100+ Free Preparatory Certificate Practice Questions

Prepare for the Egypt Basic Education Completion Certificate — Preparatory Certificate (شهادة إتمام مرحلة التعليم الأساسي / الشهادة الإعدادية) exam with instant access — no signup required.

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Sample Preparatory Certificate Practice Questions

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

1If the set X = {2} and the set Y = {3, 5}, what is the Cartesian product X × Y?

A.{(2, 3), (2, 5)}

B.{(3, 2), (5, 2)}

C.{6, 10}

D.{(2, 3), (3, 2), (2, 5), (5, 2)}

Explanation: The Cartesian product X × Y is the set of all ordered pairs (x, y) where x ∈ X and y ∈ Y. Since X has one element (2) and Y has two elements (3 and 5), X × Y = {(2, 3), (2, 5)} with n(X × Y) = 1 × 2 = 2 pairs.

2If y varies directly as x (y ∝ x) and y = 14 when x = 7, what is the value of y when x = 10?

A.20

B.5

C.28

D.17

Explanation: In direct variation, y = m x, where m is the constant of variation. Substituting y = 14 and x = 7 gives m = 14 / 7 = 2. Therefore, the relation is y = 2x. When x = 10, y = 2(10) = 20.

3If y varies inversely as x (y ∝ 1/x) and y = 6 when x = 4, what is the value of y when x = 3?

A.8

B.4.5

C.2

D.12

Explanation: In inverse variation, the product of the variables is constant: x × y = k. Here, k = 4 × 6 = 24. Therefore, when x = 3, y = k / x = 24 / 3 = 8.

4What is the common domain on which the two algebraic fractions N₁(x) = 2 / (x - 3) and N₂(x) = (x + 1) / (x² - 9) are both defined?

A.ℝ - {3, -3}

B.ℝ - {3}

C.ℝ - {-3}

D.ℝ - {0, 3}

Explanation: An algebraic fraction is defined on all real numbers except the zeroes of its denominator. The denominator of N₁ is x - 3 = 0 -> x = 3. The denominator of N₂ is x² - 9 = 0 -> x = ±3. The common domain is ℝ minus the union of both sets of zeroes: ℝ - {3, -3}.

5What is the solution set of the system of equations x + y = 5 and x - y = 1 in ℝ × ℝ?

A.{(3, 2)}

B.{(2, 3)}

C.{(4, 1)}

D.{(5, 0)}

Explanation: Add the two equations: (x + y) + (x - y) = 5 + 1 -> 2x = 6 -> x = 3. Substitute x = 3 into the first equation: 3 + y = 5 -> y = 2. Thus, the solution set is {(3, 2)}.

6Using the general formula, what are the roots of the quadratic equation x² - 5x + 6 = 0?

A.{2, 3}

B.{-2, -3}

C.{1, 6}

D.{-1, -6}

Explanation: Using x = [-b ± √(b² - 4ac)] / (2a) with a = 1, b = -5, c = 6: x = [5 ± √(25 - 24)] / 2 = [5 ± √1] / 2 = [5 ± 1] / 2. This gives x = 6/2 = 3 and x = 4/2 = 2. Solution set is {2, 3}.

7If b is the middle proportional between a and c (continued proportion), which algebraic relation is true?

A.b² = a c

B.b = a + c

C.b² = a / c

D.2b = a c

Explanation: If a, b, and c are positive terms in continued proportion, then a / b = b / c. Cross-multiplying yields b² = a c, so the positive middle proportional is b = √(a c).

8What is the range of the set of values: 12, 7, 25, 18, 9, 31?

A.24

B.19

C.31

D.7

Explanation: The range in descriptive statistics is the difference between the greatest value and the smallest value: Maximum (31) - Minimum (7) = 31 - 7 = 24.

9In descriptive statistics, which measure of dispersion is the positive square root of the mean of the squares of deviations of values from their arithmetic mean?

A.Standard deviation (σ)

B.Variance

C.Range

D.Median

Explanation: The standard deviation (σ = √[∑(x - x̄)² / n]) is the primary measure of dispersion defined mathematically as the positive square root of the variance (the mean squared deviations from the arithmetic mean).

10If A and B are two mutually exclusive events in a sample space S, and P(A) = 0.3 and P(B) = 0.5, what is P(A ∪ B)?

A.0.8

B.0.15

C.0.2

D.0.65

Explanation: For mutually exclusive events, their intersection is impossible (P(A ∩ B) = 0). Therefore, P(A ∪ B) = P(A) + P(B) = 0.3 + 0.5 = 0.8.

About the Preparatory Certificate Exam

The Certificate of Completion of Basic Education (شهادة إتمام مرحلة التعليم الأساسي), commonly called the Preparatory Certificate (الشهادة الإعدادية), is Egypt's Grade 9 completion credential and a basis for secondary-school placement. It is nationally recognized but not one centrally identical paper: governorates prepare schedules and administer examinations under Ministry subject specifications. Cairo, for example, reported 203,162 applicants and a 73% first-round pass rate in 2025/2026. The scored curriculum includes Arabic, first foreign language, Mathematics, Science, and Social Studies. Standard public-school papers are in Arabic, while language-school Mathematics and Science papers are also administered in English. This bank uses English instructions and four-option questions while preserving Arabic text where Arabic language skills are tested. It is an original study adaptation—not an official translation, reproduction, or format simulation—and cannot replace handwriting, composition, proof, or other constructed-response practice.

Assessment

Question count varies by module

Time Limit

Varies by subject and governorate timetable; there is no single nationwide paper timetable.

Passing Score

Use the current governorate result and placement rules. The reviewed official current sources do not publish one nationwide secondary-placement cutoff.

Exam Fee

Not published as one current nationwide candidate fee in the reviewed official materials. (Governorate educational directorates under Egyptian Ministry of Education and Technical Education specifications)

Preparatory Certificate Exam Content Outline

20% of this practice bank

Arabic Language & Reading

Arabic reading comprehension, vocabulary and textual cohesion, syntax and morphology, rhetorical devices, orthography, number agreement, and short-writing conventions. Arabic target text is retained because it is integral to the skill.

25% of this practice bank

Mathematics

Relations and functions, variation, algebraic equations and fractions, descriptive statistics, circle geometry, coordinate geometry, and basic trigonometry.

15% of this practice bank

Science

Motion and acceleration, forces, astronomy, chemical reactions and reaction rates, catalysts, radioactivity, cell division, and heredity.

25% of this practice bank

English Language

Reading comprehension and inference, vocabulary in context, grammar including tenses, passive voice, conditionals, relative clauses and reported speech, plus paragraph cohesion and functional writing.

15% of this practice bank

Social Studies

World and Egyptian geography, population and economic activities, together with modern Egyptian history from Muhammad Ali through the national movement, the 1919 and 1952 revolutions, and later constitutional developments.

How to Pass the Preparatory Certificate Exam

What You Need to Know

Passing score: Use the current governorate result and placement rules. The reviewed official current sources do not publish one nationwide secondary-placement cutoff.
Assessment: Question count varies by module
Time limit: Varies by subject and governorate timetable; there is no single nationwide paper timetable.
Exam fee: Not published as one current nationwide candidate fee in the reviewed official materials.

Keys to Passing

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

Preparatory Certificate Study Tips from Top Performers

1Give Mathematics and Arabic sustained practice time, including worked mathematical reasoning and handwritten Arabic reading, grammar, and composition tasks that this MCQ adaptation cannot reproduce.

2Work through current papers from your own governorate first, because governorates administer different papers and schedules even though Ministry specifications define the subject outcomes.

3In Mathematics, practice drawing geometric circle constructions and writing step-by-step proofs using proper geometric notation alongside numerical trigonometry calculations.

4For Science, memorize standard chemical reaction equations (thermal decomposition of metal carbonates, hydroxides, and nitrates) and practice drawing ray diagrams for concave mirrors and convex lenses.

5Review English grammar tenses, active/passive transformations, and reported speech rules to ensure flawless accuracy on the language structure sections.

6Create summary timelines for Modern Egyptian history (from the 1805 accession of Muhammad Ali to the 1973 October War) to easily retain chronological sequences and treaty dates.

Frequently Asked Questions

What is the Egyptian Preparatory Certificate (الشهادة الإعدادية)?

The Preparatory Certificate (Third Year of Preparatory Education / Grade 9) certifies completion of Egypt's basic-education stage and informs secondary-school placement. It is nationally recognized, but each governorate administers its papers and schedule under Ministry specifications.

Which subjects are scored in the Preparatory Certificate?

The scored subject set is Arabic Language, the first foreign language, Mathematics, Science, and Social Studies. Current paper details and schedules must be checked with the relevant governorate; this bank's question counts are a transparent study allocation, not official weights.

What score is required to enter General Secondary School (Thanaweya Amma)?

Admission cutoffs for General Secondary (الثانوية العامة) are determined by each governorate based on current capacity and results. A past range is not a reliable current rule, so candidates should use their governorate's active placement announcement.

How are the examinations formatted and administered?

Governorates administer written subject papers under Ministry specifications. Objective and constructed-response tasks can both appear, and the relevant governorate publishes the current dates, durations, and instructions.

What should a student do after an unsuccessful first-round result?

Use the current instructions and second-round timetable issued by the relevant governorate educational directorate. The reviewed sources do not establish one stable nationwide subject threshold or progression rule that should be substituted for the student's official result notice.

Is this practice bank designed for language school students?

It is useful for bilingual and language-school study, but it is not an official language-school paper. Standard public-school assessment is Arabic and language-school Mathematics and Science are also offered in English. The bank uses English framing while preserving Arabic text for sampled Arabic-language skills.