Sample of Mathematics Entrance Examination 2024 - Exam Instructions and Practice Questions

Q: What are the key exam rules candidates must follow?

Candidates have 1 hour and 10 minutes, must answer all questions, and calculators are not allowed. Answers must be written in the spaces below questions, with working shown; anything on other pages will not be marked.

Q: What conduct and material restrictions apply during the exam?

Candidates cannot leave during the first 30 minutes or last 15 minutes, and must not talk, whisper, turn around, or look at another candidate’s paper. Borrowing stationery is not allowed, and unauthorized exam materials lead to disqualification.

Q: What happens if a candidate is caught cheating or with a mobile phone?

Cheating results in disqualification, and having a mobile phone or electronic device on the candidate during the exam is treated as unauthorized materials, also leading to disqualification without a right of appeal.

Aug 25, 2026

Uploaded by Quinn

Sample Mathematics Entrance Examination 2024 provides exam rules and a full set of practice questions for candidates. It specifies a 1 hour 10 minutes time limit, requires all questions to be answered, prohibits calculators, and emphasizes that working must be shown in the allocated spaces to earn marks. Additional regulations cover timing restrictions, conduct during the exam, stationery borrowing rules, unauthorized materials, cheating consequences, pocket checks, and electronic device prohibitions. The paper includes angle, distance, algebra, function, log, trigonometry, probability, and application problems.

LanguageEnglish

CategoryExam

FormatPDF

Pages6

Reading Time15 min

AccessFree to download

Exam Instructions

General rules and prohibited actions

Additional requirements

Practice Questions

Angles in triangles and equation solving

Distance and coordinate geometry

Simplification and evaluation

Functions and right-triangle applications

Algebraic identities and logarithms

Trigonometry and circle graph probability

Oil tank and advanced trigonometric equations

Progressions and engineering strength optimization

Sample of Mathematics Entrance Examination 2024 DATE: SESSION: 1. You have 1 hour and 10 minutes for the exam. 2. Answer all questions. 3. No calculators are allowed. 4. For Open-ended questions write your answers in the spaces below the questions. Answers with no evidence of calculations will not score any marks. Workings and answers written on any other page will not be marked. Please note additional requirements: a) You are not allowed to leave during the first 30 minutes or the last 15 minutes of the examination. b) You are not allowed to talk, to whisper, to turn around or to look at another candidate’s examination, all of which are offences, and you will be penalized. If you commit this offence, you will be given a single written warning; after which if you commit a further offence, you will be reported to an assessment board without a right of appeal or refund of the exam administration fee. c) You cannot borrow another student’s stationery or materials. d) If your pen runs out of ink, you may request a replacement from the invigilator. No other stationery or materials may be provided for you by the invigilator. e) If you are found to have any unauthorized exam related materials during the examination this will constitute an offence and you will be disqualified from the exam. f) If you are caught cheating in the examination, you will be disqualified from the exam. g) Failure to show contents of your pockets or any other containers to the invigilators will be considered as an offence and you will be disqualified from the exam. h) All mobile phones and other electronic devices must be switched off and left at a place indicated by the invigilators. If you are found to have a mobile phone or other electronic device (switched on or off) on you during the exam, this will be considered as unauthorized examination materials, and you will be disqualified from the exam without a right of appeal. Applicant ID: 1. Find the angles of the triangle, ∠􀜣, ∠􀜤 and ∠􀜥 respectively. (2 marks) a) 75, 60, 45 b) 50, 40, 30 c) 100, 80, 60 d) 90, 60, 30 2. If 􀝐 < 0, and 􀝐 2 − 2􀝐 − 35 = 0, find the possible values of 􀝐? (2 marks) a) -7 and-5 b) -7 and 5 c) -5 d) 7 3. Find the distance between the points A(3, 4) and B(7 , 7) . (2 marks) a) 5 b) 25 c) 4√2 d) 4√3 4. A line in the xy-plane passes through the origin and has a slope of 25. Which of the following points lies on the line? (2 marks) a) (2 , 5) b) (1, 5) c) (5 , 5) d) (10 , 4) 5. For what value of 􀝊 is −|􀢔 + 􀫜| equal to 0? (2 marks) a) 3 b) 1 c) -3 d) There is no such value of 􀝊 6. Find the value of x. a) 8 b) 9 c) 10 d) ∅ 7. Simplify 􀝔 − 1 5 + 6􀝔 + 14 4 + 3􀝔 ~~ ~~ − 45 9 (2 marks) (2 marks) | a) 2􀝔 − 1 3 | b) 1 c) 1 3 | d) 1
−
3 | | --- | --- | --- | 8. Evaluate 10√2 × 4 × 11 × 671 + 1 (2 marks) a) 8 b) 3 c) 4 d) 9 9. Find the intervals on which function is decreasing. (2 marks) a) (−4; 4) b) (−2; 2) c) (−∞; −2) ∪ (2; ∞) d) (−16; 16) 10. If the triangle ABC is right angled at A. Given that AD is perpendicular to BC, AB = 5 cm, BC = 13 cm, and AC = 12 cm, find the length of AD. (4 marks) | a) 25 13 | b) 60 13 | c) 4 d) 3 | | --- | --- | --- | 11. If 􀝔 2 + 8􀝔 + 3 = (􀝔 + 􀜽)2 + 􀜾 for all values of 􀝔 . Find the possible values for 􀜽 and 􀜾 . (4 marks) | a) 􀜽 = 2,􀜾 = 3 | b) 􀜽 = 2,􀜾 = −13 | c) 􀜽 = 4,􀜾 = 3 | d) 􀜽 = 4,􀜾 = −13 | | --- | --- | --- | --- | 12. If 􀝔 = 1 􀝔 ∈ ℝ find the value of 􀝔 2 + 4􀝔 − 1 √5+2 , . (4 marks) a) -1 b) 0 c) 2 d) -2 13. Find the area of the shaded region, if the radius of the circle is 4 cm. (4 marks) a) 16􀟨 􀜿􀝉 2 b) 16􀟨 − 24√3 􀜿􀝉 2 c) 16􀟨 − 48√3􀜿􀝉 2 d) 16 􀜿􀝉 2 14. Solve for 􀝔 . log 2 (􀝔 − 3) +log2 (􀝔) = 2 (4 marks) | a) 􀝔1 = 4,􀝔2 = −1 | b) 􀝔 = 4 c) 􀝔1 = 1,􀝔2 = −4 | d) 􀝔1 = 1,􀝔2 = 2 | | --- | --- | --- | 15. In the right triangle, one angle measures 􀟙, where cos 􀟙 = 35. Calculate the value of sin(90 − 􀟙) . (4 marks) | a)

FAQs

What are the key exam rules candidates must follow?

Candidates have 1 hour and 10 minutes, must answer all questions, and calculators are not allowed. Answers must be written in the spaces below questions, with working shown; anything on other pages will not be marked.

What conduct and material restrictions apply during the exam?

Candidates cannot leave during the first 30 minutes or last 15 minutes, and must not talk, whisper, turn around, or look at another candidate’s paper. Borrowing stationery is not allowed, and unauthorized exam materials lead to disqualification.

What happens if a candidate is caught cheating or with a mobile phone?

Cheating results in disqualification, and having a mobile phone or electronic device on the candidate during the exam is treated as unauthorized materials, also leading to disqualification without a right of appeal.

Aug 25, 2026

Uploaded by Quinn