Inverse Functions
106 min
110 marks
1.
x
Let f(x) = x, and g(x) = 2 . Solve the equation
(f
1
o g)(x) = 0.25.
Working:
Answers:
.
(Total 4 marks)
2.
Two functions f, g are defined as follows:
f : x 3x + 5
g : x 2(1 x)
1
Find
1
(a)
f (2);
(b)
(g o f)(4).
W

Poisson Distibution
100 min
60 marks
1.
A supplier of copper wire looks for flaws before despatching it to customers.
It is known that the number of flaws follow a Poisson probability distribution
with a mean of 2.3 flaws per metre.
(a)
Determine the prob

Probability Diagram
12 min
7 marks
1.
The local Football Association consists of ten teams. Team A has a 40 % chance of winning any
game against a higher-ranked team, and a 75 % chance of winning any game against a lowerranked team. If A is currently in f

Graph of Trig Function
35 min
19 marks
1.
(a)
Sketch the graph of f(x) = sin 3x + sin 6x, 0 < x < 2.
(b)
Write down the exact period of the function f.
Working:
Answers:
.
(Total 3 marks)
2.
(a)
Sketch the graph of the function
1
C ( x) cos x cos 2 x
2
fo

Binomial Theorem
130 min
114 marks
1.
5
Find the coefficient of x in the expansion of (3x 2)
8
Working:
Answers:
.
(Total 4 marks)
2.
Given that
5
6
2
6 11
(1 + x) (1 + ax) 1 + bx + 10x + . + a x ,
1
find the values of a, b
*.
Working:
Answers:
.
(Total

Solution of Triangles
68 min
54 marks
1.
2
The area of the triangle shown below is 2.21 cm . The length of the shortest side is x cm and the
other two sides are 3x cm and (x + 3) cm.
x
3x
x + 3
(a)
Using the formula for the area of the triangle, write dow

Angles
87 min
59 marks
1.
The rectangle box shown in the diagram has dimensions 6 cm 4 cm 3 cm.
H
G
E
F
3cm
D
A
C
6cm
B
4cm
Find, correct to the nearest one-tenth of a degree, the size of the angle AHC .
Working:
Answers:
.
(Total 4 marks)
2.
Let a be the

Inverse Trig Functions
63 min
35 marks
1.
0,
The function f with domain 2 is defined by f(x) = cos x +
3 sin x.
This function may also be expressed in the form R cos(x ) where R > 0 and 0 < < 2 .
(a)
Find the exact value of R and of .
(3)
(b)
(i)
Find

Mathematical Induction
185 min
111 marks
1.
2n
Using mathematical induction, prove that the number 2 3n 1 is
divisible by 9, for n = 1, 2, . .
(7)
(Total 7 marks)
2.
(a)
2
Evaluate (1 + i) , where i =
1.
(2)
(b)
4n
n
Prove, by mathematical induction, tha

Arcs & Sector Formula
6 min
6 marks
1.
The diagram below shows a circle centre O and radius OA = 5 cm. The angle AOB = 135.
A
B
O
Find the area of the shaded region.
Working:
Answer:
.
(Total 6 marks)
1
Arcs & Sector Formula Mark Scheme
0 min
0 marks
1.
1

Counting Principles
63 min
42 marks
1.
Mr Blue, Mr Black, Mr Green, Mrs White, Mrs Yellow and Mrs Red sit around a circular table
for a meeting. Mr Black and Mrs White must not sit together.
Calculate the number of different ways these six people can sit

Inverse Functions
106 min
110 marks
1.
x
Let f(x) = x, and g(x) = 2 . Solve the equation
(f
1
o g)(x) = 0.25.
Working:
Answers:
.
(Total 4 marks)
2.
Two functions f, g are defined as follows:
f : x 3x + 5
g : x 2(1 x)
1
Find
1
(a)
f (2);
(b)
(g o f)(4).
W

Geometric Series
147 min
125 marks
1.
Find the sum of the infinite geometric series
2 4 8 16 .
3 9 27 81
Working:
Answers:
.
(Total 4 marks)
2.
The probability distribution of a discrete random variable X is given by
x
2
P(X = x) = k 3 , for x = 0,1, 2,

Inequalities
42 min
39 marks
1.
Find the values of x for which 5 3x x + 1.
Working:
Answers:
.
(Total 3 marks)
1
2.
3
Solve the inequality x 4 + x < 0.
2
Working:
Answers:
.
.
(Total 6 marks)
3.
Solve the inequality x 2 2x + 1.
Working:
Answer:
.
(Total 6

Identities
128 min
86 marks
1.
Let be the angle between the unit vectors a and b, where 0 < < . Express |a b| in terms of
1
sin
2 .
Working:
Answers:
.
(Total 3 marks)
1
2.
The function f is defined on the domain [0, ] by f( ) = 4 cos + 3 sin .
(a)
Expre

Binomial Distribution
82 min
60 marks
1.
The quality control department of a company making computer chips knows that 2% of the chips
are defective. Use the normal approximation to the binomial probability distribution, with a
continuity correction, to fi

Logarithmic & Exponential Functions
93 min
85 marks
1.
A population of bacteria is growing at the rate of 2.3 % per minute. How long will it take for the
size of the population to double? Give your answer to the nearest minute.
Working:
Answers:
.
(Total

Exponentials and Logarithms
49 min
62 marks
1.
1
x1
Solve the equation 9 = 3
2x
.
Working:
Answers:
.
(Total 4 marks)
1
2.
Solve the equation 4
3x1
2
= 1.5625 10 .
Working:
Answers:
.
(Total 4 marks)
3.
If loga 2 = x and loga 5 = y, find in terms of x

Domain & Range
17 min
16 marks
1.
The function f is given by f(x) =
1n ( x 2)
. Find the domain of the function.
Working:
Answers:
.
(Total 4 marks)
1
50
2.
Find
ln 2
r 1
r
, giving the answer in the form a ln 2, where a
.
Working:
Answer:
.
(Total 6 m

Unit 6 Shape and Space 6
Circle Theorems Work List
1.
2.
3.
4.
5.
6.
7.
Summarise the Circle Properties on page 56 and draw accurate diagrams with your compass.
Note the important Remember point on page 29.
Ex 11* Qn 1, 7, 11 (13, 14)
Ex 12* Qn 1, 4, 5, 1

KING GEORGE V SCHOOL
HONG KONG
MATHEMATICS
YEAR 12 HL
Test 3 Calculator
February 2014
Student Name:
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KING GEORGE V SCHOOL
HONG KONG
MATHEMATIC S
YEAR 12 HL
Test 4 Non-Calculator
June 2014
Student Name:
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Name:
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Name:
KGV Mathematics Department
Y12 Test 1 Higher Level
1 hour
September the 17th
[60 Marks]
Instructions to Candidates:
This paper is non-calculator.
Section A:
answer all of section A in the spaces provided.
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answer

King George V School
Annual Speech Day Prizes List (2011-12)
Prize Name
Nominator Position
Criteria
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Ezra Abraham Scholarship Y9
Ezra Abraham Scholarship Y10
Ezra Abraham Scholarship Y11
Ezra Abraham Scholarship

Graphs of Functions
488 min
391 marks
1.
The graph represents the function
f: x p cos x, p
.
y
3
x
3
1
Find
(a)
the value of p;
(b)
the area of the shaded region.
Working:
Answers:
(a) .
(b) .
(Total 4 marks)
2.
The function f is given by
2x 1
F(x) = x 3

Arithmetic Series
72 min
56 marks
1.
The second term of an arithmetic sequence is 7. The sum of the first four terms of the arithmetic
sequence is 12. Find the first term, a, and the common difference, d, of the sequence.
Working:
Answers:
.
(Total 4 mark