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Free Practice Questions for Secondary 4 Mathematics—Cultural, Social and Technical Option Ministerial Examination — Québec

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Key Facts: Secondary 4 Mathematics—Cultural, Social and Technical Option Ministerial Examination — Québec Exam

50%

Weight of épreuve unique in final course mark

Ministère de l'Éducation du Québec

3 hours

Exam duration

MEQ Official Schedule

60%

Minimum mark for course credit (DES)

Quebec Secondary Education Framework

063-420

MEQ course code (French sector: 063-420, English: 563-420)

MEQ Course Directory

4 Credits

Secondary diploma credits awarded upon passing

Diplôme d'études secondaires (DES)

100

Practice questions in this OpenExamPrep bank

OpenExamPrep

Québec Secondary 4 Mathematics CST Option (063-420) Épreuve Unique is a 3-hour exam evaluating mathematical reasoning across financial math, statistics, graph theory, and linear functions.

Sample Secondary 4 Mathematics—Cultural, Social and Technical Option Ministerial Examination — Québec Practice Questions

Try these sample questions to review concepts for the Secondary 4 Mathematics—Cultural, Social and Technical Option Ministerial Examination — Québec exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A dataset of test scores contains the values: 10, 14, 16, 20, and 20. What is the mean deviation (Écart moyen) of this dataset?
A.3.2
B.4.0
C.16.0
D.2.8
Explanation: First, calculate the arithmetic mean: $\bar{x} = \frac{10 + 14 + 16 + 20 + 20}{5} = \frac{80}{5} = 16$. Next, calculate the absolute deviation of each score from the mean: $|10-16|=6$, $|14-16|=2$, $|16-16|=0$, $|20-16|=4$, $|20-16|=4$. Finally, take the average of these absolute deviations: $EM = \frac{6 + 2 + 0 + 4 + 4}{5} = \frac{16}{5} = 3.2$.
2In a scatter plot representing two variables x and y, as x increases, the values of y consistently decrease following a straight trend line. Which term best describes this linear correlation?
A.Negative linear correlation
B.Positive linear correlation
C.Zero correlation
D.Non-linear correlation
Explanation: When one variable increases while the other decreases in a linear pattern, the relationship is classified as a negative linear correlation.
3A statistical study calculates a linear correlation coefficient of r = -0.88 between student absences and final math marks. How is this correlation classified?
A.Strong negative linear correlation
B.Weak negative linear correlation
C.Strong positive linear correlation
D.Moderate positive linear correlation
Explanation: Since |r| = 0.88 is greater than 0.85 and r is negative, r = -0.88 represents a strong negative linear correlation.
4A student draws a bounding rectangle around a scatter plot with a positive trend. The length of the rectangle along the trend line is a = 10 cm and its width is b = 3 cm. Using the rectangle estimation formula r ≈ ±(1 - b/a), what is the estimated correlation coefficient?
A.+0.70
B.+0.30
C.-0.70
D.+0.85
Explanation: For a positive trend, r ≈ +(1 - b/a) = +(1 - 3/10) = 1 - 0.30 = +0.70.
5A dataset sorted by x-values is divided into two equal groups of 4 data points. The centroid of Group 1 is M1(10, 50) and the centroid of Group 2 is M2(30, 110). What is the equation of the Mayer line (droite de Mayer)?
A.y = 3x + 20
B.y = 3x + 50
C.y = 2x + 30
D.y = 6x + 20
Explanation: Slope m = (110 - 50) / (30 - 10) = 60 / 20 = 3. Using M1(10, 50): 50 = 3(10) + b => b = 20. The equation of the Mayer line is y = 3x + 20.
6To determine a median-median regression line, data is partitioned into three equal groups yielding summary median points M1(4, 10), M2(8, 18), and M3(12, 26). What is the slope m of the median-median line?
A.2.0
B.2.25
C.1.5
D.3.0
Explanation: The slope of the median-median line is calculated using the first and third median summary points M1(x1, y1) and M3(x3, y3): m = (y3 - y1) / (x3 - x1) = (26 - 10) / (12 - 4) = 16 / 8 = 2.0.
7The linear regression equation modeling study hours (x) versus exam score (y) is y = 2.45x + 12.3. What is the predicted exam score for a student who studied for 35 hours?
A.98.05
B.85.75
C.90.25
D.102.50
Explanation: Substitute x = 35 into the regression line: y = 2.45(35) + 12.3 = 85.75 + 12.3 = 98.05.
8Two fair 6-sided dice are rolled simultaneously. What is the theoretical probability of obtaining a sum equal to 8?
A.5/36
B.4/36
C.6/36
D.1/6
Explanation: Total possible outcomes when rolling two 6-sided dice = 36. Outcomes with a sum of 8 are (2,6), (3,5), (4,4), (5,3), and (6,2), which gives 5 outcomes. P(sum = 8) = 5/36.
9Spinner A has 4 equal sectors (1 red, 3 blue). Spinner B has 5 equal sectors (2 green, 3 yellow). If both spinners are spun once, what is the probability of landing on Red on Spinner A AND Green on Spinner B?
A.1/10
B.2/9
C.3/20
D.7/20
Explanation: P(Red) = 1/4 and P(Green) = 2/5. Since the spins are independent, P(Red and Green) = (1/4) * (2/5) = 2/20 = 1/10.
10A bag contains 6 red marbles and 4 blue marbles. Two marbles are drawn sequentially without replacement. What is the probability that both drawn marbles are red?
A.1/3
B.9/25
C.2/5
D.1/2
Explanation: Probability of red on first draw = 6/10. Probability of red on second draw = 5/9. P(Both Red) = (6/10) * (5/9) = 30/90 = 1/3.

About the Secondary 4 Mathematics—Cultural, Social and Technical Option Ministerial Examination — Québec Exam

The Québec Secondary 4 Mathematics CST (Cultural, Social and Technical Option) Ministerial Examination is the mandatory provincial épreuve unique administered by the Ministère de l'Éducation du Québec (MEQ). It evaluates student proficiency in statistics, financial mathematics, geometry and measurement, networks, and algebraic functions. Passing this course contributes 4 credits toward the Secondary School Diploma (Diplôme d'études secondaires - DES). This OpenExamPrep bank is an English-language MCQ study adaptation for program knowledge and judgment; it does not reproduce or replace the official ministerial assessment format.

Exam sponsor: Ministère de l'Éducation du Québec (MEQ). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

3-hour ministerial examination with 16 tasks: Part A (6 MCQs), Part B (4 short answers), Part C (6 situations involving applications).

Time Limit

3 hours

Passing Score

Counts for 50% of final course mark; 60% required for DES credit

Exam / Certification Fees

Free for public/subsidized secondary school students in Quebec

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

25%

Statistics & Probability

Two-variable statistics, scatter plots, linear regression lines (Mayer line, median-median line), correlation coefficients, and conditional/experimental probability.

25%

Financial & Applied Mathematics

Compound interest, simple interest, annuities, taxes, asset depreciation, credit, and personal financial planning.

25%

Geometry & Measurement

Similar triangles, metric relations in right-angled triangles, trigonometry (sine law, cosine law, right triangle trig), perimeter, surface area, and volume of composite 3D solids.

15%

Networks & Graph Theory

Graphs and trees, shortest path algorithms, minimum spanning trees, chromatic number, Euler and Hamilton paths/circuits, and network optimization.

10%

Functions & Algebra

Linear functions, systems of linear equations, step functions, piecewise functions, and linear inequalities with boundary lines.

Preparing for the Secondary 4 Mathematics—Cultural, Social and Technical Option Ministerial Examination — Québec Exam

What You Need to Know

  • Passing score: Counts for 50% of final course mark; 60% required for DES credit
  • Assessment: 3-hour ministerial examination with 16 tasks: Part A (6 MCQs), Part B (4 short answers), Part C (6 situations involving applications).
  • Time limit: 3 hours
  • Exam / certification fees: Free for public/subsidized secondary school students in Quebec Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Secondary 4 Mathematics—Cultural, Social and Technical Option Ministerial Examination — Québec: Suggested Study Strategy

1Practice calculating regression lines using both the Mayer line (two group centroids) and the median-median line methods.
2Master the compound interest formula A = P(1 + r/n)^(nt) and annuity formulas for savings and loans.
3Memorize and apply metric relations in right triangles (e.g., h^2 = m * n, a^2 = m * c, b^2 = n * c).
4Learn graph theory definitions: vertex degree, Eulerian path/circuit, Hamiltonian path, graph coloring (chromatic number), and Kruskal's algorithm.
5Double check all calculations with your calculator and always verify units and decimal precision.

Frequently Asked Questions

What is the Secondary 4 CST Math Ministerial Examination in Québec?

It is the official provincial final exam (épreuve unique) created by the Ministère de l'Éducation du Québec (MEQ) for Grade 10 students enrolled in the Cultural, Social and Technical mathematics option (Course Code 063-420 in French, 563-420 in English).

How much does the épreuve unique count toward the final mark?

The provincial examination mark accounts for 50% of the student's final course mark for Secondary 4 Mathematics CST.

What tools are allowed during the CST Math exam?

Students are permitted to use a scientific or graphing calculator, a memory aid (one letter-sized sheet, both sides), and standard drawing instruments (ruler, protractor, compass).

What topics carry the highest weight on the exam?

The core topics include two-variable statistics and linear correlation, financial mathematics (compound interest, annuities, depreciation), geometry and trigonometry (sine/cosine laws, metric relations), and graph theory networks.

What passing mark is required for Secondary 4 CST Math credit?

A final weighted mark of at least 60% is required to earn the 4 secondary school diploma (DES) credits for Secondary 4 CST Mathematics.

Are these official MEQ exam questions?

No. This practice bank is independently created by OpenExamPrep to align with the MEQ Secondary 4 CST Mathematics curriculum guidelines and competencies.

Are these practice questions in the official ministerial examination format?

No. OpenExamPrep publishes an English-language multiple-choice study adaptation aligned to MEQ program content and rubrics. It is not an official translation, format simulation, or substitute for the official reading, writing, oral, constructed-response, or performance components.