set 3 mawar
TRANSCRIPT
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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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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.
3.Calculate the value of
+−−−
5
2
10
79.0 and express the answer as a decimal.
4.Calculate the value of
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 ÷−−
6.Calculate the value of
−+−
10
3
5
48.3 and express the answer as a decimal.
7.Calculate the value of
5
43.021 +÷
8.Calculate the value of
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.
(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.
● 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.
(b) On the diagram, draw
(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 .
(b) On the diagram, draw
(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
2 Solve each of the following equations:
a) x
84 =
b) 3272
4 =
+
z
3 Solve each of the following equations:
a) 410 =− y
b) ( ) ( ) 315123 +−=− p p
4 Solve each of the following equations:
a) 55 −=− p
b) t t 59240 +−=−
5 Solve each of the following equations:
a) 912 −=+ x
b) p p=
+−
7
62
6 Solve each of the following equations:
a)4
1
8=
−
k
b) ( ) ( ) 9123212 ++=− mm
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7 Solve each of the following equations:
a) 45
−=t
b) 37219 =−− y
8 Solve each of the following equations:
a) p p −−= 12
b) ( ) 18642
3−=−+ gg
9 Solve each of the following equations:
a) nn 2457 −=
b) )6(233 −−=+ hh
10 Solve each of the following equations:
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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Question 3Table shows the value of two variable, x and y of a function.
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
c) Hence, draw the graph on the function.
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Question 4Table shows the value of two variable, x and y of a function.
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
b) Based on table, plot the points on the graph paper
c) Hence, draw the graph on the function.
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Question 5Table shows the value of two variable, x and y of a function.
x -3 -2 -1 0 1 2 3 4
y -25 -15 -5 3 5 4 -10 -15
a) By using the scale of 2 cm to 1 units on x – axis and 2 cm to 5 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.
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Question 6Table shows the value of two variable, x and y of a function.
x -2 -1 0 1 2 3 4
y -19 -7 4 10 12 -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, draw
and label the axes
b) Based on table, plot the points on the graph paper
c) Hence, draw the graph on the function.
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Question 7Table shows the value of two variable, x and y of a function.
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
b) Based on table, plot the points on the graph paper
c) Hence, draw the graph on the function.
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Question 8Table shows the value of two variable, x and y of a function.
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.
b) Based on table, plot the points on the graph paper
c) Hence, draw the graph on the function.
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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
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