100+ Free SPM Add Maths Practice Questions

Pass your Sijil Pelajaran Malaysia (SPM) Additional Mathematics / Matematik Tambahan (3472) exam on the first try — instant access, no signup required.

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The first term of an arithmetic progression is 5 and the 8th term is 26. What is the common difference?

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Key Facts: SPM Add Maths Exam

An upper-secondary KSSM elective assessed by two subjective written papers (Paper 1: 80 marks, 2 hours; Paper 2: 100 marks, 2 hours 30 minutes) across 18 topics, graded A+ to G by Lembaga Peperiksaan Malaysia.

Sample SPM Add Maths Practice Questions

Try these sample questions to test your SPM Add Maths exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A function is defined by f(x) = 3x - 5. What is the value of f(4)?

A.12

B.7

C.-2

D.17

Explanation: To evaluate f(4), substitute x = 4 into f(x) = 3x - 5, giving f(4) = 3(4) - 5 = 12 - 5 = 7. Substitution of the input value is the basic skill in the Functions topic of Form 4.

2Given f(x) = 2x + 1 and g(x) = x^2, find the composite function gf(x).

A.2x^2 + 1

B.2x^2 + 2x + 1

C.(2x + 1)^2

D.4x^2 + 1

Explanation: The composite gf(x) means g(f(x)): apply f first, then g. So gf(x) = g(2x + 1) = (2x + 1)^2. In KSSM notation gf(x) substitutes f(x) into g.

3The function f(x) = 4x - 3 has an inverse f^-1(x). What is f^-1(x)?

A.(x - 3)/4

B.4x + 3

C.1/(4x - 3)

D.(x + 3)/4

Explanation: Let y = 4x - 3, then x = (y + 3)/4. Swapping variables gives f^-1(x) = (x + 3)/4. The inverse function reverses the mapping by making x the subject.

4The quadratic equation x^2 - 6x + 8 = 0 has roots p and q. What is the value of p + q?

A.6

B.-6

C.8

D.-8

Explanation: For ax^2 + bx + c = 0, the sum of roots is -b/a. Here a = 1, b = -6, so p + q = -(-6)/1 = 6. This relationship between coefficients and roots is core to the Quadratic Equations topic.

5For the quadratic equation 2x^2 + 3x + k = 0 to have two equal roots, what is the value of k?

A.8/9

B.9/8

C.3/8

D.-9/8

Explanation: Two equal roots require the discriminant b^2 - 4ac = 0. Here 3^2 - 4(2)(k) = 0, so 9 - 8k = 0, giving k = 9/8. The discriminant condition determines the nature of the roots.

6The quadratic function f(x) = (x - 3)^2 + 4 is expressed in vertex form. What are the coordinates of its minimum point?

A.(-3, 4)

B.(3, -4)

C.(3, 4)

D.(4, 3)

Explanation: In the form f(x) = a(x - h)^2 + k with a > 0, the minimum point is (h, k). Here h = 3 and k = 4, so the minimum point is (3, 4). Completing the square reveals the turning point directly.

7The quadratic function f(x) = x^2 + 2x + 5 does not intersect the x-axis. This is because its discriminant is which of the following?

A.Zero

B.Positive

C.Equal to 5

D.Negative

Explanation: The discriminant is b^2 - 4ac = 2^2 - 4(1)(5) = 4 - 20 = -16, which is negative. A negative discriminant means the curve has no real roots and does not cut the x-axis.

8Solve the simultaneous equations x + y = 5 and x^2 + y^2 = 13. Which pair is a valid solution?

A.x = 2, y = 3

B.x = 1, y = 4

C.x = 5, y = 0

D.x = -2, y = 7

Explanation: From x + y = 5, substitute y = 5 - x into x^2 + y^2 = 13: x^2 + (5 - x)^2 = 13 gives 2x^2 - 10x + 12 = 0, so x = 2 or x = 3. Thus x = 2, y = 3 satisfies both equations (4 + 9 = 13).

9Simplify 3 log_a 2 + log_a 5 as a single logarithm.

A.log_a 30

B.log_a 40

C.log_a 11

D.log_a 10

Explanation: Using log laws, 3 log_a 2 = log_a 2^3 = log_a 8, and log_a 8 + log_a 5 = log_a (8 x 5) = log_a 40. The power rule and product rule combine the terms into one logarithm.

10Solve the equation 2^(x+1) = 16.

A.x = 4

B.x = 7

C.x = 3

D.x = 8

Explanation: Write 16 as 2^4, so 2^(x+1) = 2^4. Equating the indices gives x + 1 = 4, therefore x = 3. Expressing both sides with the same base allows the indices to be compared directly.

About the SPM Add Maths Exam

SPM Additional Mathematics (subject code 3472), known in Malay as Matematik Tambahan, is an elective subject taken by upper-secondary students in Form 4 and Form 5 under the KSSM curriculum. It is assessed by two subjective written papers: Paper 1 (3472/1, 80 marks, 2 hours) made of Section A (12 questions, answer all) and Section B (3 questions, answer 2), and Paper 2 (3472/2, 100 marks, 2 hours 30 minutes) made of Section A (7 compulsory questions), Section B (answer 3 of 4) and Section C (answer 2 of 4). There is no objective multiple-choice paper; both papers are bilingual in Bahasa Melayu and English. The syllabus spans 18 topics including functions, quadratic functions, indices and logarithms, progressions, linear law, coordinate geometry, vectors, solution of triangles, index numbers, circular measure, differentiation, integration, permutations and combinations, probability distributions, trigonometric functions, linear programming and kinematics of linear motion. Results use the 11-band SPM grade scale from A+ to G, and the subject is important for science, engineering and quantitative higher-education pathways.

Questions

100 scored questions

Time Limit

Paper 1: 2 hours; Paper 2: 2 hours 30 minutes

Passing Score

11-band scale A+ to G; grade C (50 percent and above) is a credit, D and E are passes without credit, below 40 percent is grade G (fail).

Exam Fee

Free for government-school candidates (state-funded). Private candidates pay a per-session registration fee set by the Ministry of Education; no large standalone fee for this subject. (Lembaga Peperiksaan Malaysia (Malaysian Examinations Board), Ministry of Education Malaysia)

SPM Add Maths Exam Content Outline

20%

Functions and Algebra

Functions, composite and inverse functions, quadratic equations and functions, simultaneous equations, indices, surds and logarithms.

10%

Progressions and Linear Law

Arithmetic and geometric progressions, sum of terms, sum to infinity, and reducing non-linear relations to linear form.

14%

Coordinate Geometry and Vectors

Distance, midpoint, gradient, line equations, division of a segment, areas and vectors in the i-j plane.

16%

Trigonometry and Circular Measure

Sine and cosine rules, triangle area, radians, arc length, sector area, identities, double-angle formulae and equations.

22%

Calculus

Differentiation (power, chain, product rules, turning points, rates of change, optimisation) and integration (definite and indefinite integrals, area, volume of revolution).

12%

Statistics and Probability

Permutations and combinations, probability, binomial and normal distributions, and index numbers.

Linear Programming and Kinematics

Linear inequalities, optimisation over a feasible region, and kinematics of linear motion.

How to Pass the SPM Add Maths Exam

What You Need to Know

Passing score: 11-band scale A+ to G; grade C (50 percent and above) is a credit, D and E are passes without credit, below 40 percent is grade G (fail).
Exam length: 100 questions
Time limit: Paper 1: 2 hours; Paper 2: 2 hours 30 minutes
Exam fee: Free for government-school candidates (state-funded). Private candidates pay a per-session registration fee set by the Ministry of Education; no large standalone fee for this subject.

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

SPM Add Maths Study Tips from Top Performers

1Memorise which formulas are given in the provided formula booklet and which you must know by heart, so you do not waste time in the exam looking for ones that are not listed.

2Master differentiation and integration early; calculus carries the largest weight and appears in both Paper 1 and Paper 2 structured questions.

3Drill the standard formulas until automatic: arc length s = r theta, sector area = (1/2) r^2 theta, binomial mean np and variance np(1-p), and the area of a triangle (1/2)ab sin C.

4Practise full working in Paper 2 structured questions because method marks are awarded even when the final answer is wrong.

5Be fluent with both Bahasa Melayu and English mathematical terms, since the bilingual paper may use the language you are less comfortable with.

6Work through real past-year papers and trial (percubaan) papers under timed conditions to manage the 2-hour and 2-hour-30-minute limits.

7For topics like solution of triangles and probability, watch for ambiguous-case and multi-step problems that combine several skills in one question.

Frequently Asked Questions

How many papers are there in SPM Additional Mathematics and how long are they?

There are two papers. Paper 1 (3472/1) lasts 2 hours and is worth 80 marks, and Paper 2 (3472/2) lasts 2 hours 30 minutes and is worth 100 marks. Both are subjective written papers; there is no multiple-choice paper.

What is the structure of each paper?

Paper 1 has Section A (12 questions, 64 marks, answer all) and Section B (3 questions, 16 marks, answer 2). Paper 2 has Section A (7 compulsory questions, 50 marks), Section B (4 questions, answer 3, 30 marks) and Section C (4 questions, answer 2, 20 marks).

What topics does the KSSM Additional Mathematics syllabus cover?

Form 4 covers functions, quadratic functions, systems of equations, indices/surds/logarithms, progressions, linear law, coordinate geometry, vectors, solution of triangles and index numbers. Form 5 covers circular measure, differentiation, integration, permutations and combinations, probability distribution, trigonometric functions, linear programming and kinematics of linear motion.

How is SPM Additional Mathematics graded?

It uses the 11-band SPM scale from A+ (highest) to G (fail). Grade C (50 percent and above) counts as a credit (kepujian); grades D and E are passes without credit; below 40 percent is grade G (gagal).

Is the exam in Malay or English?

The papers are bilingual, printed in both Bahasa Melayu and English since the 2003 medium switch, and candidates may answer in either language.

Is Additional Mathematics compulsory for SPM?

No, it is an elective subject usually taken by science-stream and some other upper-secondary students. It is not compulsory, but it is required or preferred for many science, engineering and quantitative tertiary programmes.

Are calculators allowed in SPM Additional Mathematics?

Yes. A non-programmable scientific calculator is permitted in both papers, and a printed formula booklet (senarai rumus) is provided with the question paper.

100+ Free SPM Add Maths Practice Questions

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