Latih Tubi Akhir Mate K2 PMR 2012

TUISYEN KITA | cgnash

PENCETUS BIJAK MATEMATIK

1 Latih Tubi Akhir PMR 2012

DIRECTED NUMBERS

INTEGER, FRACTION AND DECIMAL

1. Calculate the value of

4

32.115


2

1

5

217.0 and express the answer as a decimal.


5

2

10

79.0 and express the answer as a decimal.

SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS

1.

a)

b)

2.

a)

b)

3.

a)

b)

ALGEBRAIC EXPRESSIONS

1. Factorise each of the following expressions:

a) prpq

b) 64 a

c) xxy 39 d) xyy 123

Calculate the value of

1. - 48 (-2) 12 =

2. -17 + 3 (-4) + 20 =

3. -5 (-64) (-8) =




2. Factorise completely each of the following expressions:

a) 92 m b) 22 259 qr

c) 33 2 p d) 2250 p

e) nmmnm 362 2 f) 276368 yxxy

3. Express as a single fraction in its simplest form.

a) Express 28

26

2

1

p

p

p

as a single fraction in its simplest form.

.

b) Express mp

p

m 2

32

2

5 as a single fraction in its simplest form.

.




LOCI

1. The Diagram in the answer space shows four squares. X, Y and Z are three moving

points in the diagram.

a) X moves such that it is equidistant from straight lines AB and CD. Using the

letters in the diagram, state the locus of X.

b) On the diagram, construct

(i) the locus of Y such that KY = KE.

(ii) The locus of Z such that it is equidistant from points A and C.

c) Hence, mark with symbol , all the points of intersection of loci Y and Z.

Answer: (a) .

(b), (c)

D C H

E K

A

G

B F




2. The diagram in the answer space shows a circle with centre O drawn on a square

grid of equal squares with side of 1 unit. POQ is a diameter of the circle. X, Y and Z

are moving points inside the circle.

(a) X is the point which moves such that it is always 4 units from the

centre O. Describe fully the locus of X.

(b) On the diagram, draw

(i) the locus of the point Y which moves such that its distance

from the line PQ is always 3 units.

(ii) the locus of the point Z which moves such that its is

equidistant from the point P and the point Q.

(c) Hence, mark with the symbol , the intersection of the locus of Y

and the locus of Z.

Q P




3. (a) The diagram shows a rhombus ABCD

X is a moving point in the rhombus such that it is always equidistant from AB

and BC. By using the letter in the diagram, state the locus of X.

(b) ABCDE is a regular pentagon as shown in the answer space. On the diagram,

draw

(i) the locus of Y such that YD = CD.

(ii) the locus of Z such that it is equidistant from points B and C.

(c) Mark at the intersection of locus of Y and the locus of Z in (b).

Answer: (a)

(b) (i), (ii)

(c)

A B

C D

A

B

C

D E




ALGEBRAIC FORMULAE

1. Given that 5)3(2

k

p, express p in terms of k.

2. Given that r = 1 and s = 4, thus 23 )1( sr

3. Given that 5)4(2

r

rp, thus r =

4. Given that 33

5

kp, thus p =

LINEAR EQUATIONS

1 Solve each of the following equations:

a) 754 ff

b) 81284

3 pp


a) x

84

b) 3272

4

z


a) 912 x

b) pp

7

62

LINEAR INEQUALITIES

1. Solve each of the following inequalities:

a) s + 7 > 5

b) 5t + 3 < 7 + 8t

2. List all the integer values of p which satisfy both the inequalities

74 p and p43 27 3. List all the integer values of w which satisfy both the inequalities

12 w and w34 10

4. List all the integer values of x which satisfy both the inequalities 6x 13 and 13

x




INDICES

1. 21

5

2

932

2.

2

3

1

2

1

3

1

626

3. 21

3

12 927

4.

2

2

1

3

1

3

1

255

5. 32

43

3

39

6.

2

3

2

18

7. 306 223 kkk

8. 24243 yxxy

9. 1322 xyyx

10. 31232 yxxy




GRAPH OF FUNCTIONS

x 0 1 2 3 -3 -1 -2

y

Question 1 Table shows the value of two variable, x and y of a function.

x -3 -2 -1 0 1 2 2.5 3

y 35 16 9 8 7 0 -8 -19

The xaxis and the y-axis are provided on the graph paper .

a) By using the scale of 2 cm to 10 units, complete and label the y-axis. b) Based on table, plot the points on the graph paper c) Hence, draw the graph on the function.




Question 2 Table shows the value of two variable, x and y of a function.

x -2 -1 0 1 2 3 4

y 32 18 8 2 0 2 8

a) By using the scale of 2 cm to 1 units on x axis and 2 cm to 4 units on y-axis, draw and label the axes

b) Based on table, plot the points on the graph paper

c) Hence, draw the graph on the function.




B

TRANSFORMATION

1. In diagram, triangle B is the image of triangle A under transformation M

y

4

2

4 2 2 4 x

2

A

4

Describe in full transformation M

2. Diagram PQRS was drawn on a square grid.

P

Q

R

S

Draw the image of PQRS under a rotation of 900 anticlockwise about point O




3. Diagram shows P is the image of P under 900 clockwise rotation about point T drawn on a Cartesian plane

y

4

P

2

4 2 0 2 4 x

2

Q

4

M

On the diagram, mark and label

a. point T

b. point M, the image of point M under the same rotation

c. state the coordinate of image M




4. Diagram in the answer space shows triangle PQR drawn on a square grid.

P

Q R

Draw the image of triangle PQR under a rotation of 900 clockwise at the centre M.




5. Diagram below shows three triangles, P, Q and R which are drawn on a Cartesian plane

10

K 8

6

4

P

2

Q

a. Q is the image of P under a rotation 900. State

i. The direction of the rotation

ii. The coordinates of the centre the rotation

b. R is the image of P under transformation M. Describe in full transformation M

6 2 4 4 2




6. Diagram T in the answer space was drawn on a square grid of equal squares. Draw the image of triangle T under an enlargement with centre P and scale factor 3.

T

P

7. Diagram below shows, S is the image of P under an enlargement.

S

P

a) On a Cartesian plane in the answer space, mark T, the centre of enlargement

b) Calculate the area of image, in unit2.

1

3

4

5

2

6

1 3 4 5 2 6

y

10 9 8 x

7

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Latih Tubi Akhir Mate K2 PMR 2012