Additional Mathematics (2)

ADDITIONAL MATHEMATICSFUNCTIONS Paper 1 question 1,2 and 3, paper 2 (not famous)

TYPES OF RELATIONS AND FUNCTIONS ARROW DIAGRAM, ORDERED PAIRS AND GRAPH DOMAIN, CODOMAIN, OBJECT, IMAGE AND RANGE FUNCTIONS ABSOLUTE VALUE FUNCTIONS COMPOSITE FUNCTIONS INVERSE FUNCTIONS VALUE OF WHICH IS MAPPED ONTO ITSELF

VALUE OF SUCH THAT THE FUNCTION IS NOT DEFINED PROBLEMS IN COMPOSITE FUNCTIONS COMPARING PROBLEMS IN FUNCTIONS

1. Diagram 1 shows the relation between set and set

State(a) the range of the relation,(b) the type of relation.

2. In Diagram 2, the function maps to and the function maps to

8 5

2

Determine

(a)(b)

3. Given the functions and , where and are constants, find

the value of and of .

Mr. thiyaku Bsc. Statistics (UM)

where and are constants, and

4. Given the function and the composite function find

(a)

(b ) the value of when .

5. Given the function find the values of such that

6. The following information is about the function and the composite function

Find the value of and of


ADDITIONAL MATHEMATICSQuadratic equations Paper 1 question 3,4 and 5

QUADRATIC EQUATION AND ITS ROOTS SOLIVING QUADRATIC EQUATIONS BY

FACTORISATION COMPLETING SQUARE FORMULA

FORMING A QUADRATIC EQUATION FROM GIVEN ROOTS FORMING A NEW QUADRATIC EQUATIONS FROM GIVEN QUADRATIC EQUATION THE TYPES OF ROOTS OF QUADRATIC EQUATIONS

1. Form the quadratic equation which has the roots and .

Give your answer in the form , where and are constants.

2. The straight line does not intersect the curve Find the range of values of

3. Solve the quadratic equation Give your answer correct to three decimal places.

4. A quadratic equation has two equal roots.


Find the possible values of

5. (a) Solve the following quadratic equation:

(b)The quadratic equation where and are constants, has two equal roots. Express in terms of .


ADDITIONAL MATHEMATICSQuadratic functions Paper 1 question 5 and 6

QUADRATIC FUNCTONS AND THEIR GRAPHS MAXIMUM AND MINIMUM VALUE GRAPH SKETCHING QUADRATIC INEQUALITIES

1. Find the range of values of for which .

2. Diagram 2 shows of the function where is a constant.

O

-3

Diagram 2

Find(a) The value of ,(b) The equation of the axis of symmetry,(c) The coordinates of the maximum point.

3.


The curve has the minimum point , where is a constant. State (a) The value of ,(b) The value of ,(c) The equation of the axis of symmetry.


ADDITIONAL MATHEMATICSIndices and logarithm Paper 1 question 7,8 and 9

Fundamental of Indices

Zero Index,

Negative Index,

Fractional Index,

Laws of Indices

Fundamental of Logarithm

Law of Logarithm

Changing the Base

1. Solve the equation


2. Given that and express in terms of and





7. Given that express in terms of

8. Solve the equation .



10. Given that find the value of

ADDITIONAL MATHEMATICSCoordinate geometry Paper 1 question 14, paper 2 section B

1. Diagram 3 shows a straight line with the equation .

The point lies on -axis and the point lies on -axis

Q

P O

Diagram 3

Find the equation of the straight line perpendicular to and passing through .

2. A point moves along the arc of a circle with centre . The arc passes through

and (a) Find

(i) The equation of the locus of the point ,

(ii) The values of .

(b) The tangent to the circle at point intersects the -axis at point . Find the area of

triangle , where is the origin.

3. Diagram 13 shows a straight line with the equation


Q

P O Diagram 13

Find the equation of the straight line which is perpendicular to and passes through the

point .

4. Diagram 14 shows and are three points on a straight line.

Diagram 14

It is given that . Find the coordinates of

5. Diagram 10 shows triangle The equation of the straight line is

0

Diagram 10

(a) Find


(i) Coordinate ,

(ii) The coordinates of if

(b) Given that the area is units2, find the positive value of

(c) Find the equation of the straight line .

(d) A point moves such that .

Find the equation of the locus for

ADDITIONAL MATHEMATICSVector Paper 1 question 15

1. Given and The point and are collinear.Find the value of

2. Diagram shows is a parallelogram such that and

B C

A

O

Find the unit vector in the direction of .

3. Diagram shows two triangles, and Point lies on . Line and line

intersect at point T.

W

A

T B


M

O

It is given that and

(a) Express in terms of and

(i)

(ii)

(b) Given that and where and are constants. Find the value of

and .

4. Diagram shows a parallelogram drawn on a Cartesian plane.

Q

R P

O


Find

5. In Diagram, is a quadrilateral. and are straight lines. D

E C

A B


(a) Express in terms of and/or :

(i)

(ii)


Show that the points and are collinear,

If and find

6. Diagram shows two vectors, and .

A(4,3)

O

-5 B

Express

(a) in the form

(b) in the form .

ADDITIONAL MATHEMATICSStatistics Paper 1 question 23 or 24

1. The mean of four numbers is The sum of the squares of the number is and the standard deviation is .Express in terms of .

2. Diagram is a histogram which represents the distribution of the marks obtained by 40 pupils in a test.

(a) Without using an ogive, calculate the median mark.


(b) Calculate the standard deviation of the distribution.

3. A set of positive integers consist f 2, 5 and The variance for this set of integers is 14. Find the value of

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

Score Number of pupils10 – 19 120 – 29 230 – 39 840 – 49 1250 – 5960 – 69 1

(a) It is given that the median score of the distribution is 42. Calculate the value of .(b) Use the graph paper to answer this question.

Using scale of 2 cm to 10 scores on the horizontal axis and 2 cm to pupils on the vertical axis, draw a histogram to represent the frequency distribution of the scores.Find the mode score.

(c) What is the mode score if the score of each pupil is increased by 5?5. A set of data consist of five numbers. The sum of the numbers is 60 and the sum of the

squares of the numbers is 800.Find, for the five numbers (a) The mean,(b) The standard deviation.

6. Table shows the cumulative frequency distribution for the scores of 32 students in a competition.

Score <10 <20 <30 <40 <50Number of students 4 10 20 28 32

(a) Based on Table above, copy and complete Table below.Score 0 – 9 10 – 19 20 – 29 30 – 39 40 – 49

Number of students

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

7. A set of seven numbers has a mean of 9.


(a) Find .(b) When a number is added to this set, the new mean is 8.5.

Find the value of .

8. Table shows the marks obtained by 40 candidates in a rest.Marks Number of candidates10 – 19 420 – 2930 – 3940 – 49 1050 – 59 8

Given that the median mark 35.5, find the value of and .Hence state the modal class.

ADDITIONAL MATHEMATICSTrigonometry Paper 1 question 23 or 24

1. Solve the equation for

2. (a) Prove that

(b) Sketch the graph of for .Hence using the same axes, draw a suitable straight line to find the number of

solutions o the equations for.

State the number of solutions.



4. (a) Sketch the graph of for .(c) Hence using the same axis, sketch a suitable graph to find the number of solutions to the

equation for .State the number of solutions.


6. Sketch the graph of for .Hence, using the same axes, sketch a suitable straight line to find the number of solutions

for the equation for

7. Given that where is a constant and Find in terms of :(a)(b)


8. Prove that .

Sketch the graph of for Hence using the same axes, sketch a suitable straight line to find the number of solutions for

the equation for State the number of solutions.

ADDITIONAL MATHEMATICSIndex number Paper 2 question 13

Table 1 shows the prices and the price indices of four ingredients, and used in making biscuits of a particular kind. Diagram 2 is a pie chart which represents the relative amount of the

ingredients and used in making these biscuits.

Ingredients Price per kg (RM) Price index for the year 2004 based on the year 2001Year 2001 Year 20040.80 1.00 X2.00 Y 1400.40 0.60 150

z 0.40 80

80

60

100

120 PQRS


ADDITIONAL MATHEMATICSPROBABILITY Paper 1 question 23 0r 24

1. Table shows the number of coloured cards in a box.

Colour Number of CardsBlack 5Blue 4

Yellow 3

Two cards are drawn at random from the box.Find the probability that both cards are of the same colour.


2. The probability that Hamid qualifies for the final of a track event is while the probability

that Mohan qualifies is .Find the probability that(a) Both of them qualify for the final,(b) Only one of them qualifies for the final.

3. The probability that each shot fired by Ramli hits a target is .(a) If Ramli fires 10 shots, find the probability that exactly 2 shots hit the target.

(b) If Ramli fires n shots, the probability that all the n shots hit the targets is . Find the value of n.

4. The probability of Sarah being chosen as a school prefect is while the probability of Aini

being chosen is .Find the probability that (a) Neither of them is chosen as a school prefect,(b) Only one of them is chosen as a school prefect.


5. The probability that a students is a librarian is 0.2. Three students are chosen at random. Find the probability that(a) All three are librarians,(b) Only one of them is a librarian.


Additional Mathematics (2)

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