. Find y when x = 6.
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A) 8
B) 9
C) 12
D) 10
Q6. Find the volume of a cone with base radius 3 cm and height 7 cm. (Take π = 22/7)
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A) 66 cm³
B) 44 cm³
C) 88 cm³
D) 99 cm³
Q7. A bag contains 4 red balls, 3 blue balls and 5 green balls. A ball is drawn at random. Find the probability that it is blue.
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A) 1/5
B) 1/3
C) 1/4
D) 3/4
Q8. Triangle ABC is similar to triangle PQR. AB = 6 cm corresponds to PQ = 15 cm, and BC = 8 cm. Find the length of QR.
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A) 12 cm
B) 20 cm
C) 18 cm
D) 16 cm
Part 2 — Short-Answer Questions (12 marks, 2 marks each)
1. A ladder 13 m long leans against a wall. The foot of the ladder is 5 m from the base of the wall. How high up the wall does the ladder reach?
2. Factorise completely: 2x² + 8x.
3. Solve the simultaneous equations: 2x + y = 11, x − y = 1.
4. Find the surface area of a sphere with radius 7 cm. (Take π = 22/7)
5. The cost of printing is directly proportional to the number of pages. If printing 40 pages costs $6, find the cost of printing 150 pages.
6. A fair six-sided die is rolled once. Find the probability of rolling a number greater than 4.
Part 3 — Open-Ended Questions (8 marks, 4 marks each)
1. The sum of two numbers is 32. Three times the smaller number is 8 more than the larger number. (a) Form two equations to represent this situation. (b) Find both numbers. Show your full working.
2. A rectangular field measures 24 m by 18 m. A path runs diagonally across the field from one corner to the opposite corner. (a) Find the length of the diagonal path. (b) The farmer wants to fence around the triangular region on one side of the path. Find the perimeter of this triangular region. Show your full working.
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