Admissions Pack September2017
The National Mathematics and Science College
Contents
1Personal information1 2Academic information1 3Mathematics Entrance Examination2
3.1Section A (3)
3.2Section B (7)
4English Entrance Examination12
4.1Section A (12)
4.2Section B (13)
1Personal information
Name:
Date of birth://
Address:
Email:
Telephone:
2Academic information
Plea complete the form below to the best of your knowledge,giving your most recent grades. We will require to e evidence of yourfinal academic results before enrolment.For mathematics, plea give any international AS modules studied C12,S1).
Current school/college:
Subject Grade Exam board Date awarded
3Mathematics Entrance Examination
This asssment is designed to determine your potential for studying mathematics at The National M
athematics and Science College.The u of a calculator is not permitted.You may u additional paper for rough working,but do ensure that you show all of the important steps in your working on the exam paper.Section A will be graded according to a mark scheme and you should attempt all questions in this ction.You are expected to respond to at least one question from Section B,and you are invited to respond to as many as you can.You do not need to answer all questions in Section B.Marks will be awarded for style,persistence and creativity.Good luck.
Time allowed:60minutes
Formulae
Trigonometry
•The cosine rule states that:
a2=b2+c2 2b c cosA
•The sine rule states that:sinA
a =
sinB
b
=
sinC
c
•The area of a triangle may be given by:
Area=1
2
a b sinC
Quadratic Equations
•The solution to the equation
a x2+
b x+c=0
is given by
x= b±p b2 4a c 2a
Geometry
•The volume of a cone of radius r and height h is given by
1
3
⇡r2h
3.1Section A
1.(a)[1]
Expand and simplify:p(q 2p) 3q(p 2q)
(b)Factori fully:
i.[2]
14x2y 2x y2
ii.[2]
a2 25b2
iii.[2]
x2 6x+9
(c)i.[3]
Solve the equation,expressing your solution as a fraction in simplest form:
3
x 2
5
3x 6
=2
ii.[2] Prove,by substituting into the left-hand side,that your solution is correct.
