102660015-15-Days-Programme-Part-3

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 the value 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 defined by . Calculate the mean of the 7 numbers.

QUESTION 4 A set of data , which consists of 5 numbers, is defined by . 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 mean of . Given that the sum of the numbers is 480, find the value of

QUESTION 8 A set of positive integers consists of and . Given that the mean for the set of data is 9, find the value of

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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 the value 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 40 and the sum of the squares 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 mean of 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 the new 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

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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 a variance of 35 and it is given that . Find (a) the mean, (b) the value of

QUESTION 3

The mean of five numbers is . The sum of the squares of the numbers is 120 and the standard deviation is . Express in terms of .

QUESTION 4

The mean of six numbers is . The sum of the squares 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 56 and the sum of the squares of the numbers is 720. Find, for the eight numbers (a) the mean (b) the standard deviation

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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 the set of data are 24 and 6 respectively. Given a second set of data , find for the second data (a) the mean (b) the standard deviation

QUESTION 6 Given that the mean and the standard deviation of the set of data are 12 and 8 respectively. Given a second set of data , find for the second 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 2 respectively. Find the median and variance for the set of numbers .

QUESTION 8 The scores, , obtained by 50 students in a test has a mean of 65 and a standard deviation of 8. (a) Find the sum of the scores, and the 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.

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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 students

12 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

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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.

Score Number of students 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 the value 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

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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.

Score Number of students 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 <60 <70 No. of students

5 14 34 65 88 96 100

Table 4 shows the time taken by 100 students to reach their school. (a) Based on Table 4, copy and complete the table below.

Time 0-9 10-19 20-29 30-39 40-49 50-59 60-69

No. of students

(b) Without drawing an ogive, find the interquartile range of the distribution.

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DAY 08 : CIRCULAR MEASURE QUESTION 1

Diagram 1 shows a sector AOB of a circle with centre O. Given that and OD= 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 perpendicular to 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

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

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 given that . OA = AB = OD = DC = 4cm. Find (a) the length, in cm, of arc BC

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

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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 of the 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 shows a 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 a major sector OPQ of a circle with centre O and angle 297 . If the length 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

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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 Diagram 2 shows a sector AOB of a circle with centre O. Given and the length of chord AB is 16 cm. Find (a) the radius, in cm, of the sector. (b) the area, in cm2, of the sector. .[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 Diagram 4 shows a circle 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 Diagram 5 shows a circle 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 Diagram 6 shows a circle 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 ]

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DAY 11 : CIRCULAR MEASURE 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 length of 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 ].

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Diagram 1 shows a circle 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 . Given that 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

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Diagram 1 shows a circular sector OAC with centre O and radius of 4 cm and

. AB is an arc of a circle with 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 (c) the area, in cm2, of the shaded region

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DAY 14 : CIRCULAR MEASURE 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 cm and 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 and BCD 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

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Diagram 3 shows a semicircle OPST with centre O inscribes in a triangle PQR. Line PQ and line RQ are both tangents to the circle with centre O at points P and S respectively. Given that PQ = 12 cm and , by

using (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 Diagram 4 shows a sector 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,

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

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Date post:	27-Oct-2014
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102660015-15-Days-Programme-Part-3

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