MFM 2P1
UNIT 1- ALGEBRA
1. Simplify.
-
REVIEW NOTE
5x2 +lx—7—9x2 —4x—2
Date:
(Collect Like Terms)
=5x2 —9x2 +7x—4x—7—2
=—4x2 +3x—9
(_5x2y34xy2)
2. Simplify.
=
(Numbers with Numbers, Powers with Powers)
(Multiply powers with the same base, keep the base, add expo
nents.)
—20x3y5
(1ox33.t2y4)
3. Simplify.
30x5y4
—
5xy2
6x4y2
=
.
4. Simplify using the Distributive Property.
a) 2x(6x—3)
b)
2x(6x—3)
(x—4Xx+9)
(x—4Xx÷9)
=x2+9x—4x—35
=12r—6x
=x2+5x—36
5. Simplify.
—
=
=
=(2x+5X2x+5)
=4r+lOx+lOx+25
=4x 2 +20x+25
4Cr —3XX —5)
I tip.. the “inomial
=
c) (2x+5)2
4(2x2
4(2x2
—
—
Si
II
—Ri2 44xi,()
rt and p t the answer in brackets.)
MFM 2P1
UNIT i-ALGEBRA
-
jIEVIEW
/
c?cnL
1. Simplify.
a) —12x2 —4x+1I+7x’ —lOx—6
c) 4x2 —xy+3xy—3x2 +7xy
b) 14x2 —5x+1O—8x2 —6x—19
d) 6x2y—2x2y2 —llx2y+5x2y2 —3xy
2. Simplify.
(8xy—5y)
a)
b)
(_3x2y(2.y2)
(3xyX_2x2y)_4xy2)
c)
3. Simplify.
35x4y3
a)
b)
6x2y2
c)
—48x8y6
48x5y3
c)
_6xç2 —5x)
4. Simplify.
4x(5x+7)
a) 3(2x—5)
b)
d) 7—2(Sx—5)
g) (3x2 ÷l7xy)_(12x2 —3xy)
i) 2x(x+y)—3x(2x—3y)
e) (x—9Xx+7)
f) (2x+9)2
h)
j)
(3x2 _5.,y)_(3.çy_7y2)
2x(3x—5y)—x(2y+3x)
5. Simplify.
•
a) (x+lXx+4)
d) (2x+IXx+3)
b)
(x+3Xx—3)
c)
e) (x÷2)’
f)
(3x—2XSx÷4)
6. Simplify.
a)
3(x—lXx—4)
b)
—4(x—3X2x—5)
c) —3(2x—yX2x+y)
d) 3(x—5)2
Answers:
1. a) —5x2 —14x+5
2. a) —4O.’2
3. a)
—
7x3y
b) 6x2 —lIx—9
b) —6xy3
c) 24x3y3
b) 4x3
c)
L)
20x1 +28x
—9x2 +2Oxv
v2 F5x+4
I,)
.‘
x2+4x+4
i)
lSx+2x—R
4. a) 6x—15
1) 4x2 +16x i-l
c) x2 +9xy
—
d) —5x2y+3x2y2 —3xy
x3y2
c) —6x3 +30x1
) 3x2 —Sxy+7y2
-
lOx+ 25
d) 17—16x
I) —4x2 ÷11
ci)
2x2 +7x
e) x —2x—63
j) 3x2 —l2xy
f3
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MFM 2P1
1. Solve.
UNIT 2- SOLVING EQUATIONS
REVIEW NOTE
Bx+4=2x+16
8x+4—2X=2x+16—2X
6x +4 = 16
6x +4—4=16—4
6x
=
6x
—
12
12
66
x=2
2. Solve.
3(x —4)— 5(x + 2) = —2(3x
—
i)
3(x —4)—5(x + 2)= —2(3x— i)
3x
—
12
—
5x
—
10 = —6x + 2
3x—5x-12-lo=—6x÷2
—2x-22
=—6x+2
4x—22=2
4x
=
24
x=6
3. Solve.
x x—1
—+————=12
2
5
i o3) + 1 0(-1) = i 0(12)
FtE1+I61tz’1= 1002)
a
ix+ 1x—2= 120
?x— 2 = 120
7x=122
4Multiply each term by the lowest common denominator.
tSimplifv the fractions
UNIT 2- SOLVING
MFM 2P1
UATI
S
-
REVIEW
Solve.
a) 5x+4=2x+1O
b) Sx—3=lOx—9
c) 4+3x=25—4x
d) —6—3x=5x+1O
2. Solve.
a) 3x+Sx=32
d) —3(x+2)=24
g) 3(x+I)+2(x+2)=—32
b) —2x—4+6x=9
e) 5ç—3)= to
h)(5x—1)—4=—2(x+3)+6x
c) 3(2x—5)=3
1) 2+4)=1—3x+3
i) 2G—4)—5G+1)=4(x—5)
3. Solve.
x
a) —=—5
2
x x
b) —+—=12
24
c)
x+2
x+1
+1=—
4
3
d)
2x+1
3
=
x—2
5
4. Solve and check.
.
a) Sx—2=—37
b) 3x+5=9x—7
Answers:
1. a) x=2
b) x=3
c) x=3
d) x=—2
2. a) x=4
b)
c) x=3
d) x=—1O
g) x=—
h) x=—1
i)
3. a) x=-IO
b) x=16
c) x=14
d)
4. a) x=—7
b)
1) x=—
.
x=1
e) x=5
b) t&(3)09
lox
tc)5xt±o
5xr QX= 1b+
XE
3
ccL
-
c) *÷3)=st
3
r33-57c
Jç,+Q
x3
2
a) 3x÷Sx= 3z
8xtaz
b) -2-’-f+ Lx 9
c)
(c2):-S) 3
G1iSc3
S
d) _3Lx+2)tf
3t
t
t
213zh3xt3
2$+fc,
5jt
1°U5
3)c+3Xz4-2
S
-3
-jo
3&+l)+2(xta)3z
3tgtt
3Z
--
51=
-
S
2DL_=_ct1+c{
—
I
.
•) Q&-’Q-S(xl) = fCx-s)
-.8 St-5 4x-2o
3Dc—132 q)ç-20
2o+13
-
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-
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2-
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b)
c)
t+Z_
-+1 X+
3
.
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S
12.6)
3z.+G+
3x-x-
Lac LLt÷+
3
x-=
3
S
3d)
jQxts
lox 3x
-
.
—‘--5
x=-JL
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MFM 2P1
UNIT 3- FACTORING
1. Common Factor.
-
REVIEW
N
12x4 —20x3 +24x5
4x3(3x_5÷6x2)
/
NN
*
*
This is what’s left over.
This is what you have to
multiply 4x3 by
to get what you started with.
The Greatest Common Factor
—
—
the largest number that goes into
x is common to
all 3
evenly
terms, take out the one with the lowest exponent,
x3
2. Factor the following Simple
x2—5x—24
12, 20 and 24
Trinomial (The Number Game).
-
*
Number
Find 2
=(x—8Xx+3)
3.
Factor the following Difference of Squares.
Game:
numbers that multiply to
—24 and add
to
—5
A2-B2 =(A—BXA+B)
16x2 —25
Think: What
is being squared to give us lóx2? Put
Think: What
is being squared to give us
it here. (4x)
=(4x—5X4x+5)
.
I
Put one plus and one minus between die 4x and
jIC
5.
25?
Put
it here.
MFM 2P1
.
UNIT 3- FACTORING
-
REwEWçPRAcEiO
1. Factor.
+5x
a) 2x+6
b) 6x—9
c) x2
e) 8x+4xy
0 lOx+15y—20z
g) 12x5—20x+24x4
d) 2x2 +8x
2. Factor.
a) x2+4x+3
d) x2+5x—36
g) x2+3x—18
b) x2—lOx+25
e) x2—2x—48
h)x2—8x—20
c) x2—9x+20
0 x2+lóx+64
1) x2+5x+6
3. Factor.
x2—4y2
a) x2—9
b) x2—36
c) x2—100y2
d)
e) 121x2 —144
f) 64x2 —1
g) 16x2 —25y2
1) 81x —49y2
b) 9x2+I8xy
1) 8x3—4x2
e) x2—1
g) 4x2—49y2
b) 3(2x—3)
4. Factor.
a) 4x—20
e) x2—4x+4
d) x2+2x+1
h) x2—lOx+24
Answcrs
1. a) 2(x+3)
e) 4x(2+y)
0
5(2x+3y—4z)
c) x(x+5)
d) 2x(x+4)
g) 4x(3x —5+6x)
2. a)
b)
(x—5Xx—5)
c) (x—5Xx—4)
(x+3Xx+I)
e) (x—8Xx+6)
i) (x+3Xx+2)
3. a) (x+31x—3)
(i ix--iXI Is—I:)
.
•
a,
4(5—))
(v—’tv—2)
(x+6Xx—3)
0(x+8Xx+8)
g)
b) (v+6Xx—6)
0 (1xt 1X8x—1)
c) (x+1oyx—1Ov)
‘)
‘(a !v)
c’2x —fl
0
(4xt5y4x—5y)
c
(.
IXx—I)
(x ?v(2x_7v)
(x+9Xx—4)
d)
h) (x—lOXx+2)
d) (x+2vXx—2v)
g)
(+
7yX9x—7y)
d) (x+lXx÷I)
(v—otr—4)
kQ)23(4
b
b)Gx9
t2(z+3)
.xCx*5)
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MFM 2P1
.
UNIT #4-SIMILAR TRIANGLES
REVIEW NOTE
I. a) Why are the following triangles similar?
—
aft
CorreSfoflJ
b) Determine the values of the variables x andy to 1 decimal place if necessary.
E
A
x
16.5
11
C
3)
B
D
8
12
F
Solution:
In AABC and AUFE
AB BC AC
DFFEDE
11
12
8
y
—
x
16.5
1
118
12 y
11= x
12 16.5
12
11
16.5111”i = 16.S1_i_
—
=
y
8
lI)
8.7=y
I2}
8
15.1 =x
L16.S
fr
2. a) Why are the following triangles similar?
cnrrespondftj QflJ[tS Q(e
PLL&L
b) Determine the values of the variables x andy to I decimal place if necessary.
A
x
11
B
C
26
45
D
Solution:
E
3)
En AABC and AADE
ABBC
ADDE
11_ 8
37 3)
AC
AE
x
x +45
—
•1
11
37
37
11
8
—
11= x
37 x+45
y
y
8
÷45]
+
3)
S
=
45)[.t] = (37)(x +
(37)(x
I lxi- 4Q5
=
F
6x
—
37x
UNIT 4- SIMILAR
MFM 2P1
.
V I I
1. i) Mark all equal angles.
ii) Determine the value of x andy to I decimal place using similar triangles.
A
a)
59.4
P/”>N Q
C
y
12
b)
Q
P
y
10
T
z
8
A
c)
15
M
30
F
knswers:
x
P
50
7
:.6 ABCL
flsct
pg
59.4
C)
%5.G
3
X12
• L)
ArzLAr’\P
£IPQ°LTz1?
72
ZR
j?T
/P
30+15
NW
F1’\
JLtJI!i
x
)2x Sfl5)
x=SC[5)
ii
xt
10
1
S
)
Li_s
a
‘
‘f5xr
I5(&-’-x)
t5zc-9So4\Sx-
5O
8
[S
30
MFM 2P1
.
UNITS- TRIGONOMETRY
REVIEW NOTE
Date:
1. a) Name the 3 sides of the following triangle relative to angle A using the full names.
Opposite
Hypotenuse
Adjacent
b) Define the following ratios using the full names of the sides above
I) Cos(A) =
Adjacent
Hypotenuse
ii) Tan(A)
Opposite
Adjacent
=
=
iii) Sin(A)
Opposite
Hypotenuse
2. Use your calculator to determine the following to 4 decimal places.
.
a) sin(32°)=
.5299
b) sin(8°)
.1392
c) cos(27°)
.8910
d) tan(81j
6.3138
=
3. Determine the value of angle A to the nearest degree.
a) tan(A) = 1.327
A
530
b) tan(A)
=
1235
1000
A=
510
4. Determine the value of x to I decimal place.
a)C
x
I
b)
x
15
C
B
Jdj
Sui(G) =
=
•t
490
•q(J )° =
Sin(21°)-
Hjp
‘5
—
5.
Determine angle 9 to the nearest degree.
9
Solution:
Cos(9) =
Cos(9) =
Hyp
14
o CosI
=
k14
O=50
6. From the top of a fire tower the ANGLE OF DEPRESSION to a log cabin is 26°. Determine the distance
to the cabin from the base of the tower if the tower is 75m high. Include a labeled diagram in your
solution.
Let x m be the distance from the cabin to the tower.
26°
Angle of Depression
Tan(C)=2
Adj
75m
I \ 75
Tan26 )=—
xm
C
X
=
75
Tan(26j
x=153.8
The distance i 15 .8 m.
.
UNITS- TRIGONOMETRY
MFM 2P1
.
-
REVIE1c\
1. Use your calculator to determine the following to 4 decimal places.
a) sin(52°)
)
g) tan(45°)
)
h) cos (57°)
)
i) sin (76°)
b) cos(68°
c)
tanØ4°
d) cos(31°
e)
tan
(800
0
)
j)
cos(2°)
2. Determine the value of angle A to the nearest degree.
a) tan(A)
.
=
b) cos(A)
1.327
=
0.643
c) sin(A)
=
829
1000
d) tan(A)
=
1235
1000
3. Determine the value of x to 1 decimal place.
a)
L
15
F
b)
x
x
A
3
c)
D
I
32
20
E
G
x
4. Determine angle 0 to the nearest degree.
8
5
13
5. A 13 ft ladder is placed against a wall. If the angle the ladder makes with the ground is 52°, how far up
tb’ wall does tI 2 ladder reach?
.
Ans ners;
3.
4.
a) x12.3
fl
0=390
i?
Ii.
b) xJl.l
T) 0
= 440
c) x 42.5
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