# Ujian Matematik Tambahan

Topics: Arithmetic mean, Standard deviation, Arc Pages: 6 (862 words) Published: March 22, 2013
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. 6 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 Arc length, s = r θ 7. Area of sector , A=
1 2 r θ 2

2

x =
σ =

∑ 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

σ=

∑ 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) ……………………… (b) ………………………

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 ……………………... 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 ]

Answer ……………………... 4. The mean of the set of numbers 2.5, 3.6, 4.3, 5.8, x is 4.2 . Find the standard deviation of the set of data. Give your answer correct to three decimal places [3 marks]

Answer…………………….. ________________________________________________________________________ 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 :………………………………… __________________________________________________________________________ _ 6 (a) Convert 231 o 11 ' to radian (b) Convert 1.455 to degree and minutes [ 2 marks ]

Answer ……………………... 7 Diagram 1 shows a sector AOB with centre O . A
5c m

O

5c m

B

DIAGRAM 1
Find the area of the shaded segment

[ 4 marks]

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 :…………………………… 9 Diagram 3 shows two arcs, AD and BC, for two circle with centre O and radius OA and OB respectively.

12 cm

θ 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) θ, in radian b) the are of the shaded region ABCD. [4 marks]

Answer ………………………………… __________________________________________________________________________ _ 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

B

O

D θ...