1 霹雳怡保培南独立中学 SEKOLAH MENENGAH POI LAM (SUWA) IPOH SECOND MONTHLY TEST 2021 SUBJECT: ADDITIONAL MATHEMATICS TIME: 1405 - 1535 (1 HOUR 30 MINUTES） DATE: 4-8-2021 (WEDNESDAY) MARK NAME : ____________________________ STUDENT NO.: _____________ CLASS : S1AI , SIZI ____________________________________________________________________ INSTRUCTIONS: • Answer all the questions. • Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. • Write your name, student number and class on all the work you hand in. • Write your answers on the separate writing paper. • You should use a calculator where appropriate. • Omission of essential working will result in the loss of marks. • At the end of the examination, fasten all your work securely together. • The number of marks for each question or part question is shown in brackets [ ]. • The total mark for this paper is 60. 1. (a) Find the number of four-letter codes that can be formed from the letters in the word MICROWAVES if no letters can be repeated. [1] (b) Hence, how many of these codes start with a vowel? [2] 2. An entrance test to a private school contains 6 questions in Part A and 7 questions in Part B. Each candidate needs to answer 10 questions, of which at least 4 questions are from Part A. Find the number of ways a candidate can answer these 10 questions. [4] ___________________________________________________________________ This paper consists of 3 printed pages including cover page. Prepared by : Checked by： ………………….. …………………… (Mr.Ong Eik Hooi) (Ms.Ling Soon Ching) ONG Eik Hooi Ling Soon Ching
2 3. A textile shop sells certain fabric shirts in four sizes, namely S, M, L and XL. If the stocks available in the store are arranged in a line on a shelf. There are 3 of size S, 4 of size M, 4 of size L and 1 of size XL. (a) How many possible arrangements are there if (i) there are no restrictions, [1] (ii) the first fabric shirt is of a size S and the last fabric shirt is of a size XL, [2] (iii) all the fabric shirt of size M are next to each other. [2] (b) Four pieces of this certain fabric shirts are to be selected by Mr. John for his four daughters. Find the number of different possible selections if (i) no fabric shirt of a size M is chosen, [2] (ii) one of each type of fabric shirt (size S, M, L, and XL) is chosen. [2] 4. (a) Find the first three terms, in ascending powers of y, in the expansion (2 + ) 5 . [3] (b) Hence, find the coefficient of 2 in the expansion of (2 + 3 − 4 2 ) 5 . [2] 5. (a) Find the coefficient of 3 in the expansion of (3 + 4) 4 . [2] (b) Find the coefficient of in the expansion of ( − 3 ) 5 . [3] 6. The progression is 9,13,17, x, …, 97. (a) Identify whether this sequence is arithmetic progression or geometric progression. [1] (b) Write down the value of x? [1] (c) Find the number of terms in this progression. [2] (d) Find the sum of this progression. [2] 7. The first four terms of a geometric progression are 5, 4, 3.2 and 2.56. (a) Write down the common ratio. [1] (b) Find the sum of first 20th term in this progression, leaving your answer correct to 3 significant figures. [3]
3 8. The fourth term of an arithmetic progression is 7 and the tenth term is 16. Find the first term, a and the common difference, r. [4] 9. The third and fourth terms of geometric progression are 1 3 and 2 9 respectively. Find the first term of this progression and the positive common ratio of this progression. Hence, find the sum to infinity of this progression. [4] 10. Differentiate each of the following with respect to x. (a) 7 − 2 3 + 4 [2] (b) (2 − 3) 8 [2] (c) ( + 2)√ [3] (d) 2 5−2 [3] 11. Given that a curve has equation = 2 + 16 , where x > 0, find (a) d d , [2] (b) d 2 d 2 . [2] Hence or otherwise, find (c) the coordinate and nature of the stationary point on the curve. [2] -----------------------------------End of Question Paper-------------------------------
