100+ Free THPT Math Practice Questions

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Question 1

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The solution set of the inequality log₂(x − 1) < 3 is which of the following?

(1; 7)

(−∞; 9)

(9; +∞)

(1; 9)

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Key Facts: THPT Math Exam

A 90-minute, 22-question objective Mathematics paper (12 multiple-choice + 4 true/false clusters + 6 short-answer = 34 sub-items) scored out of 10, taken by over 1.2 million candidates in June under Vietnam's 2018 curriculum; graduation now weights the exam 50/50 with school records.

Sample THPT Math Practice Questions

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

1The antiderivative (nguyên hàm) of the function f(x) = e^x is which of the following?

A.e^(x+1)/(x+1) + C

B.x·e^(x-1) + C

C.e^x/x + C

D.e^x + C

Explanation: The exponential function e^x is its own derivative, so it is also its own antiderivative: ∫e^x dx = e^x + C. This is one of the basic antiderivative formulas in the Grade 12 syllabus.

2In the plane Oxyz, the plane (P): x − 3y − z + 8 = 0 has which of the following as a normal vector (vectơ pháp tuyến)?

A.(1; −3; −1)

B.(1; −3; 8)

C.(1; 3; 1)

D.(−1; −3; −1)

Explanation: For a plane ax + by + cz + d = 0, a normal vector is (a; b; c). Reading off the coefficients of x, y, z in x − 3y − z + 8 = 0 gives (1; −3; −1).

3The solution set of the inequality log₂(x − 1) < 3 is which of the following?

A.(−∞; 9)

B.(1; 9)

C.(9; +∞)

D.(1; 7)

Explanation: The condition x − 1 > 0 gives x > 1. Since log base 2 is increasing, log₂(x − 1) < 3 means x − 1 < 2³ = 8, so x < 9. Combining gives 1 < x < 9.

4The function y = (2x + 1)/(x − 1) has a horizontal asymptote (tiệm cận ngang) given by which equation?

A.y = 1

B.x = 1

C.y = 2

D.y = −1

Explanation: For a rational function (ax + b)/(cx + d), the horizontal asymptote is y = a/c. Here a = 2 and c = 1, so y = 2/1 = 2. Equivalently, the limit as x → ±∞ equals 2.

5Given the geometric sequence (cấp số nhân) with first term u₁ = 3 and common ratio q = 2, what is the value of the fifth term u₅?

A.24

B.96

C.30

D.48

Explanation: The general term of a geometric sequence is uₙ = u₁·q^(n−1). For n = 5: u₅ = 3·2⁴ = 3·16 = 48.

6The derivative of the function f(x) = sin(2x) is which of the following?

A.2cos(2x)

B.cos(2x)

C.−2cos(2x)

D.2sin(2x)

Explanation: Using the chain rule, d/dx[sin(u)] = cos(u)·u′. With u = 2x, u′ = 2, so f′(x) = cos(2x)·2 = 2cos(2x).

7In the plane Oxyz, the distance from the point A(1; 2; 2) to the origin O is which of the following?

A.√5

B.3

C.5

D.9

Explanation: The distance from A(x; y; z) to O equals √(x² + y² + z²) = √(1 + 4 + 4) = √9 = 3.

8A box contains 4 red balls and 6 blue balls of identical size. Drawing one ball at random, what is the probability that it is red?

A.0.6

B.0.24

C.0.4

D.0.1

Explanation: By the classical definition of probability, P(red) = (favourable outcomes)/(total outcomes) = 4/10 = 0.4.

9The value of the definite integral ∫ from 0 to 1 of (2x) dx is which of the following?

A.2

B.1/2

C.0

D.1

Explanation: An antiderivative of 2x is x². Evaluating x² from 0 to 1 gives 1² − 0² = 1.

10The cubic function y = x³ − 3x has local extrema at which x-values?

A.x = −1 and x = 1

B.x = 0 and x = 3

C.x = √3 and x = −√3

D.x = 0 only

Explanation: y′ = 3x² − 3 = 3(x² − 1). Setting y′ = 0 gives x² = 1, so x = ±1. Since y′ changes sign at both points, they are the local extrema.

About the THPT Math Exam

The Mathematics paper of Vietnam's National High School Graduation Examination (Kỳ thi tốt nghiệp THPT) is a 90-minute objective test taken by more than 1.2 million candidates each June, and from 2025 it is built on the 2018 General Education Program. The paper has 22 questions worth 34 scored sub-items in three formats: 12 four-option multiple-choice questions (Part 1), 4 true/false cluster questions of four sub-statements each (Part 2, with partial-credit scoring), and 6 short-answer numeric items (Part 3). Content draws about 70% from Grade 12 — applications of derivatives and curve survey, antiderivatives and integrals, spatial coordinate geometry in Oxyz, conditional probability with the total-probability and Bayes formulas, and grouped-data statistics — and about 30% from Grade 11. The exam is scored out of 10; since 2025, graduation eligibility combines exam results with the candidate's school records at a 50/50 ratio, and previous vocational/certificate bonus points were eliminated. Mathematics is one of two compulsory subjects (alongside Literature) and a key score for university admission.

Questions

100 scored questions

Time Limit

90 minutes

Passing Score

Scored out of 10; no fixed single-subject pass mark. From 2025, graduation is decided on a 50/50 combination of exam scores and Grade 12 school records.

Exam Fee

No fee for school candidates; the exam is state-funded. Free candidates register through their provincial Department of Education and Training. (Ministry of Education and Training (Bộ Giáo dục và Đào tạo, MOET), via provincial Departments of Education and Training)

THPT Math Exam Content Outline

22%

Applications of derivatives & curve survey

Monotonicity, extrema, max/min, asymptotes (horizontal, vertical, oblique) and graph survey of cubic and rational functions.

23%

Spatial coordinate geometry (Oxyz)

Vectors, scalar product, distances, equations of lines, planes and spheres, and point-to-plane distance.

18%

Probability

Classical and conditional probability, counting, the total-probability and Bayes formulas, independence and discrete random variables.

13%

Antiderivatives & integrals

Antiderivatives, definite integrals, areas, volumes of revolution and motion applications.

10%

Exponentials & logarithms

Exponential and logarithmic equations, inequalities, identities and growth/decay modelling.

Statistics (grouped data)

Mean, mode, range, interquartile range, variance and standard deviation for grouped data.

Sequences, trigonometry & spatial geometry

Arithmetic/geometric sequences and series, trigonometric equations, and spatial geometry of solids.

How to Pass the THPT Math Exam

What You Need to Know

Passing score: Scored out of 10; no fixed single-subject pass mark. From 2025, graduation is decided on a 50/50 combination of exam scores and Grade 12 school records.
Exam length: 100 questions
Time limit: 90 minutes
Exam fee: No fee for school candidates; the exam is state-funded. Free candidates register through their provincial Department of Education and Training.

Keys to Passing

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

THPT Math Study Tips from Top Performers

1Master the Grade 12 curve-survey routine: domain, monotonicity, extrema, all asymptotes (including the oblique asymptote of rational functions), the variation table, and the sketch.

2Drill Oxyz coordinate geometry — vectors and scalar product, equations of lines, planes and spheres, point-to-plane distance, and relative positions — since it is the single heaviest topic on the paper.

3Make the total-probability formula and Bayes' formula automatic using tree diagrams and 2×2 tables; conditional-probability word problems are a signature of the 2018-curriculum exam.

4Practise the short-answer (Part 3) items hardest: they are application-level, give no options, and demand exact computation of integrals, volumes, optimisation values and probabilities.

5For the true/false clusters, evaluate each of the four sub-statements independently and aim for all four correct, because only a fully correct cluster earns the maximum point.

6Memorise the grouped-data statistics formulas — mean, range, interquartile range, variance and standard deviation — and be able to interpret their meaning, not just compute them.

7Budget your 90 minutes: secure the 12 recognition-level multiple-choice questions quickly, then spend the bulk of your time on the partial-credit and short-answer sections.

Frequently Asked Questions

How long is the THPT Mathematics exam and how many questions does it have?

The Mathematics paper lasts 90 minutes and contains 22 questions worth 34 scored sub-items: 12 four-option multiple-choice questions, 4 true/false cluster questions (4 sub-statements each), and 6 short-answer numeric items. This format applies from the 2025 exam under the 2018 curriculum.

How is the Mathematics paper scored?

The paper is scored out of 10. Part 1 gives 0.25 point per correct multiple-choice answer (3 points total); Part 2 uses partial credit — 0.1 for 1 correct sub-statement, 0.25 for 2, 0.5 for 3, and 1.0 for all 4 (4 points total); Part 3 gives 0.5 point per correct short answer (3 points total).

What is the passing requirement for graduation?

There is no fixed single-subject pass mark. From 2025, graduation eligibility is decided on a 50/50 weighting of exam results and the candidate's Grade 12 school records, and former vocational/certificate bonus points were eliminated.

What topics does the Mathematics exam cover?

About 70% of items come from Grade 12 — applications of derivatives and curve survey, antiderivatives and integrals, spatial coordinate geometry in Oxyz, conditional probability with total-probability and Bayes formulas, and grouped-data statistics — and about 30% from Grade 11 (trigonometry, sequences, exponentials/logarithms, classical probability, spatial geometry).

When is the THPT exam held in 2026 and is there a fee?

The 2026 examination runs on 11–12 June 2026, with Mathematics on the afternoon of 11 June for 90 minutes; results are announced at 8:00 on 1 July 2026. There is no exam fee for school candidates as the exam is state-funded.

Why are the true/false and short-answer formats considered harder?

The true/false clusters require fully correct reasoning on all four sub-statements to earn the maximum point — random guessing has only a 1/16 chance of full marks — and the short-answer items give no options, so candidates must compute an exact value rather than eliminate distractors.

100+ Free THPT Math Practice Questions

Vietnam THPT Exam - Mathematics