PracticeVideosBlogFlashcardsEspañol
All Practice Exams

100+ Free Egypt STEM Schools Entrance Exam Practice Questions

Prepare for the Egypt STEM Schools of Excellence Entrance Examination (اختبارات القبول بمدارس المتفوقين في العلوم والتكنولوجيا STEM) exam with instant access — no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately
100+ Questions
100% Free

Loading practice questions...

Sample Egypt STEM Schools Entrance Exam Practice Questions

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

1Real numbers a and b satisfy a + b = 7 and a² + b² = 29. What is the value of a³ + b³?
A.133
B.203
C.343
D.63
Explanation: First use a² + b² = (a + b)² - 2ab: 29 = 49 - 2ab, so ab = 10. Then a³ + b³ = (a + b)³ - 3ab(a + b) = 7³ - 3(10)(7) = 343 - 210 = 133.
2A right triangle has legs of lengths a and b and hypotenuse c. If the radius of its inscribed circle (incircle) is r, which of the following formulas correctly expresses r in terms of a, b, and c?
A.r = (a + b - c) / 2
B.r = (a + b + c) / 2
C.r = (a * b) / (2 * c)
D.r = sqrt(a * b) / 2
Explanation: The area of any triangle is A = r * s, where s = (a + b + c) / 2 is the semi-perimeter. For a right triangle, area A = (a * b) / 2. Also, the tangents from the right angle vertex to the incircle form a square of side r, so the segments along the legs are r and a - r, and r and b - r. The tangents to the hypotenuse are equal, so c = (a - r) + (b - r) = a + b - 2r, which rearranges directly to 2r = a + b - c, or r = (a + b - c) / 2.
3What is the remainder when 3^100 is divided by 7?
A.4
B.1
C.2
D.6
Explanation: We analyze powers of 3 modulo 7: 3^1 ≡ 3 (mod 7), 3^2 ≡ 2 (mod 7), 3^3 = 27 ≡ 6 ≡ -1 (mod 7), 3^4 ≡ 4 (mod 7), 3^5 ≡ 5 (mod 7), 3^6 ≡ 1 (mod 7). The cycle length is 6. Dividing the exponent 100 by 6 gives 100 = 6 * 16 + 4. Therefore, 3^100 ≡ (3^6)^16 * 3^4 ≡ 1^16 * 81 ≡ 81 (mod 7). Since 81 = 7 * 11 + 4, the remainder is 4.
4If the roots of the quadratic equation 2x^2 - 8x + k = 0 differ by 2, what is the value of k?
A.6
B.4
C.8
D.10
Explanation: Let the roots be r1 and r2. By Vieta's formulas, r1 + r2 = -(-8)/2 = 4 and r1 * r2 = k/2. We are given |r1 - r2| = 2. Squaring both sides yields (r1 - r2)^2 = 4. Using the algebraic identity (r1 - r2)^2 = (r1 + r2)^2 - 4(r1 * r2), we substitute: 4 = 4^2 - 4(k/2) => 4 = 16 - 2k => 2k = 12 => k = 6.
5Two circles of radii 16 cm and 9 cm are externally tangent. What is the length of their common external tangent segment between the two points of tangency?
A.24 cm
B.25 cm
C.14 cm
D.12 cm
Explanation: The center distance is d = R + r = 25 cm, while the perpendicular offset between the two radii is R - r = 7 cm. The tangent segment L is the other leg of a right triangle: L = √(25² - 7²) = √576 = 24 cm. Equivalently, L = 2√(Rr) = 2√(16 × 9) = 24 cm.
6How many positive integers less than 1,000 are divisible by neither 5 nor 7?
A.686
B.313
C.714
D.657
Explanation: The positive integers less than 1,000 are 1 through 999 (total N = 999). Number of multiples of 5: floor(999/5) = 199. Number of multiples of 7: floor(999/7) = 142. Number of multiples of both 5 and 7 (i.e., multiples of 35): floor(999/35) = 28. By the Principle of Inclusion-Exclusion, the number of integers divisible by 5 or 7 is 199 + 142 - 28 = 313. Thus, the number divisible by neither is 999 - 313 = 686.
7Let a = log₂(x) and b = log₂(y), where x and y are positive. If xy = 64 and x/y = 4, what is a?
A.4
B.2
C.6
D.8
Explanation: Taking base-2 logarithms gives a + b = log₂(64) = 6 and a - b = log₂(4) = 2. Adding the equations gives 2a = 8, so a = 4. Equivalently, xy = 64 and x/y = 4 imply x² = 256 and, because x is positive, x = 16.
8A bag contains 5 red balls and 4 blue balls. Two balls are drawn at random one after another without replacement. What is the probability that both drawn balls are of different colors?
A.5/9
B.4/9
C.5/18
D.20/81
Explanation: Total balls = 5 + 4 = 9. The total number of ways to choose 2 balls out of 9 is C(9, 2) = (9 * 8) / 2 = 36. The number of favorable outcomes (one red and one blue) is C(5, 1) * C(4, 1) = 5 * 4 = 20. Therefore, the probability is 20 / 36 = 5/9. Alternatively: P(Red then Blue) = (5/9) * (4/8) = 20/72; P(Blue then Red) = (4/9) * (5/8) = 20/72; Total = 40/72 = 5/9.
9In triangle ABC, angle C = 90 degrees. D is a point on hypotenuse AB such that CD is perpendicular to AB. If AD = 4 cm and DB = 9 cm, what is the length of CD?
A.6 cm
B.6.5 cm
C.sqrt(13) cm
D.36 cm
Explanation: By the Geometric Mean Theorem (Euclid's Theorem for right triangles), the altitude to the hypotenuse is the geometric mean of the two segments of the hypotenuse: CD^2 = AD * DB. Substituting the given values: CD^2 = 4 * 9 = 36, so CD = sqrt(36) = 6 cm.
10A worker can complete a job alone in 12 days, and a second worker can complete the same job alone in 18 days. If they work together for 4 days and then the first worker leaves, how many additional days will it take the second worker alone to finish the remaining work?
A.8 days
B.6 days
C.10 days
D.7 days
Explanation: The work rate of the first worker is 1/12 job/day, and the second worker is 1/18 job/day. Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36 job/day. In 4 days of working together, they complete 4 * (5/36) = 20/36 = 5/9 of the job. The remaining work is 1 - 5/9 = 4/9 of the job. Working alone at 1/18 job/day, the second worker takes (4/9) / (1/18) = (4/9) * 18 = 8 days to finish.

About the Egypt STEM Schools Entrance Exam Exam

The Egypt STEM Schools Entrance Examination is the Ministry of Education's one-round electronic admission assessment for STEM Schools of Excellence (مدارس المتفوقين في العلوم والتكنولوجيا), which remain current under Ministerial Decision 303 of 2025. The latest fully extractable admission rules reviewed are for 2025/2026 entry: they require Egyptian nationality, same-year completion of basic education, age no greater than 18 on 1 October 2025, and either at least 274.5/280 (98%) or at least 266/280 (95%) with a full mark in English, Mathematics, or Science. The examination has Mathematics, Science, English, and IQ components; candidates must pass each component and are then ranked by the considered total and school preferences. Those instructions allow candidates to choose Arabic or English for the applicable test language and set a fee of EGP 250. Official rules reviewed do not publish fixed item counts, durations, item types, equal weights, or component cut scores. This bank is an original English-language four-option study adaptation—not an official translation, reproduction, or format simulation. Applicants must verify the active intake notice because eligibility thresholds and fees are intake-specific.

Assessment

Question count not published by the exam provider

Time Limit

No per-candidate duration is published in the reviewed official admission rules.

Passing Score

Meet the Ministry's undisclosed success criterion in each of the four components, then rank competitively by the components' considered total and stated school preferences.

Exam Fee

EGP 250 in the latest fully extractable official instructions reviewed (2025/2026 entry); verify the active intake notice. (Egyptian Ministry of Education and Technical Education — Central Unit for Gifted and Talented Schools)

Egypt STEM Schools Entrance Exam Exam Content Outline

25% of this practice bank; official weight not published

Mathematics & Quantitative Reasoning

Higher-order algebra, polynomial manipulation, coordinate geometry, Euclidean geometry proofs, trigonometry, combinatorics, probability, number theory, and non-routine problem solving.

25% of this practice bank; official weight not published

Integrated Natural Sciences

Physics (mechanics, electricity, optics, waves), Chemistry (stoichiometry, periodic trends, atomic structure, reactions), and Biology (cell biology, human physiology, genetics, ecosystems, and experimental design).

25% of this practice bank; official weight not published

English Language & Scientific Literacy

Advanced academic and scientific vocabulary, reading comprehension of expository and scientific texts, textual inferences, identifying logical fallacies, and grammatical error identification.

25% of this practice bank; official weight not published

Cognitive Aptitude & Abstract Logical Reasoning (IQ)

Raven's-style progressive matrices, 2D and 3D spatial rotation, number sequence patterns, conditional syllogisms, verbal and numerical analogies, and critical analytical deduction.

How to Pass the Egypt STEM Schools Entrance Exam Exam

What You Need to Know

  • Passing score: Meet the Ministry's undisclosed success criterion in each of the four components, then rank competitively by the components' considered total and stated school preferences.
  • Assessment: Question count not published by the exam provider
  • Time limit: No per-candidate duration is published in the reviewed official admission rules.
  • Exam fee: EGP 250 in the latest fully extractable official instructions reviewed (2025/2026 entry); verify the active intake notice.

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

Egypt STEM Schools Entrance Exam Study Tips from Top Performers

1Practice non-routine competition-style mathematics: Standard textbook exercises are not enough; focus on problem-solving puzzles from Math Olympiads and kangaroo math competitions involving number theory and geometry.
2Sharpen abstract spatial reasoning and Raven's-style IQ matrices: Dedicate daily practice to sequence recognition, folded shape nets, mirror images, and diagrammatic logic.
3Understand scientific principles conceptually: Be prepared for questions that ask you to interpret experimental data, graph relationships between physical variables, or predict reaction outcomes rather than reciting definitions.
4Strengthen English scientific reading: Practice reading technical articles and scientific abstracts in English to build reading speed and vocabulary for expository passages.
5Practise under several self-imposed time budgets, because the reviewed official rules do not publish the live component durations or per-question pacing.
6Review Middle School Science thoroughly: Revisit Grade 7–9 concepts in electricity (Ohm's law, circuit series/parallel calculations), optics (refraction index, lenses), and genetics (Punnett squares).

Frequently Asked Questions

What are Egypt's STEM Schools and what is the entrance exam?

Egypt's STEM Schools of Excellence (مدارس المتفوقين في العلوم والتكنولوجيا) are selective public secondary schools with integrated STEM curricula. The Ministry administers a one-round electronic entrance assessment with Mathematics, Science, English, and IQ components.

Who is eligible to sit the STEM entrance exam?

Under the latest fully extractable notice reviewed, for 2025/2026 entry, applicants had to be Egyptian, complete Grade 9 (الشهادة الإعدادية) in that same year, be no older than 18 on 1 October 2025, and earn at least 98% (274.5/280), or at least 95% (266/280) plus a full mark in Mathematics, Science, or English. Applicants must check the active intake notice because these thresholds and dates can change.

What subjects are tested on the STEM entrance exam?

The official admission rules name four components: Mathematics, Science, English Language, and IQ. They do not publish fixed item counts, item types, durations, or equal weights. This bank assigns 25 questions to each only as a transparent study allocation.

In what language is the exam delivered?

The latest fully extractable admission instructions reviewed allow the applicant to choose Arabic or English as the applicable examination language. This bank uses English throughout and therefore is not an official translation or substitute for practising in the language selected at registration.

How are students selected for admission?

A candidate must first meet the success criterion for every component. The Ministry then ranks candidates by the considered total of the four components and applies their school preferences. Public rules do not disclose the component cut scores or a fixed nationwide admission score.

Where are STEM schools located in Egypt?

The list of available schools and seats is intake-specific. Applicants should use the current Ministry application portal and admission notice rather than an older campus count.