# AS Entrance Examination Sample Paper Mathematics Instructions

## Transcription

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. Note: In this section, you do NOT need to show your working. Please fill in your final answers 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 AD (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