SET 3 MAWAR

7/27/2019 SET 3 MAWAR

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1

DIRECTED NUMBERS

Calculate the value of

1. - 48 × (-2) ÷ 12 =

2. -17 + 3 × (-4) + 20 =

3. -5 – (-64) ÷ (-8) =

4. -6 + (-3) =

5. 25 – (-3)×

(-4) + 3 =

6. 98 – 3 (12 + 48 ÷ 6) =

7. 44 ÷ 2 (4+7) =

8. 44 ÷ (-4) – 21 ÷ 7 =

9. 36 ÷ (-6 – 3) – (-40) =

10. 66 ÷ (-6) + [ 6 – (-5) ] × 4 =

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2

INTEGER, FRACTION AND DECIMAL

1.Calculate the value of ( )

4

32.115 ×−÷

2.Calculate the value of

2

1

5

217.0 ÷+− and express the answer as a decimal.


+−−−

5

2

10

79.0 and express the answer as a decimal.


5

6

5

2

3

2÷

− and express the answer as a fraction in its lowest

terms.

5.Calculate the value of ( )

8

55.018 ÷−−


−+−

10

3

5

48.3 and express the answer as a decimal.


5

43.021 +÷


5

21

4

1

2

12 ÷

+ and express the answer as a fraction in its

lowest terms.

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SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS

1. a)b)

2. a) b)

3. a) b)

4. a)b)

5.a) b)

6.a) b)

7

a) b)

8. a) b)

9. a) b)

10.a) b)

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ALGEBRAIC EXPRESSIONS

1. Factorise each of the following expressions:

a) pr pq − b) 64 +a

c) x xy 39 − d) xy y 123 −

e) 22 p pq − f ) 2

64 y y −

g) 2

123 mmn + h) rsr 8162

+

i) pr pq 86 + j) 264 mmn −

k) x xy 93 − l) pq p 962−

m) mqmn 105 − n) mpnm 862+

p) x xy 48 − q) pq p 82 −

r) y xy 39 − s) 228 q pq −

t ) q pq 106 − u) xy x 63 −

v) q pq 64 2− w ) x xy 36 −

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2. Factorise completely each of the following expressions:

a) 92−m b) 22

259 qr −

c) 332− p d) 2

250 p−

e) 1882− p f) 22

312 y x −

g) 22123 p y − h) 22

123 n p −

i) 22182 y x − j) 2

205 y−

k) 22273 q p − l) 22

254 y x −

m) 22188 y x − n) 2

250 k −

o) d bdxbx 44 −+− p) nmmnm 10653 2+++

q) nmmnm 3622

+++ r) 276368 +++ y x xy

s) y xy x 3224129 +−− t) df decf ce 9632 −−+

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

a) Express2

8

26

2

1

p

p

p

−+ as a single fraction in its simplest form.

.

b) Expressmp

p

m 2

32

2

5 −− as a single fraction in its simplest form.

.

c) Express xy

y

x 3

32

6

7 ++ as a single fraction in its simplest form.

d) Express xy

y

x 2

6

2

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

.

e) Express pq

q

p 8

210

4

−−

2 as a single fraction in its simplest form.

f) Express pq

q

p 8

210

2

−−

1as a single fraction in its simplest form.

g) Express

−

−mp

p

m

5

11

10

3as a single fraction in its simplest form.

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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 CH

EK

A

G

BF

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2. The diagram in the answer space is drawn on a square grid of sides 1 unit.

(a) P is a moving point inside the square JKLM such that PL = 5 units. Using a

letter in the diagram, state the locus of P.

(b) Q and R are two points inside the square JKLM. On the diagram, construct

(i) the locus of Q such that Q is equidistant from points K and M ,

(ii) the locus of R such that the perpendicular distance of R from line HI

is 1 unit.

(c) On the diagram, using symbol⊗ , mark all the possible points of intersection

of locus Q and R.

Answer: (a) ……………………………………

(b), (c)

J K

L M

H

I

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3. The diagram shows square EFGH drawn on grid of equal squares with sides of 1 unit.

(a) W is a moving point which moves such that its distance from the lines EF and

EH is the same. By using the letters in the diagram, state the locus of W.

(b) On the diagram, draw

(iii) the locus of the point X that is at the constant 6 units from E .

(iv) the locus of the point Y that is at a constant 5 units from straight line

FG.

(c) Then, with the symbol⊗ , mark the intersection of locus X and locus Y .

Answer: (a) ………………………………………………..

E F

H G

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4. 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.


(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.

● QP

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5. (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

CD

A

B

C

DE

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6. The diagram in the answer space shows a square PQRS drawn on a square grid with

sides 1 unit. X, Y and Z are three moving points in the diagram.

(a) X is a point which moves such that it is equidistant from straight lines PQ and

QR. By using the letters in the diagram, state the locus of X.


(i) the locus of point Y which is always 4 units from the point Q.

(ii) the locus of point Z which is always 5 units from straight line PS.

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

of Z.

Answer: (a) ……………………………

(b) (i), (ii), (c)

QP

RS

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7. Diagram in the answer space shows a square, TUVW. Point O is the point

of intersection of diagonals TV and UW.MN is a straight line. X and Y are two points

moving inside the diagram.

On the diagram,

(a) Construct;

(i) the locus of X such that XM=XN

(ii) the locus Y given that OY=2.5 cm

(b) Hence, mark with the symbol ⊗ all the intersections of the locus of X and

the locus of Y

VN

T M U

O

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8. Diagram in the answer space shows a square PQRS. M and N are two moving

points in the diagram. By constructing suitable loci, mark the points when M and N

are 5 cm from R and equidistant from P and R.

Hence, measure the distance, in cm, between the point M and the point N.

P Q

S R

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9. Diagram in the answer space shows a square ABCD drawn on a grid of equal

squares with sides of 1 unit.

On the diagram

(a) construct the locus of point M moving at a distance of 4 units from K

(b) construct the locus of a moving point which is equidistant from the points R

and T

Mark ⊗ for all the points that satisfy the loci in (a) and (b)

● ●

●

D C

BA

T

K

R

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10. Diagram in the answer space shows a rhombus. S , X and Y are three moving points

In the diagram.

(a) S is the point which moves such that its distance from point A and point C are

the same. By using the letters in the diagram, state the locus of S .


(i) the locus for the point X that is constantly 2 cm from the line AC ,

(ii) the locus for the point Y that is constantly 4 cm from the point A

(c) Hence, state the number of intersection points of the locus of X and

the locus of Y .

Answer:

(a) …………………………………………………………………

(b) and (c)

D

C

B

A

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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

r p, thus r =

4. Given that 523

32−=

− p

p, thus p =

5. Given that 232+= m p , express m in terms of p .

6. Given that 33

5 =−k p , thus p =

7. Given that2

37

2nm += , express n in terms of m .

8. Given that

12

2

−

=

p

k , thus p =

9. Given that t L

rs=

3, express L as the subject of the formula.

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10. Given that p = – 2 and r = – 3, the value of )7(2

pr

p− is

11. Given that b = 4 and k = – 3, then =−2k bk

12. Given that a = 4 and b = – 2, then =−

b

ab22

13. Sam buys p mangoes at 40 sen each and q oranges at 50 sen each.He sells the mangoes at 55 sen each and the oranges at 70 sen each.Write the expressions of total profits, T, in sen, from the sales of all themangoes and oranges.

14. Danial has RM 500. He spends all his money to buy x shirts and y trousers. Given that the prices of a shirt and a pair of trousers areRM 20 and RM 120 respectively. Write the equation which involves x and y .

15. Table below shows the number of balls in a box.

Colour Number of Balls

Red x

Blue x2

1

White 4− x

If the total number of balls in the box is y , write the equation involvingx and y.

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LINEAR EQUATIONS

1 Solve each of the following equations:

a) 754 −= f f

b) ( ) 81284

3−=−+ p p


a) x

84 =

b) 3272

4 =

+

z


a) 410 =− y

b) ( ) ( ) 315123 +−=− p p


a) 55 −=− p

b) t t 59240 +−=−


a) 912 −=+ x

b) p p=

+−

7

62


a)4

1

8=

−

k

b) ( ) ( ) 9123212 ++=− mm

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a) 45

−=t

b) 37219 =−− y


a) p p −−= 12

b) ( ) 18642

3−=−+ gg


a) nn 2457 −=

b) )6(233 −−=+ hh


a) y y 6162 −−=

b) ( ) 1343

12 =+− k k

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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 6+ x ≤ 13 and 1

3>

x

5. List all the integer values of x which satisfy both the inequalities 25 >+ x and

24

x− ≥ 3

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

3

x ≤ 1 and 721 <− x

7. List all the integer values of x which satisfy both the inequalities 153 <− x and

x3

12 − ≤ 3

8. List all the integer values of x which satisfy both the inequalities x−3 ≥ 0 and 1

33 <+

x

9. List all the integer values of x which satisfy both the inequalities 32 + x ≤ 7 and 5

2

3 <− x

10. List all the integer values of x which satisfy both the inequalities 3

22 <−

xand

( )13 − x ≤ 2y

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INDICES

1. 2

1

5

2

932−

÷ 2.

2

3

1

2

1

3

1

626

××

−

3. ( ) 2

1

3

12 927

−

× 4.

2

2

1

3

1

3

1

255

××

5. ( )32

43

3

39−

×

6.

2

3

2

18

−

7. ( ) 306223 k k k ×−× 8. ( ) ( )2424

3 −−÷ y x xy

9. ( ) ( )1322 −

÷ xy y x 10. ( ) ( )31232 y x xy

−÷

11. ( ) ( ) y x xy322

÷ 12. ( )543

2 nm

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GRAPH OF FUNCTIONS

x0 1 2 3-3 -1-2

y

Question 1Table 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 x–axis 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.

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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 paperc) Hence, draw the graph on the function.

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x -3 -2 -1 0 1 2 3

y -20 0 10 12 15 18 40

a) By using the scale of 2 cm to 1 units on x – axis and 2 cm to 10 units on y-axis, draw and

label the axesb) Based on table, plot the points on the graph paper


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x -3 -2 -1 0 1 2 3 4

y -25 -15 -2 3 5 3 -5 -15

a) By using the scale of 2 cm to 1 units on x – axis and 2 cm to 5 units on y-axis, drawand label the axes



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x -3 -2 -1 0 1 2 3 4

y -25 -15 -5 3 5 4 -10 -15


and label the axes



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x -2 -1 0 1 2 3 4

y -19 -7 4 10 12 -5 -15


and label the axes



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x 0 1 2 3 4 5 6

y 5 2 -3 -10 -15 -20 -25

a) By using the scale of 2 cm to 1 units on x – axis and 2 cm to 10 units on y-axis, draw and

label the axis



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x -3 -2 -1 0 1 2 3

y 0 6 8 8 6 5 0

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



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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

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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 drawnon 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

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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 90

0

clockwise at the centre M .

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

10

K 8

6

4 P

2Q

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

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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 52 6

y

1098 x

7

7/27/2019 SET 3 MAWAR


SET 3 MAWAR

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