Term 4G3

Sec 3 A-Math EOY practice paper

The end-of-year examination is the big Sec 3 assessment, covering every chapter taught in the year in one sitting. It is the closest thing to a national-paper experience before Sec 4, so stamina 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 1–7)
Format: 13 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 · 7 pages

13 multiple-choice questions and structured questions with answer lines. The full Sec 3 year (Chapters 1–7).

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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: quadratic functions, surds, polynomials and partial fractions, binomial expansions, exponential and logarithmic functions, coordinate geometry with circles, and trigonometric functions, identities and graphs.

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. You may use lg 2 = 0.301, lg 3 = 0.477 and lg 5 = 0.699.

1
The function f is defined by f(x) = 5 + 4x − 2x².
1. (a)
  Express f(x) in the form a(x + b)² + c.
  [3]
2. (b)
  State the maximum value of f(x) and the value of x at which it occurs.
  maximum =[2]
3. (c)
  Explain why f(x) can never be greater than your answer to (b).
  [2]
2
Do not use a calculator in this question.
1. (a)
  Simplify (√7 − 3)(2 + √7), giving your answer in the form p + q√7.
  [3]
2. (b)
  Rationalise the denominator of 12/(√7 + 2).
  [3]
3
The polynomial f(x) = x³ − 6x² + 9x − 4.
1. (a)
  Show that (x − 1) is a factor of f(x), and factorise f(x) completely.
  [4]
2. (b)
  Write down all the solutions of f(x) = 0.
  [2]
4
Express (4x² + 15x + 13)/((x + 1)(x + 2)²) in partial fractions.
1. Show the substituted values and the coefficient comparisons.
  [7]

Revision checklist

Re-derive the completing-the-square results for both positive and negative x² coefficients.
Practise one of each surd type: expansion, rationalisation, and an equation with a validity check.
Factorise a cubic end to end: factor theorem, division, complete factorisation.
Set up a three-fraction partial-fraction decomposition with a repeated factor.
Convert between degrees and radians and quote exact special-angle values in any quadrant.
Solve a full circle question: centre-radius form, tangent, and an inside/outside test.

Exam tips

Budget roughly 1.5 minutes per mark — 60 marks in 90 minutes is tight, so keep moving.
Show the method line for every transformation — completing the square, cover-up values, sign changes.
For trigonometry, state the quadrant reasoning, not just the answers.
Keep a running check that every equation you solve actually satisfies the original.

Questions about the EOY

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

Everything from the Sec 3 year: quadratics, surds, polynomials and partial fractions, binomial expansions, exponential and logarithmic functions, coordinate geometry and circles, and trigonometric functions, identities and graphs.

How should I revise for the EOY?

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

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 past examination papers.