Term 4G2 / G3

Sec 3 E-Math EOY practice paper

The end-of-year examination covers every chapter taught in the Sec 3 year in one sitting — thirteen chapters from number work through mensuration. It is the closest thing to a national-paper experience before Sec 4, so pacing and coverage matter as much as technique.

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Total marks: 60
Time: 1 h 30 min
Covers: The full Sec 3 year (Chapters 1–13)
Format: 14 structured questions

The paper and mark scheme

Set out like a school paper, with a separate mark scheme for checking.

Question paper

EOY Practice Paper

60 marks · 1 h 30 min · 6 pages

14 multiple-choice questions and structured questions with answer lines. The full Sec 3 year (Chapters 1–13).

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Mark scheme

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EOY Practice Paper — mark scheme

Answers · Marking points · 4 pages

Model answers with a mark for each creditworthy point — for marking at home or in class.

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What’s tested

The full Sec 3 year: numbers and their operations, ratio, rate and speed, percentage, algebraic expressions and formulae, equations and inequalities, functions and graphs, set language, matrices, angle geometry, congruence and similarity, circle properties, trigonometry and mensuration.

How to use this paper

1Print the paper, or open the PDF and write on paper.
2Set a timer for 1 h 30 min and work without notes.
3Mark your answers with the mark scheme, one point at a time.
4Redo every question you lost marks on, then revise that topic.

Preview

The first questions of Section A, as they appear on the paper.

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Section A: Structured questions[60 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless told otherwise.

1
Answer all parts of this question.
1. (a)
  Express 0.0000382 in standard form.
  Answer =[1]
2. (b)
  Evaluate √48.5, correct to 2 decimal places.
  [1]
3. (c)
  By writing each number correct to 1 significant figure, estimate the value of (39.8 × 4.12) ÷ 0.198.
  [2]
2
A sum of money is divided between Kai and Lin in the ratio 4 : 7. Lin receives $63 more than Kai.
1. (a)
  Find the total sum of money.
  [2]
2. (b)
  Express Kai’s share as a percentage of the total sum, correct to 3 significant figures.
  [1]
3. (c)
  The total sum is increased by 15%. Find the new total.
  [1]
3
A saver places $5,000 in an account. Interest rates are unchanged over the period considered.
1. (a)
  Find the simple interest earned in 2½ years at 3.2% per year.
  [2]
2. (b)
  Find the value of the investment after 2 years if interest is instead 3.2% per year, compounded yearly.
  [2]
4
Answer all parts of this question.
1. (a)
  Factorise 3x² − 75 completely.
  [2]
2. (b)
  Expand and simplify (2x − 3)(x + 5) − 2(x² − 4x).
  [2]

Revision checklist

Run one of each number type: standard form arithmetic, a 1 s.f. estimate, and a bound.
Solve a full pair of simultaneous equations and a factorisable quadratic without hesitation.
Complete the square and read off a turning point, then solve from the completed-square form.
Count a two-set Venn problem end to end: both, only, neither, and a probability from the regions.
Chain circle theorems with reasons, and run one cosine-rule and one ½ab sin C computation.
Compute a cylinder volume and total surface area with π kept symbolic until the end.

Exam tips

Budget about 1.5 minutes per mark — 60 marks in 90 minutes rewards moving on quickly.
Geometry answers need reasons attached: name the property as you use it.
Keep π exact inside mensuration working and round only the final answer.
Mark the questions you skip and return with a strategy; never leave a whole part blank.

Questions about the EOY

What is tested in the Sec 3 E-Math EOY?

Everything from the Sec 3 year: number and operations, ratio, rate and speed, percentage, algebra through matrices, polygon geometry, congruence and similarity, circle properties, trigonometry with the sine and cosine rules, and mensuration with cylinders and sectors.

How should I revise for the EOY?

Work through the topical questions chapter by chapter first, then sit this paper in one 90-minute block and mark it strictly with the scheme. Log every dropped mark against its chapter and re-drill the two weakest chapters before the real paper.

Is this paper based on a real school paper?

No. QuizQuip papers are original material written against the syllabus. QuizQuip is not affiliated with MOE or SEAB and does not host school or past examination papers.