Solution Key
Bedmas
a) -4
g) -702
m) 28
b) -6
h) 3
n) 32
c) 2
i)-17
o)-45
d) -8
j) 0
p) 42
e) 120
k) 4
f) 0
l) 10
Fraction Work
a)  6
f ) 1
b)5
5
16
1
3
 11
h)
12
22
i )8
45
1
j )2
2
c)4
g)
1
12
e)  4
d )2
 22
75
4
q)
9
1
r )1
72
21
s )1
55
23
27
121
l)  2
280
5
m)4
6
16
n)  1
63
1
o)  5
3
p)
k )1
Laws of Exponents
1. B = 3 e = 7
2. 39
b=-2 e = 5
28
B = 3 e = -2
X10
B = x e=-2
-38
B=2y e=3
3. 21
4. X10
5. 9x2
55
A12
A6b10
X2
38
512x16y12
a11
48
221
6. 1
1
7.
9
8. 16
9. x7y2
1
1
9
16
b2
c2
X2
1
(xy) 3
(-2) 15
16 x 4
36 y 6
1
1
729
1
A2m
37
61
64
80
a7b7c
1
27 a
b
1
1
2 34
1
2(35)
4
B = -5x e=25
Algebra Skills
1.
a) 1 monomial
e) 3 trinomial
b) 2 binomial
f) 2 binomial
c) 1 monomial
g) 3 trinomial
d) 3 trinomial
h) 1 monomial
2.
a) 1
e) 3
b)3
f)5
c)4
g)11
d)9
h)6
3.
a)2
e)5
b)4
f)3
c)5
g)6
d)5
h)9
4.
a)1
e)6
b)2
f)5
c)4
g)3
d)4
h)6
5.
a) 8x-5y+6
b)2a2+3ab+3b2
c)-x2+9xy
d)3a2b+6ab2
e)11+4x -9y
f)2pk-7p2k2+3p2k
g)5a4+3a2+7
h)0
i)5x2y2-7x3y2
j)6ab3-3a2b2
6.
a)8x -12
b)12a2 -15a
c)10a3-6a2+8a
d)5k3-15k2+10k
e)4c3+4c2-8c
f)16x2-17x
g)9a3b4+7a2b3
h)7x-15
i)-15b4-40b3+70b3
j)9x5y7+26x4y5
7.
a)49-4x2
b)a2-16
c)2x2-14x+20
d)8x2+2xy-15y2
e)8n2-18n-35
f)9a2-4c2
g)2x2+2xy-12y2
h)7a2-3a-14
i)15x2+39x-84
j)7x2-2x-11
1
k) x 2  6
6
2
3
5
l) x 2  x 
9
2
4
m)12a4 -a2 -20
8.
a) P = 6x + 20, P = 32 units
A = 2x2+ 17x + 21, A = 63 units2
c) A = .5x2 + 7x + 24, A = 40 u2
b) P = 10x + 12, P = 32 u
A = 6x2 + 5x + 1, A = 35 u2
d) A = x2+ 5.5x+6, A = 21 u2
9.
a)6(2x-3)
b)3(x2-2)
c)2(4x2-x-6)
d)6(y2-2y-1)
e)7(2k2-3k-5)
1
f) ( x  3)
4
g)4x(3x2-2)
h)2a(2a2-4a-1)
i)(6ax)(1-2x)
j)6x2y(2x-3)
k)9ac(a-2-3c)
1
l) xy(2 xy  1)
3
m)(2x-1)(3-4y)
n)(a-3)(x-1)
o)(2x-5y)(3a-1)
p)(x+1)(a2-3a-2)
q)(3x-5)(x-1)
r)(2c+5)(3c-2)
10.
a) (x+5)(x+2)
b)prime
c)(m-12)(m+3)
d)(c+7)(c+8)
e)(c-7)(c-4)
f)(y+7)(y-5)
g)(v+5)(v+3)
h)prime
i)(t-10)(t+3)
Solving Equations (Algebra Skills #2)
1.
a)2
b)5
c)-4
d)-8
e)5
f)-3
g)2
h)3
i)14
j)4
2.
a) let n be the number
n+15
c) 2n - 18
2
1
e) n  n
3
2
g) n+7=2
h)let L be larger and S be smaller
L – S = 10
j) 1st = x, 2nd = x + 1, 3rd = x + 2
l) 1st = x, 2nd = x + 2, sum 2x+2
n) let x be the number, 12x
p) let x be larger, y be smaller,
x + y = 15
k)-3
l)-3
m)-3
2
n)
3
o)1
1
x6
2
d) let n be the number, 2(n-8)
f) let L = length, W= width L- W=60
h) let n be the number, 2n - 8
i) let x be larger and y be smaller,
x + y = 14
k) 1st = x, 2nd = x + 2, 3rd = x + 4,
4th = x + 6
m) 1st = x, 2nd = x +2, 3rd = x + 4,
3(3x+6)
o)let n be the number .10n - 5
b) let x be the number,
3.
a) L=2w, 2L + 2w= P, 6w = P
c) L = 2w-4, 4w-8+2w, P = 6w - 8
e) L – 8 =w, L = w + 8,
P=2w +16+2w, P = 4w + 16
4.
a) let n be the number, 3n – 5 = 10,
n=5
c) 3(n + 5) = -9, n = -8
e) n + 2 = 2n – 5, n = 7
g) 5(n – 3) = 10, n = 5
i) 5n + 2 = 3n + 8, n = 3
k) 2x + 1 = 3x + 3 – 5, x = 3
m) L = 5w, 2L + 2w = 48, L + W = 24
5w + w = 24, w = 6, L = 30
o) .54(38) = n, n = 20.52
b) L = 2w + 6, 4w +12 + 2w,
P = 6w+12
d) L = w + 18, P = 4w + 36
f) w = 3L – 4, P = 8L - 8
n
 7, n  28
4
d) 4 + n = 2n – 6, n = 10
f) 2n – 3=n, n = 3
h) 2(2n+1)= 3(n-5), n = -17
j) 6n – 5=4(n-5)+7, n= - 4
l) 2(n) + (n+1)=7, 3n = 6, n = 2
n) 2w + 2L = 36, w + L = 18, w = L,
L=9
p) 37 = .04x, x = 925
b)
5.
a)
d)
d
v
t
v f  vi
t
a
6.
a) y = 2x – 1
d) y 
3
x3
2
b)
2a
h
ab
e)
H
R
bc 2T
2E
V
M

1 s2
f)
  D  h
k  32

c)
3
x2
2
e) y=-12x +15
b) y 
c) y 
5
x
3
Linear Functions
1. graph of solution to be put in
2. A(1,2), B(4,-2),C(-5,-3), D(-4,2), E(6,0), F(-2,0), G(0,3), H(4,3), I(1,-1),
J(-7,0), K(0,-3)
3. a) rises to the right so positive
b) rises to the left so negative
c) rises to the right so positive
d)rises to the right so positive
e) rises to the left so negative
4. AB = negative
DE = negative
BC = positive
NP = zero
KM = negative
GH = undefined
FD = positive
5.
a) 1
b)
 85
16
c)
1
6
6, 7, and 9
8.
a) m =
2
,b  2
3
b) m 
9. see above solution
3
,b  7
5
c) m=1, b= 0
d) m = 3, b = -5
10. and 13.
11.
2
x5
3
1
c) y 
x4
4
a) y 
b) y  4 x  9
d ) y  x  8
12.
AD  y  8 x  26
4
8
x
3
3
4
LM  y  x  3
3
3
11
KL  y 
x
2
2
3
29
NM  y 
x
2
4
KW  y 
1
7
x
2
2
5
13
BC  y  x 
2
2
2
22
CD  y  x 
5
5
AB  y 
13. see above answer
14. and 15.
16. a) W
b) M
c)Q
17.
a) M(-2,3) A(2,4) T(3,0) H(-3,-2)
M’(3,-2) A’(4,2) T’(0,3) H’(-2,-3)
b) it is a reflection in the line y-x
( x, y )  ( y , x )
c) graph to be inserted
d)S
e)W
f)S
18.
a)
needs to be inserted
graph
T’(-4,-2) A’(0,6) D’(4,-6)
b) lengths increase by a factor of two, the area increases, and angles don’t
change
Congruent Triangles
1a) yes, SSS b) yes, SAS c) no d) yes, SAS e) no
f) yes, SSS g) no h) yes, SAS
2. a) AC = XY, angle C = angle Y, CB = YZ, SAS
b) PR = SR, PQ = QS, QR = QR, SSS
c) TY = KL, angle Y = angle L, RY = JL, SAS
d) BC = DC, angle ACB = angle DCE, AC = CE, SAS
e) AD = CB, AB = CD, BD = DB, SSS
f) WX = YX, angle WXZ = angle YXZ, XZ = XZ, SAS
3. to follow
Similar Triangles