JOM TANYA SIFU
15 Days Programme : Part 3
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 is 6. Find the value of
QUESTION 6 A set of five numbers has a mean of 9. Find
and
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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JOM TANYA SIFU
15 Days Programme : Part 3
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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JOM TANYA SIFU
15 Days Programme : Part 3
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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JOM TANYA SIFU DAY 04: STATISTICS QUESTION 1 A set of data consists of and . Determine the interquartile range of the data.
15 Days Programme : Part 3
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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JOM TANYA SIFU
15 Days Programme : Part 3
DAY 05: STATISTICS QUESTION 1 Table 1 shows the marks acquired by a group of students in a competition. Marks No. of students
1- 5
6-10
11- 15
16- 20
21- 25
12
7
5
4
2
Find (a) the median mark (b) the standard deviation
QUESTION 2 Table 2 shows the distribution of scores o btained 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 Cumulative Wages 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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JOM TANYA SIFU 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.
15 Days Programme : Part 3
QUESTION 2 (use graph paper) Table 2 shows the frequency distribution of the masses, each to the nearest kg, of luggage collected at a n 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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JOM TANYA SIFU 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.
15 Days Programme : Part 3
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
QUESTION 4 Time < 10 < 20 < 30 < 40 < 50 <60 <70 No. of 5 14 34 65 88 96 100 students Table 4 shows the time taken by 100 students to reach their school. (a) Based on Table 4, copy and complete the table below. 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Time No. of students
(b) Without drawing an ogive, estimate the median score.
(b) Without drawing an ogive, find the interquartile range of the distribution.
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JOM TANYA SIFU
15 Days Programme : Part 3
DAY 08 : CIRCULAR MEASURE QUESTION 1
QUESTION 2
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 3
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 4
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 ]
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
]
QUESTION 6
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 ]
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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JOM TANYA SIFU
15 Days Programme : Part 3
DAY 09 : CIRCULAR MEASURE 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 of the sector.
QUESTION 3
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 4
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
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.
the sector.
QUESTION 5
QUESTION 6
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.
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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JOM TANYA SIFU
15 Days Programme : Part 3
DAY 10 : CIRCULAR MEASURE QUESTION 1 QUESTION 2 Diagram 1 shows a circle with centre O. Given that the length of the minor arc AB is 12.57 cm 2 , find the length, in cm, of the radius. (use
QUESTION 3
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 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 55cm 2, find (a) the value of , in radian (b) the length, in cm, of the radius[use ]
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 5
QUESTION 6
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 ]
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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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JOM TANYA SIFU 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 2 (c) the area, in cm , of the shaded region. [use ]
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15 Days Programme : Part 3
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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JOM TANYA SIFU DAY 12 : CIRCULAR MEASURE QUESTION 1 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.
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15 Days Programme : Part 3
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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JOM TANYA SIFU DAY 13 : CIRCULAR MEASURE QUESTION 1 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
15 Days Programme : Part 3
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
(b) the length, in cm, of the radius BC (c) , in radian (d) the area, in cm2, of the shaded region
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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JOM TANYA SIFU 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.
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15 Days Programme : Part 3
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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JOM TANYA SIFU
15 Days Programme : Part 3
DAY 15 : CIRCULAR MEASURE QUESTION 1
QUESTION 2
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
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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, 2 (c) the area, in cm , of the shaded region
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