 # AS Entrance Examination Sample Paper Mathematics Instructions

```Candidate Name: _______________________
Candidate Number: _______________________
Dulwich College International High School Programme Suzhou
AS Entrance Examination Sample Paper
Mathematics
Date:
Time: 1 hour
Instructions
1. Do not open this examination booklet until you are told to do so.
2. Answer all the questions in Section A and B.
3. All the answers and solutions need to be filled in answer sheets.
4. Unless otherwise stated in the question, all numerical answers
must be given exactly or to three significant figures.
5. This examination booklet comprises the cover page and 3 pages
of questions.
6. The total number of marks for this paper is 60.
Section A: Filled-in questions.
into the corresponding spaces on the answer sheet. The total number of marks is 48.
1.
Find the sum of the arithmetic series
17 + 27 + 37 +...+ 417.
2x
2.
Solve the equation 9x–1 =  1 
 3
3.
 P 
 in terms of x , y and z.
Let log10P = x , log10Q = y and log10R = z. Express log10 
3 
 QR 
4.
The first three terms of an arithmetic sequence are 7, 9.5, 12.
.
2
5.
6.
(a)
What is the 41st term of the sequence?
(b)
What is the sum of the first 101 terms of the sequence?
Solve the equation log9 81 + log9
1
+ log9 3 = log9 x
9
The number of hours of sleep of 21 students are shown in the frequency table below
Hours of sleep
Number of students
4
2
5
5
6
4
7
3
8
4
10
2
12
1
Find
(a)
the median;
(b)
the lower quartile;
(c)
the interquartile range.
1
7.
Three of the following diagrams I, II, III, IV represent the graphs of
(a)
y = 3 + cos 2x
(b)
y = 3 cos(x + 2)
(c) y = 2 cos x + 3.
Identify which diagram represents which graph.
y
I
y
II
4
2
1
2

? ?

–
?
x

? ?

–

?



?

3

5
2
4
1
–
x

?

y
IV

? ?


x

?

?
y
III

?

3

?


x

?

2
1
–
?
8.
9.

? ?


?

Consider the function f(x) = 2x2 – 8x + 5.
(a)
Express f(x) in the form a (x – p)2 + q, where a, p, q 
(b)
Find the minimum value of f(x).
.
The equation x2 – 2kx + 1 = 0 has two distinct real roots. Find the set of all possible values of k.
2
10.
A triangle has sides of length 4, 5, 7 units. Find, to the nearest tenth of a degree, the size of the
largest angle.
11.
If A is an obtuse angle in a triangle and sin A = 5 , calculate the exact value of sin 2A.
13
12.
ABCD is a rectangle and O is the midpoint of [AB].
D
A
C
O
B
Express each of the following vectors in terms of OC and OD
(a)
CD
(b)
OA
(c)
Section B: Written response.
Note: In this section, working MUST be shown. Please write down your full solutions on the
answer sheet provided. Without showing your working, no credit will be offered even though your
final answer is correct. The total number of marks is 12.
1.
Given that sin   cos   15 , is acute angle, evaluate sin   cos , sin   cos , tan
3
``` # 6.4 Solving Trigonometric Equations Using Identities: Warm # Embry-Riddle Aeronautical University Jacobs MA 243 Final Examination (Sample)   