15 Days Programme_Part 3

7/31/2019 15 Days Programme_Part 3

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JOM TANYA SIFU 15 Days Programme : Part 3

Prepared by : Pn Hayati Aini Ahmad Page 1

DAY 01 : STATISTICS

QUESTION 1

A set of numbers has a mean of 6.Given that the sum of the numbers is 42, find thevalue of

QUESTION 2

A set of data consists of 9 numbers. Given the sum of

the numbers is 108, find the mean of the 9 numbers.

QUESTION 3

A set of data, which consists of 7 numbers, is definedby . Calculate the mean of the 7 numbers.

QUESTION 4

A set of data, which consists of 5 numbers, is definedby . Calculate the mean of the 5 numbers.

QUESTION 5

Given that the mean of the set of data and is 6. Find the value of

QUESTION 6

A set of five numbers has a mean of 9. Find

QUESTION 7

A set of data which consists of 12 numbers has a meanof. Given that the sum of the numbers is 480, find thevalue of

QUESTION 8

A set of positive integers consists of and. Given that the mean for the set of data is 9, find thevalue of

Date of completion: Checked by:


2/15



DAY 02: STATISTICS

QUESTION 1

A set of six numbers has a mean of 8.

(a) Find (b) When a number is removed from this set, the new

mean is 9. Find the value of

QUESTION 2

A set of five numbers has a mean of 9. When a number

is taken out of this set, the new mean is 8.5. Find thevalue of.

QUESTION 3

A set of six numbers has a mean of 9 and a variance of

3. When a number, k is added to this set, the mean

remains unchanged.

(a) Find the value of k

(b) Calculate the new variance

QUESTION 4

A set of data consists of five numbers. The sum of the

numbers is 62 and the sum of the squares of the

numbers is 786. The two new numbers, 9 and 13, are

added to the set of data. Find,

(a) the new mean (b) the new standard deviation

QUESTION 5

A set of data consists of five numbers. The sum of the


numbers is 356.

(a) Find the mean and the variance for the five

numbers.(b) When a number is added to this set, the mean is

unchanged. Hence, find the variance of this new set

of data.

QUESTION 6

A set of eight numbers, has a meanof 3.5.

(a) Find (b) A second set of six numbers with a mean of 4 is

added to this first set of eight numbers. Find thenew mean of this combined set of numbers.

QUESTION 7

The mean of a set of numbers, and , is 5.5. Find(a) the value of k

(b) the new mean if each of the numbers is decreased

by 2 and then multiplied by 7

QUESTION 8

A set of data consists of nine numbers. The sum of the

numbers is 108.

(a) Find the mean for the nine numbers

(b) Find the new mean of the set of data if every value

in the set is increased by 2



3/15



DAY 03: STATISTICS

QUESTION 1

A set of positive integers consists of and. Given that the mean for the set of data is . Find(a) the value of (b) the variance for the set of data

QUESTION 2

A set of eight number , has avariance of 35 and it is given that . Find(a) the mean, (b) the value of

QUESTION 3The mean of five numbers is . The sum of thesquares of the numbers is 120 and the standard

deviation is . Express in terms of.

QUESTION 4The mean of six numbers is . The sum of thesquares of the numbers is 150 and the variance is .Express in terms of.

QUESTION 5

The standard deviation of five numbers is 2 and the

sum of squares of these numbers is 145. Find the mean

of these numbers

QUESTION 6

A set of data consists of eight numbers. The sum of the


numbers is 720. Find, for the eight numbers

(a) the mean (b) the standard deviation



4/15



DAY 04: STATISTICS

QUESTION 1

A set of data consists of and .Determine the interquartile range of the data.

QUESTION 2

A set of data consists of 40, 68, 72, 78, 84 and 90.

Determine the interquartile range of the data.

QUESTION 3

A set of data consists of . Find(a) the mean

(b) the standard deviation of the set above

QUESTION 4

Given a set of numbers 7, 12, 15, 19 and 20, find the

standard deviation of the numbers.

QUESTION 5

Given that the mean and the standard deviation of theset of data are 24 and 6respectively. Given a second set of data

, find for thesecond data

(a) the mean (b) the standard deviation

QUESTION 6

Given that the mean and the standard deviation of theset of data are 12 and 8respectively. Given a second set of data

, find for thesecond data

(a) the mean (b) the variance

QUESTION 7

Given that the median and the standard deviation of

the set of data are 5 and 2respectively. Find the median and variance for the set

of numbers .

QUESTION 8

The scores, , obtained by 50 students in a test has amean of 65 and a standard deviation of 8.

(a) Find the sum of the scores, andthe sum of the squares of the scores, .

(b) An error occurred in the calculation of scores

obtained by students where an additional of 3

marks is wrongly added to each score obtained by

the students. Calculate the corrected mean and the

standard deviation.



5/15



DAY 05: STATISTICS

QUESTION 1

Table 1 shows the marks acquired by a group of students

in a competition.Marks 1- 5 6-10 11- 15 16- 20 21- 25

No. of

students12 7 5 4 2

Find (a) the median mark (b) the standard deviation

QUESTION 2

Table 2 shows the distribution of scores obtained by 10

students in a Mathematics quiz.

Score Number of students

1 - 3 2

4 - 6 3

7 - 9 4

10 - 12 1

Find the interquartile score.

QUESTION 3

Table 3 shows the cumulative frequency distribution of

the daily wages of 40 workers in a factory.

Daily

Wages

Cumulative

frequency

20 24 8

25

29 14

30 34 23

35 - 39 31

40 44 36

45 - 49 40

Find (a) the mean wage (b) the standard deviation

QUESTION 4

Table 4 shows the marks obtained by a group of students

in a test.

Marks Frequency

10 - 19 4

20 29 9

30

39 12

40 - 49 6

50 - 59 5

Find (a) the median mark (b) the variance



6/15



DAY 06: STATISTICS

QUESTION 1 (Use graph paper)

Table 1 shows the frequency distribution of the Biology

scores obtained by 80 Form Five students in an

examination.


11 - 20 6

21 - 30 8

31 - 40 12

41 - 50 15

51 - 60 10

61 - 70 18

71 - 80 11

Using a scale of 2 cm to 10 scores on the horizontal axis

and 2 cm to 2 students on the vertical axis, draw a

histogram. Hence, find the mode score.

QUESTION 2 (use graph paper)

Table 2 shows the frequency distribution of the masses,

each to the nearest kg, of luggage collected at an airport.

Mass(kg) No. of luggages

20 - 24 18

25 - 29 22

30 - 34 29

35 - 39 40 - 44 25

(a) The mean mass of the luggage was 32.75 kg. Find thevalue of.

(b) Calculate the median mass of the luggages

(c) Draw a histogram to represent the data in Table 4

and estimate the mode mass of this distribution

QUESTION 3

The marks obtained by a group of students in a test is

shown in Table 3. The mean mark of the students is

48.25. Calculate

Marks Number of students

20 - 29 8

30 39 15

40 - 49 22

50 - 59 60 - 69 10

70 - 79 8

(a) the value of (b) the median of the marks

QUESTION 4

Table 4 shows the frequency distribution of the age of a

group of residents in a town. Given the mean age if the

group is 50.25. Calculate

Age(Years) Number of residents

30 39 12

40 49 50

59 30

60 - 69 14

(a) the value of (b) the median age of the group



7/15



DAY 07 : STATISTICS

QUESTION 1

Table 1 shows the frequency distribution of the scores

obtained by 25 students in a game. It is given that the

median score is 35.5.


1 10 2

11

20 3

21 30 5

31 40 41 50 51 - 60 4

(a) Find the value of and of(b) Hence, calculate the mean score.

QUESTION 2

Table 2 shows the frequency distribution of the lifespans of a

type of batteries.

Lifespan(hours) No. of batteries

12 - 19 3

20 - 27 28 - 35 10

36 - 43 16

44 - 51 14

52 - 59 9

(a) It is given that the median lifespan of the

distribution is 40 hours. Calculate the value of(b) Using a scale of 2 cm to 8 hours on the horizontal

axis and 2 cm to 2 batteries on the vertical axis,

draw a histogram to represent the frequency

distribution of the lifespans of the batteries. Find the

mode lifespan of the batteries

QUESTION 3

Score < 15 < 20 < 25 < 30 < 35

No. of students 3 10 15 26 30

Table 3 shows the scores obtained by a group of 30

students in a test.

(a) Based on Table 3, copy and complete the table

below.Hence, calculate the mean score.

Score 10-14 15-19 20-24 25-29 30-34

No. of

students

(b) Without drawing an ogive, estimate the median

score.

QUESTION 4

Time < 10 < 20 < 30 < 40 < 50


8/15



DAY 08 : CIRCULAR MEASURE

QUESTION 1

Diagram 1 shows a

sector AOB of a circle

with centre O. Given that

andOD= DA= OC= CB= 4 cm.

Find

(a) the length, in cm, of arc AB

(b) the area, in cm2, of the shaded region.[use ]

QUESTION 2

Diagram 2 shows a

sector OAB of a

circle with centre O

and radius 10 cm.

Given that and AC is perpendicularto OB. Find

(a) the length, in cm, of arc AB

(b) the area, in cm2, of the shaded region. .

[use ]

QUESTION 3

Diagram 3 shows a

sector OPQR of a circle

with centre O. Given the

radius of the sector is 8

cm. Find, the area, in

cm2, of the shaded

region.[use ]

QUESTION 4

Diagram 4 shows a

sector OPQ with

centre O and a

radius of 13 cm. Find

(a) the length, in cm,

of arc PQ


QUESTION 5

Diagram 5 shows two

sectors OEF and OKL with a

common centre O. Given

OE : EK =2 : 1 and arc

length of KL is 18 cm. Find

the area of the shaded

region, in cm2 .[use ]

QUESTION 6

Diagram 6 shows a

sector BOC of a circle

with centre O. It is giventhat . OA= AB = OD = DC = 4cm.

Find

(a) the length, in cm, of

arc BC




9/15




QUESTION 1

Diagram 1 shows a

sector OPQ of a circle

with centre O and

radius 14 cm. If the

length of the arc PQ is

24.6 cm, find the area ofthe sector.

QUESTION 2

Diagram 2 shows a sector

OPQ of a circle with centre

O and radius 8 cm. If the

length of the arc PQ is 9 cm,

find the area of the sector.

QUESTION 3

Diagram 3 showsa sector OPQ of a

circle with centre

O and angle 0.75

radian. If the

length of the arc

PQ is 20.96 cm,

find the area of

the sector.

QUESTION 4

Diagram 4 shows amajor sector OPQ of a

circle with centre O

and angle 297. If thelength of the major arc

PQ is 35 cm, find the

area of the sector.

QUESTION 5

A circle of radius 2.5 cm

has a minor sector with an

area of 6.25 cm2. Calculate

(a) the angle of the minor

sector in radians,

(b) the perimeter of the

major sector.

QUESTION 6

Diagram 6

shows a

semicircle

OPQR with

centre o. Given

that the length

of arc PQ is 6.4

cm, calculate

(a) the radius of sector OPQ

(b) the area of sector OQR



10/15




QUESTION 1

Diagram 1 shows a circle

with centre O. Given that

the length of the minor

arc AB is 12.57 cm2 , find

the length, in cm, of the

radius. (use

QUESTION 2


AOB of a circle with centreO. Given andthe length of chord AB is

16 cm. Find

(a) the radius, in cm, of thesector.

(b) the area, in cm2, of thesector. .[use ]

QUESTION 3

Diagram 3 shows two

sectors, OAB and OCD. AOD

and BOC are straight lines.

Given OA=3OD, find

(a) the length, in cm, of arc

CD

(b) the area, in cm2, of

sector OAB.

[use ]

QUESTION 4


with centre O. The length

of the minor arc PQ is 20

cm and the area of the

minor sector POQ is 55cm2,

find

(a) the value of, in radian(b) the length, in cm, of the

radius[use ]

QUESTION 5


with centre O. The length of

the major arc PQ is 34 cm

and the angle of minor

sector POQ is , find(a) the value of, in radian(b) the length, in cm, of the

radius[use ]

QUESTION 6


with centre O. The length

of the minor arc PQ is 12

cm and the angle of the

major sector POQ is .Find(a) the value of, in

radian

(b) the length, in cm, of

the radius

[use ]



11/15




QUESTION 1

Diagram 1 shows a

circle PQR with centre

O and a radius of 10 cm.

OABC is a sector with

centre O and a radius of

22 cm. Given the lengthof arc ABC is 35 cm.

Find(a) , in radians(b) the perimeter, in

cm, of the shaded

region

(c) the area, in cm2, of

the shaded region. [use ]

QUESTION 2

In Diagram 2, POQ is a sector of a circle with centre O

and a radius of 34 cm. TUQ is a semicircle with centre

V and a radius of 5 cm. It is given that S is the midpoint

of OP and OR = 15 cm. Calculate

(a) , in radians(b) the perimeter, in cm, of the shaded region

(c) the area, in cm2, of the shaded region

[use ].



12/15




QUESTION 1


PQRS with centre O and

radius 10 cm. PQTS is a

sector of a circle with

centre P that inscribed in

the circle PQRS. Calculate(a) the length, in cm, of

the arc QTS,

(b) the area, in cm2, of

the shaded region.

QUESTION 2

Diagram 2 shows a

trapezium ABCD

where line DPA is

parallel to line CB,

, CB = DP and . Giventhat PA = 6 cm and

P is the midpoint of

line DA, find

(a) the length of line AB, in cm

(b) the perimeter of the shaded region, in cm.

(c) the area of the shaded region, in cm2



13/15




QUESTION 1

Diagram 1 shows a

circular sector OAC

with centre O and

radius of 4 cm and

.AB is an arc of a circlewith centre C and BCO

is a straight line.[Use Calculate

(a) the length, in cm, of

arc AC

(b) the length, in cm, of the radius BC

(c) , in radian(d) the area, in cm2, of the shaded region

QUESTION 2

Diagram 2 shows a sector PQR of a circle with centre P

and radius 12 cm. RSQT is a circle with centre O. The

straight lines PQ and PR are tangents to the circle at

point Q and R respectively. [Use

Calculate

(a) the length, in cm, of radius OQ

(b) the length, in cm, of the arc QSR




14/15




QUESTION 1

Diagram 3 shows a

circle with centre O and

has a radius of 5 cm.

OBC is a sector of a

circle with centre O. It is

given that AD = 8 cmand the area of sector

OBC : the area of sector

OAD = 4 : 1. Calculate

[use ].

(a) the value of, in radian(b) the area, in cm2, of the sector OBC

(c) the perimeter, in cm, of the shaded region.

QUESTION 2

In Diagram 4, ABC and ACD are two right angled

triangles. ACE is a sector of a circle with centre A and

radius 4 cm. It is given that AB = 5 cm, ED = 3 cm andBCD is a straight line. Calculate [use ].(a) , in radian(b) the perimeter, in cm, of the shaded region

(c) the area, in cm2, of the unshaded region



15/15




QUESTION 1

Diagram 3 shows a

semicircle OPST with

centre O inscribes in a

triangle PQR. Line PQ

and line RQ are both

tangents to the circlewith centre O at points

P and S respectively.

Given that PQ = 12 cm

and , byusing (a) find , in radians(b) find the radius of the semicircle, in cm

(c) calculate the perimeter of the shaded region

(d) calculate the area of the shaded region

QUESTION 2


OACB with centre O and

radius 14 cm. EAB is a sector

with centre A. Arc BDE

intersects the straight line

OB at point D. Given that

. Calculate

[Use (a) the length, in cm, of

straight line AB,

(b) the perimeter, in cm, of

the shaded region,



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15 Days Programme_Part 3

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