Ujian Matematik Tambahan

Sekolah Menengah Sains Muzaffar Syah Melaka 75450 Air Keroh Melaka Ujian 2 2007 Additional Mathematics Form 4 Time : 75 Minuets INFORMATION FOR CANDIDATES 1 This question booklet consists of three parts, Section A and Section B. and Section C Answer All Question in Section A and B and two Question of section C 2 Give only one answer/ solution to each question. 3 Show your working . It may help you to get marks. 4 The figures/diagrams given in a problem in this question booklet would provide useful information to solve the problem. However, it might not be drawn to scale. 5 Write the answer in the answer sheets provided. All solution methods must be clearly shown. You may loose marks if important working steps are not properly shown. 7 The marks for each question or part-question are shown in brackets. 8 You may use a non- programmable scientific calculator. The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used . 1 x = ?x N 6 Ar c length, s = r ? 7. Area of sector , A= 1 2 r ? 2 2 x = ? = ? fx ? f ? (x ? x ) N 2 8. = y=uv, 3 ?x N 2 dy dv du =u +v dx dx dx ?x 2 9 2 4 ?= ? f ( x ? x) ? f = ? fx ? f 2 ?x 2 du dv v ? u u y = , dx = dx 2 dx , v dy v dy dy du = ? dx du dx 10 5 ?1 ? ?2N? F? M = L+? C ? fm ? ? ? ? ? Section A 1 Answer all questions The mean of x+ 3, 2x – 5, x + 7, x and 3x + 7, is 12 . Find (a) the value of x (b) median [ 4 marks ] Answer : (a) †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ (b) †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 2. A set of examination marks a1 , a2, a 3, a 4, a5, a6, has a mean of 5 and standard deviation of 1. 5 Find (i) the sum of the marks, ? a , (ii) the sum of the squares of the marks, ?a 2 [ 3 marks ] Answer †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 3. The mean of a set of four positive integers is 6. When a number y is taken out from the set, the mean becomes 5. Find the value of y. [ 3 marks ] Answe r †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 4. The mean of the set of numbers 2. 5, 3. 6, 4. 3, 5. 8, x is 4. . Find the standard deviation of the set of data. Give your answer correct to three decimal places [3 marks] Answer†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. ________________________________________________________________________ 5 Marks Number of student 1 -20 2 21 – 40 1 41- 60 5 61 – 80 14 81 – 100 8 Table above shows the marks obtained by a group of students I a monthly test. Find the standard deviation of the marks. Give your answer correct to two decimal places. [ 4 marks ] Answer :†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ __________________________________________________________________________ _ 6 (a) Convert 231 o 11 ‘ to radian (b) Convert 1. 455 to degree and minutes [ 2 marks ]Answer †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 7 Diagram 1 shows a sector AOB with centre O . A 5c m O 0. 5 rad 5c m B DIAGRAM 1 Find the area of the shaded segment [ 4 marks] Answer :†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 8 r A O 63 o B Diagram 2 shows a circle with centre O. Given that the length of the major arc AB is 62. 21 cm, find the length of the radius, r , in cm. [3 marks ] DIAGRAM 2 Answer :†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 9 Diagram 3 shows two arcs, AD and BC, for two circle with centre O and radius OA and OB respectively. 12 cm ? 10 cm 10 cm DIAGRAM 3 Given that the length of arc BC is 12 cm , OD is 10 cm and OD : DC = 5 : 2 Find , a) ? , in radian b) the are of the shaded region ABCD. 4 marks] Answer †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ __________________________________________________________________________ _ Section B Answer two question only [ 20 marks ] 1 Table 1 shows the marks of 80 students in an examination. Marks No of Students 50 – 59 8 60 – 69 25 TABLE 1 (a) Calculate the mean marks of the student. [ 3 marks ] 70 – 79 22 80 – 89 18 90 – 99 7 (b) Draw a histogram and estimate its mode [ 4 marks ] (c) Without drawing an ogive, calculate the median marks of the students [ 3 marks ] 2 Diagram 4 shows sector AOB and sector OED with centre O and E respectively . OCE is a right angle triangle. A cm C BO D ? RAJAH 6 E Given that ? AOB is 500 , OA = 10 cm , OE = 8 cm and OB : BC = 2 : 1. Calculate (a) (b) (c) ? and radian, [2 marks] perimeter of the shaded region in cm, [4 marks] area of the shaded region in cm2. [4 marks] 3 a) Find the value of 4 3 i) limit x ? 3x + 2 x x>4 x 2 ? 64 ii) limit n >8 x ? 8 [3 marks] b) Find dy of y = 3Ãâ€"2 by using first principle dx [2 marks] c) Differentiate the following with respect to x 1 i) y = x + ? 5 ii) y = 2Ãâ€"3 ( 3x -5)4 x 128 d) Given that f(x) = 2x – 3 find f ? (2 ) x [ 3 marks ] [ 2 marks ] END OF QUESTION PAPER Prepared By †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. Pn Saripah Ahmad Approved by,