Mathematics Entrance Test - April 2013 - One-hour ten-minute exam without calculators

Aug 25, 2026

Mathematics entrance test for April 2013 with a one-hour ten-minute time allowance. Instructions require answering all questions quickly, using only pens, pencils, erasers and rulers, and prohibiting calculators. Candidates must present all rough calculations and write final answers neatly beneath each question, with no evidence of working resulting in no marks. The questions cover solving equations, arithmetic progression sums, algebraic functions, age-word problems, circle geometry with angle calculations, and a savings/penny schedule leading to a purchase date.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Instructions

Time and materials rules

Question 1

Algebraic equation and number problem

Question 2

Solving an equation with powers

Question 3

Age relations and total sum

Question 4

Circle geometry and quadrilateral angles

Question 5

Quadratic function parameters and graph features

Question 6

Savings schedule and purchase date

Entrance test Mathematics April 2013 Time allowed: One hour ten minutes Answer all questions. It is advised that you work quickly and that you leave behind questions that are taking you too long to answer. You should only bring in writing material (pens, pencils, erasers, rulers). No calculators are allowed. All your rough calculations have to be presented. Answers with no evidence of calculations will not score any marks. Use the blank pages of the exam paper to do your rough work, THEN write your answer neatly under the question. Answers that are not written under the question neatly may not get marked. Nothing should be removed from the exam room. The sum of n terms of the arithmetic progression a, a+d, a+2d, a+3d…is S = ~~ ~~n2 [ 2a + (n−1)d ] THIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES Question 1 a)Solve 5x –(4x-7) (3x-5) = 6 – 3(4x-9)(x-1) b) Find a number such that if 5, 15 and 35 are added to it, the product of the first and third results is equal to the square of the second Answer: a) x = , b) the number is 3 3 Question 2 Solve 27x 2 + 1 = 28x 4 . Answer: x = or Question 3 I have two brothers. I am eight years older than my younger brother. The difference of my age from my younger brother’s age is twice the difference of my age from my big brother’s age. We are now getting old, so the sum of our ages is now 164. How old am I? Answer: I am year old Question 4 In the diagram below AOB is a diameter of the circle with centre O. If BC = CD and angle ∠ ODA = 50o, calculate the angles ofthe quadrilateral ABCD A D C B 50o O Answer: ∠ ABC = , ∠ BCD = , ∠ CDA = , ∠ DAB = Question 5 The curve y = x2 + bx + c, where b and c are constants, passes through (1,-10) and (4,8) . Find the values of b and c and draw the curve. Make sure you show clearly the points where the curve meets the axes and also the minimum value of y. Answer: b = and c = Question 6 A Nintendo DS costs one hundred and twenty British pounds sterling (£120) . I decide today, 17th April 2013, to put 10p aside. Tomorrow I’ll put 15p, the day after 20p, the day after that 25p and so on, increasing the amount by 5p every day. At which date will I have enough to buy the Nintendo? £1 = one pound = 100 pennies = 100p Answer:

FAQs

How long is the Mathematics entrance test and what is expected from candidates?

The time allowed is one hour ten minutes, and candidates must answer all questions quickly and completely.

Are calculators allowed, and how should rough work be handled?

Calculators are not allowed. Rough calculations must be presented using the blank pages, and final answers must be written neatly under each question.

What topics are included in the sample questions?

The test includes algebraic equation solving, arithmetic progression sums, quadratic functions, age-related word problems, circle geometry angle calculations, and a daily savings/pennies schedule.

Aug 25, 2026

Uploaded by Seraphina