1 霹雳怡保培南独立中学 SEKOLAH MENENGAH POI LAM (SUWA) IPOH SECOND MONTHLY TEST 2021 SUBJECT: MATHEMATICS TIME: 1405-1535 (1 HOUR 30 MINUTES） DATE: 3-8-2021 (TUESDAY) MARK NAME : ____________________________ STUDENT NO.: _____________ CLASS : S1YI, S1PIN ____________________________________________________________________ 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. Shade the region in each of the Venn diagrams below. (a) A ∩ B ’ [2] ____________________________________________________________________ This paper consists of 8 printed pages including cover page. Prepared by : Checked by： ………………….. …………………… (Mr.Ong Eik Hooi) (Ms.Ling Soon Ching) ONG Eik Hooi Ling Soon Ching
2 Shade the region in each of the Venn diagrams below. (b) C ’ ∪ D [2] (c) (E ∩ F)′ ∩ G [2]
3 2. Use the Diagram I to answer the following questions. Diagram I (a) State whether each of the following statements is True (T) or False (F). (i) 7 ∈ P, [1] (ii) 1 ∉ Q, [1] (iii) { 7 , 14 } ⊆ Q. [1] (b) List the elements in set P. [1] (c) Describe in words the elements of the set Q. [1] (d) List the elements contained in the set P ’ ∩ Q. [1] (e) Find the values of n (P ’ ∪ Q). [1]
4 3. ξ = { x : x is an integer such that 1≤x ≤12}. A ={ x : x is a prime number } B = { x : x is a multiple of 3} C = { x : x is a factor of 12} (a) Complete the Venn diagram to illustrate the information given. [3] (b) List the element(s) of the set (i) C, [1] (ii) A ∩ C, [1] (iii) B ’∩ C. [1] (c) Find the value(s) of (i) n ( A ∪ B ∪ C )’, [1] (ii) n ( A ∪ C ’ ) . [1]
5 4. The Diagram II shows a universal set ξ, the sets A and B and the elements in them. Diagram II (a) List the elements in the sets (i) A ∪ B ’ , [1] (ii) A ’∩ B ’ , [1] (iii) A∩ B ’ . [1] (b) Write down the relation between set A and set B in the set notation form. [1] 5. A football team plays two matches. The tree diagram shows the probability of the team winning or losing the matches. Find the probability that the football team wins at least one of the two matches. [3]
6 6. Box A contains five cards numbered 1, 2, 4, 5 and 8. Box B contains four cards numbered 3, 5, 7 and 9. One card is drawn from Box A and another card is drawn from Box B. The product of the numbers on the two cards are calculated and displayed in the possibility diagram. (a) Complete the possibility diagram. [4] (b) Hence, calculate the probability that the product of the two numbers (i) consists of two digits, [1] (ii) is exactly divisible by 4, [1] (iii) is a perfect square. [1] 7. A bag contains 8 red balls, 12 blue balls and x yellow balls. (a) If a ball is drawn at random, the probability that it is yellow ball is 2 7 . Find the value of x. [2] (b) Two balls are drawn at random from the bag, one after another without replacement. Find the probability that (i) both balls are red, [1] (ii) at least one ball is yellow. [2] × 1 2 4 5 8 3 5 7 9 Box A Box B
7 8. In a game, a die and 2 boxes of coloured chips are used. The die is numbered 1, 2, 3, 4, 5 and 6. Box A contains 3 black chips, 4 white chips and 3 green chips. Box B contains 2 black chips, 5 white chips and 3 red chips. If a player throws a number which is divisible by 3, he draws a chip from Box A. Otherwise the player draws chip from Box B. (a) Complete the probability tree diagram. [6] (b) Hence, find the probability that (i) a black chip is drawn, [2] (ii) a red or green chip is drawn. [2]
8 9. Diagram III A wheel is divided into ten sectors numbered 1 to 10 as shown in the Diagram III. The sectors 7, 8, 9 and 10 are shaded. The wheel is spun and when it stops the fixed arrow points to one of the sectors. (Each sector is equally likely.) (a) The wheel is spun once so that one sector is selected. Find the probability that (i) the number in the sector is even, [1] (ii) the sector is shaded, [1] (iii) the number is odd or the sector is shaded, [1] (iv) the number is even and the sector is shaded. [1] (b) The wheel is spun twice so that each time a sector is selected. Find the probability that (i) both sectors are shaded, [2] (ii) one sector is shaded and one is not, [2] (iii) the sum of the numbers in the two sectors is equal to 18. [2] --------------------------------------------End of Question Paper---------------------------------------- 2 3 4 1 10 9 8 5 6 7
