1 霹雳怡保培南独立中学 SM POI LAM (SUWA) IPOH SECOND MONTHLY TEST 2021 MATHEMATICS DATE: TIME : 02 AUGUST 2021 (Monday) 1405-1535 (1 Hour 30 Minutes) NAME：______________________ REG NO:_________________ CLASS: S2ZI / S2XIN INSTRUCTIONS • Answer all the questions. • Write your name and student registration number in the boxes at the top of the page. • Use a black or dark blue pen. • You may use an HB pencil for any diagrams or graphs. • Do not use an erasable pen or correction fluid. • All answers are to be written on the both sides of the writing paper. • You must show all necessary working clearly. Omission of essential working will result in loss of mark. • You should use a calculator where appropriate. INFORMATION • The total mark for this paper is 60. • The number of marks for each question or part question is shown in brackets [ ]. Do Not Turn Over This Page Until You Are Told To Do So This paper consists of 10 printed pages including cover page. Prepared by ： ONG EIK HOOI ……………………… (MR. ONG EIK HOOI) Checked by： LING SOON CHING ……………………………… (MS. LING SOON CHING) For Examiner Used Section Question Full Mark Mark Obtained A 1 − 20 40 B 21 5 22 4 23 2 24 4 25 5 Total 60
2 Section A [40 marks] Answer all questions in this section. 1 Express 2110 as a number in base four. A 414 B 314 C 1014 D 1114 2 Given that 11112 + 2 = 1010112, find the value of . A 10100 B 11100 C 100100 D 111101 3 Given that 22315 = 2(5) 3 + (5) 2 + 3(5) + 1, find the value of − . A 1 B 2 C 3 D 4 4 What is the digit value of digit 7, in base ten, in the number 7654008? A 229376 B 28672 C 3584 D 56
3 5 Which of the following is not a statement? A Add 4 to 7 and multiply the sum by 3. B Malaysia is a continent. C 2 5 is greater than 3 5 . D −3 is prime number. 6 Ms. Jane Irene plants 100 roses in her garden. 1 5 of them are yellow roses, 1 4 of them are red roses and the remaining are white roses. What is the number of white roses, in base four? A 3114 B 3124 C 3134 D 554 7 Calculate the sum of 10101112 and 101012 in base seven. A 1537 B 2137 C 2237 D 3137 8 3 > , ∈ R Which of the following is not the counter-example of the statement above? A = 1 2 B = 1 C = 2 D = −3
4 9 Which pair of statement and its negation is incorrect? Statement(p) Negation (~p) A All perfect squares are even numbers. Not all perfect squares are even numbers. B { } is a proper subset of {, , }. { }is not a proper subset of {, , }. C 16 is divisible by 4. 4 is not divisible by 16. D − 1 7 is greater than − 1 8 . − 1 7 is not greater than − 1 8 . 10 Premis 1 : If > 3, then 3 > 9. Premis 2 : 5 > 3. What is the conclusion of above premises to form a valid argument? A 9 > 3 B 15 > 3 C 15 > 9 D 3 < 9 11 Complete premise 1 to form a valid argument. Premise 1 : …………………………………… Premise 2 : ≠ 5 Conclusion : 3 ≠ 125 A If = 5, then 3 = 125. B If √ 3 = 5, then = 125. C If 3 = 125, then = 5. D If = 125, then √ 3 = 5. 12 Which of the following graphs with degrees of vertices can be drawn? A 3, 4, 4, 5, 5 B 3, 4, 5, 4, 2 C 3, 3, 5, 1, 5 D 1, 1, 3, 3, 5
5 13 Given number sequence 1, 10, 25, 46, … 1 = 3(1 2 ) − 2 10 = 3(2 2 ) − 2 25 = 3(3 2 ) − 2 46 = 3(4 2 ) − 2 … Form a strong inductive conclusion of the number sequence above. A 2 , = 1,2,3,4, … B 3 2 , = 1,2,3,4, … C 3 2 − 2 , = 1,2,3,4, … D 3 − 2 , = 1,2,3,4, … 14 The diagram below shows a graph such that the weight is distance, in km. Find the shortest path from A to E. A A → B → E B A → → → C A → B → D → E D A → D → E
6 15 The diagram below shows a network. Which of the following is true? A = { ,, , , ,, } B = {(,), (, ), (, ), (, ), (, ), (,), (, ), (, )} C () = 6 D Sum of degrees = 14 16 Diagram below is the Venn Diagram with the universal set, ξ = A ∪ B ∪ . Which one represented by the shaded region? A ( ∪ ) ′ ∩ B ∩ ( ∩ ) ′ C ∪ ∩ ′ D ( ∪ ′ ) ′ ∩
7 17 The Venn diagram shows the number of elements in sets X, V and W. It is given that ξ = X ∪ V ∪ W and n(ξ) = 56. Determine the value of k. A 2 B 4 C 6 D 8 18 Given that the universal set, ξ = X ∪ Y ∪ , ∩ = and = ( ∪ ) ′ . Which of the following Venn Diagram show correct relationship? A B C D
8 19 A total of 100 children need to choose their favourite food from burger, salad and nasi lemak. 50 children choose burger, 60 children choose nasi lemak, 5 children choose burger and salad, 3 children choose nasi lemak and salad, and 22 children choose burger and nasi lemak. If only one child chooses all the three types of food, calculate the number of children who choose salad only. A 10 B 11 C 12 D 13 20 The diagram below shows a network. What is the degree of vertex F ? A 1 B 2 C 3 D 4
9 Section B [20 marks] Answer all questions in this section. 21. Diagram I show part of the graph of the quadratic function where () = ( − )( − ) where < . Point P is the minimum point of the graph of the quadratic function. (a) Calculate the value of i. , ii. , iii. . (b) Determine the equation of the axis of symmetry. (c) State the coordinates of the point P. [ 5 marks] 22. (a) Calculate the value of the following. i. 1407 + 3027 = ii. 2759 − 2189 = (b) Fill in the blank with numbers in ascending order according to 638 , 1101002 , 110101 2 , 110110 2 , 678 [ 4 marks] 23. Shade the region in the Venn diagrams below. (A ∪ B) ’ [ 2 marks] Diagram I
10 24. (a) State whether the following statement is True or False. The sum of interior angles of a square is 360o . (b) Write down two implications based on the following statement. is a root of 3 − 1 = 0 if and only if = 1. (c) Write down Premise 2 to complete the following argument. Premise 1 : If is an odd number, then k +1 is an even number. Premise 2 : Conclusion : 9 is an odd numbers. [ 4 marks] 25. (a) Diagram II show a graph with a loop and multiple edges. State i. V and n (V) ii. E and n (E) iii. Sum of degrees (b) Draw a graph based on the given information. = {1 , 2 , 3 , 4 } = { (1,2), (1,3), (1,3), (2,2), (2,3), (3,4), (4,4)} [ 5 marks] --------------------------------------End of Question Paper---------------------------------- Diagram II