Modul Revision

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Module Revision 2013

Form 4: Chap 6: Coordinate Geometry

A. Distance between A (x1, y1) and B (x2 , y2).

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B.

Example

3) Parallelogram

*

Midpoint of the diagonals is the same.

Find the mid-pt of the diagonal to proof the parallelogram.


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C. P divides AB internally in the ratio m:n

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D. Gradient

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E Area

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F.

G.

Exercise

PAPER 11. Given thatEFis a straight line such that the coordinates of the points E andFare (1, 4) and (5, 12)

respectively. Find the equation of the locus of a point that moves so that it is equidistant from point E

and pointF. [4 marks]

2 Find the equation of a moving point Q(x,y) which is equidistant from pointA(1, 2) and pointB(0, 3).

[4 marks]

3 Find the equation of the straight line that passes through the point P( 4, 1) and is parallel to the line

2 5 3 0x y [3 marks]

4 Given thatP(h, 3), Q(2, 1) andR (8, 1) are collinear. Find the value of h. [3 marks]


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5 Given that the pointPmoves so that its distance from the pointA(2, 3) is 4 units. Find the equation of

the locus of the pointA. [3 marks]

6 Given that PQR is a straight line and the coordinates of the points Pand Q are (1, 2) and (3, 1)

respectively. IfPQ: QR= 1 : 3, find the coordinates of the pointR.

[4 marks]

7 C is a point on the straight line that joins A(3, 6) and B(7, 1) such that 3AC = 2CB, find the

coordinates of the point C. [4 marks]

8 The coordinates of the three vertices of a triangle are (1, 5), (2b, a) and (2a,b). Given that a+ b= 0

and the area of the triangle is 18 unit2. Find the value of a and of b. [4 marks]

9 Find the equation of the straight line that passes through the point (1, 5) and is perpendicular to the

straight line that joins point (2, 6) and point (3, 8). [4 marks]

10 A(2h, h),B(p, t), and C(2p, 3t) are three points on a straight line.BdividesACinternally in the ratio 2 :

3. Expresspin terms of t. [4 marks]

11 Diagram 1 shows the straight lineABwhich is perpendicular to the straight line CBat the pointB.

DIAGRAM 1

The equation of the straight line CBis 2 1y x .

Find the coordinates ofB. [3 marks]

y

x

A(0, 4)

B

O

C


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PAPER 2

12 In Diagram 2, 90ABC , and the equation of the straight lineBC is 2 6 0y x .

(a) Find

(i) the equation of the straight lineAB,

(ii) the coordinates of pointB. [5 marks]

(b) The straight lineAB is extended to a pointDsuch thatAB:BD= 2 : 3.

Find the coordinates of the pointD. [2 marks]

(c) A point Pmoves such that its distance from point A is always 5 units. Find the equation of the

locus ofP. [3 marks]

13 Solution to this question by scale drawing will not be accepted.

Diagram 3 shows a parallelogram ABCD. The coordinates of points A, Band Care (4, 4), (2, 9)

and (4, 1) respectively. Find

(a) the coordinates the point of intersection of the diagonalsACandBD. [2 marks]

(b) the coordinates of the pointD. [2 marks]

(c) the area of the parallelogramABCD. [3 marks]

(d) the equation of the locus of a moving pointP, such that 3AP= 2CP. [3 marks]

y

DIAGRAM 3

A

B

C

D

x0

y

DIAGRAM 2

A (4, 9)

B

C

x0

2y+x+ 6 = 0


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14 Solution to this question by scale drawing will not be accepted.

Diagram 4 shows the triangleAOBwhere Ois the origin. Point Clies on the straight lineAB.

DIAGRAM 4

(a) Calculate the area, in unit2, of triangleAOB. [2 marks]

(b) Given thatAC: CB= 3 : 2, find the coordinates of C. [2 marks]

(c) A pointPmoves such that its distance from pointAis always twice its distance from pointB.

(i) Find the equation of the locus ofP.

(ii) Hence, determine whether or not this locus intersects they-axis. [6 marks]

x

y

A(3, 4)

O

B(6, 2)

C


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Chapter 7: Statistics

UNGROUPED DATA

GROUPED DATA

Without Class Interval With Class Interval

MEAN

(a) is the mean of the data.(b) is the summation of the data.(c) is the number of the data. (Bil. Data)

(a) f : frequency(b) x : valueof the data (c) f : frequency(d) x : mid-pointof the data

MODE

Value that has highest frequency.

Example:A set of integers consists of 20, 19, 17, 19, 15, 16,

16, and 19, find the mode.

Ans:_________

Example:

Number of

Goals1 2 3 4 5

Number of

Teams

16 8 13 4 2

Find the mode of the data.

Ans:_________

Modal Class= The class with highest frequency.

Modeis obtained from the highest barof a histogram

with the procedure as shown below.

frequency Modal class

mode

ME

DIAN

(a) Before find the median, arrange the set of data inascending or descending order.

(b) Median is the value that lies in the middle of aset of data.

Median is the value that lies in the middle of a set

of data.

(a)L : lower boundary of the median class.(b)N : total frequency.

(c)F : cumulative frequency before the median class.(d) C : size of the class ( upper boundary lower

boundary)

(e): frequency of the median class.


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RANGE

I.Q.R

VAR

@

STD.DEV

22

2, x

N

xVariance

VarianceDeviation,Standard

22

2, x

f

fxVariance


*xis the value of the data

22

2, x

f

fxVariance


*xis the midpoint of the data

Effects of Uniform Changes In Data

+k -k k k

Mean, Median, Mode +k -k k kRange, Interquartile Range No Changes k k

Standard Deviation No Changes k k

Variance No Changes k2

k2


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PAPER 1

1. A set of integers consists of 20, 19, 17, 19, 15, 16, 16, and 19, find

(a) the mean,

(b) the mode,

(c) the median. [4 marks]

2 Three integersy,xandx+ 6 has a mean of 9 and a median of 8. Given that x>y, findthe value ofxand

ofy. [3 marks]3 The mean and the variance of a set of six numbers are 6 and 8 respectively. A new number, a, is added to

the set of numbers and the mean does not change. Find

(a) the value of a

(b) the standard deviation of the new set of numbers. [4 marks]

4 The mean of four numbers is m . The sum of the squares of the numbers is 100 and the standard

deviation is 3k. Express min terms of k. [3 marks]

5 The marks obtained by nine pupils in an Additional Mathematics test are 30, 25, 33, 42, 27, 51, 65, 45 and

57. Find(a) the range,

(b) the interquartile range of the marks. [3 marks]

6 Table 1 shows the number of goals scored in a football competition.Number of Goals 1 2 3 4 5

Number of Teams 16 8 p 4 2

TABLE 1

Find

(a) the maximum value forp , if the mode is 1,

(b) the minimum value forp , if the mean goal scored is more than 2. [3 marks]

7 A set of positive integers consists of 2, 5 and m. The variance for this set of integers is 14. Find the value

of m. [4 marks]

PAPER 28 The mean for a set of six numbers 7, 2, 8, 3, 6 andyis 6.

(a) Find the value ofy. [2 marks]

(b) Hence, find the standard deviation of the set of numbers. [4 marks]

9 Table 2 shows the marks of 80 pupils in a mathematics test.

Marks Number of Students

30 39 9

40 49 11

50 59 22

60 69 25


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70 79 8

80 89 5

TABLE 2

Find

(a) the modal class,

(b) the mean,

(c) the median marks of the mathematics test without using an ogive. [7 marks]

10 The sum of a set of ten numbers is 62 and the sum of the squares of the numbers is 438.

(a) Find the mean and standard deviation of the ten numbers. [3 marks]

(b) A number, 5, is taken from that set of numbers, find the new mean and standard deviation of the

remaining nine numbers. [3 marks]

11 A set of data consists of ten numbers. The sum of the numbers is 150 and the sum of the squares of the

numbers is 2472.

(a) Find the mean and the variance of the ten numbers [3 marks]

(b) Another number is added to the set of data and the mean increases by 1.

Find

(i) the number added,

(ii) the standard deviation of the eleven numbers. [4 marks]

12 Diagram 1 is a histogram which represents the distribution of the marks obtained by 40 students in a test.

DIAGRAM 1

Marks

Number of Pu ils

0.5 30.5 0.5

14

10.5 20.5 40.5 50.50

2

4

6

8

10

12


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(a) Without using an ogive, calculate the median mark. [3 marks]

(b) Calculate the standard deviation of the distribution. [4 marks]

13 Table 3 shows the distribution of the mass of 100 pupils in a primary school.

Masa (kg) Frequency

20 24 12

25 29 14

30 34 30

35 39 27

40 44 17

TABLE 3

(a) Draw an ogive to show the distribution of the mass of the pupils. [4 marks]

(b) From the ogive drawn, find

(i) the median,

(ii) the interquartile range of the distribution. [3marks]

14 Table 4 shows the frequency distribution of the scores of a group of pupils in a game.

Score Number of pupils

10 19 1

20 29 2

30 39 8

40 49 12

50 59 k

60 69 1

TABLE 4

(a) It is given that the median score of the distribution is 42.

Calculate the value of k. [3 marks]

(b) Use the graphpaper provided by the invigilator to answer thisquestion.

Using a scale of 2 cm to 10 scores on the horizontal axis and 2 cm to 2 pupils on the vertical axis,

draw a histogram to represent the frequency distribution of the scores.

Find the mode score. [4 marks]

(c) What is the mode score if the score of each pupil is increased by 5? [1 mark]


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