Download MathB70 Review KEY I. Algebraic Expressions 1) Simplify: 6−4∙8

MathB70 Review KEY
I.
Algebraic Expressions
1) Simplify: 6 − 4 ∙ 8 − 12
6 – 32 – 12
–26 – 12
–38
2) Simplify: 59 + 32 ÷ 8 ∙ 6
59 + 4 · 6
59 + 24
83
3) Multiply: 16(14p + 5)
224p + 80
4) Multiply: −12ሺ‫ ݍ‬− 7ሻ
–12q + 84
5) Simplify: 52x – (24x + 13)
28x – 13
6) Simplify: 7‫ ݔ‬ହ − 3‫ ଼ ݔ‬− 6‫ ݔ‬ହ + 4‫଼ ݔ‬
ଷ
ଵ
7) Simplify: −‫ ݔ‬+ ସ + 73‫ ݔ‬ଶ − ‫ ݔ‬− ଶ − 5‫ ݔ‬ଶ
‫ ଼ݔ‬+ ‫ݔ‬ହ
68‫ ݔ‬ଶ − 2‫ ݔ‬+
1
4
8) Add: ሺ9‫ ݔ‬ଶ − 2‫ ݔ‬+ 17ሻ + ሺ8‫ ݔ‬ଶ + 6‫ ݔ‬− 53ሻ
17‫ ݔ‬ଶ + 4‫ ݔ‬− 36
9) Subtract: ሺ5‫ ݔ‬ସ + 9‫ ݔ‬ଷ − 1ሻ − ሺ7‫ ݔ‬ଶ − 9‫ ݔ‬+ 1ሻ
5‫ ݔ‬ସ + 9‫ ݔ‬ଷ − 1 − 7‫ ݔ‬ଶ + 9‫ ݔ‬− 1
5‫ ݔ‬ସ + 9‫ ݔ‬ଷ − 7‫ ݔ‬ଶ + 9‫ ݔ‬− 2
10) Multiply: 2‫ݔ‬ሺ6‫ ݔ‬ଶ − 8‫ ݔ‬+ 9ሻ
11) Multiply: ሺ‫ ݔ‬ଶ + ‫ ݔ‬+ 8ሻሺ‫ ݔ‬− 8ሻ
12) Multiply: ሺ‫ ݔ‬+ 4ሻሺ‫ ݔ‬− 4ሻ
13) Multiply: ሺ5‫ ݔ‬+ 4ℎሻଶ
12‫ ݔ‬ଷ − 16‫ ݔ‬ଶ + 18‫ݔ‬
‫ ݔ‬ଷ − 8‫ ݔ‬ଶ + ‫ ݔ‬ଶ − 8‫ ݔ‬+ 8‫ ݔ‬− 64
‫ ݔ‬ଷ − 7‫ ݔ‬ଶ − 64
‫ ݔ‬ଶ − 16
ሺ5‫ ݔ‬+ 4ℎሻሺ5‫ ݔ‬+ 4ℎሻ
25‫ ݔ‬ଶ + 20ℎ‫ ݔ‬+ 20ℎ‫ ݔ‬+ 16ℎଶ
25‫ ݔ‬ଶ + 40ℎ‫ ݔ‬+ 16ℎଶ
1
=
14) Evaluate the polynomial for x = 7.
II.
3‫ ݔ‬ଶ − 2‫ ݔ‬+ 4
3ሺ7ሻଶ − 2ሺ7ሻ + 4
3 ∙ 49 − 14 + 4
147 − 14 + 4
137
15) Evaluate the polynomial when x = 9 and y = –2.
‫ ݔ‬ଶ + ‫ ݕ‬ଶ + ‫ݕݔ‬
ሺ9ሻଶ + ሺ−2ሻଶ + ሺ9ሻሺ−2ሻ
81 + 4 − 18
67
Linear Equations of Two-Variables
16) Plot the following points. A) (3,2) B) (–4, –5) C) (2, –6) D) (–3, 3)
17) Determine whether (–8, –3) is a solution of 8x + 2y = –7.
8(-8)+2(-3) = -7
-64 – 6 = -7
-70 = -7
NO
2
ଵ
18) Graph the equation ‫ ݔ = ݕ‬− 2.
ଷ
19) Graph the equation y = –6x.
20) Find the slope to the line that goes through the given points.
ሺ3,1ሻ ܽ݊݀ ሺ7,10ሻ
‫ݕ‬ଶ − ‫ݕ‬ଵ 10 − 1 9
݉=
=
=
‫ݔ‬ଶ − ‫ݔ‬ଵ
7−3
4
21) Find the slope and y-intercept of the line y = –4x – 8.
Slope = –4, y-intercept (0,–8)
22) Find the slope and y-intercept of the line 6x + 3y = 6.
3y = –6x + 6
y = -2x + 2
slope = -2, y-intercept (0,2)
3
23) Use the intercepts to graph the equation 3x + 4y = 12.
x-intercept (4,0)
y-intercept (0,3)
24) Use the intercepts to graph the equation 8x – 5y = 40.
x-intercept (5,0)
y-intercept (0,-8)
III.
Factoring
Factor Completely
ଷ
25) ૠ݉ ݊ − 35݉ଶ ݊ଶ + 21݉݊
26) ܿ ଶ + 144 − 24ܿ
27) 8ܿ ଷ + 1
28) ‫ ݏ‬ଶ + 13‫ ݏ‬+ 30
ૠ࢓࢔ሺ࢓૛ − ૞࢓࢔ + ૜ሻ
ܿ ଶ − 24ܿ + 144
ሺܿ − 12ሻሺܿ − 12ሻ
ሺ2ܿ + 1ሻሺ4ܿ ଶ − 2ܿ + 1ሻ
(s + 3)(s + 10)
4
29) 15‫ ݕ‬ଶ + 11‫ ݕ‬+ 2
(5y + 2)(3y + 1)
ଷ
ଶ
30) ‫ ݎ‬− 6‫ ݎ‬− 36‫ ݎ‬+ 216
31) ‫ ݏ‬ଶ − 2‫ ݏ‬− 63
IV.
‫ ݎ‬ଶ ሺ‫ ݎ‬− 6ሻ − 36ሺ‫ ݎ‬− 6ሻ
ሺ‫ ݎ‬− 6ሻሺ‫ ݎ‬ଶ − 36ሻ
ሺ‫ ݎ‬− 6ሻሺ‫ ݎ‬− 6ሻሺ‫ ݎ‬+ 6ሻ
(s + 7)(s – 9)
Solving
Solve the following
32) −40 + ‫ = ݕ‬41
+40
+40
y = 81
33) 7‫ ݔ‬+ 7 = 35
-7
-7
7x
= 28
x =
4
34) 9‫ ݕ‬− 3 = 19 − 2‫ݕ‬
+2y +3
+3 +2y
11y
= 22
y=2
35) 2ሺ‫ ݔ‬− 6ሻ + 8 = 4ሺ‫ ݔ‬+ 2ሻ − 6
2x – 12 + 8 = 4x + 8 – 6
2x – 4 = 4x + 2
-4x +4 -4x +4
-2x
=
6
x = -3
36) ܵ = 6ߨ‫ ݀ݒ‬+ 6ߨ‫ ݒ‬ଶ ݂‫݀ ݎ݋‬.
37) 7 − 4‫ > ݔ‬1 − 3‫ݔ‬
-7 +3x
-7 +3x
-x
> -6
x
< 6
ଶ
38) 5ܾ − 24 = 26ܾ
ܵ − 6ߨ‫ ݒ‬ଶ = 6ߨ‫݀ݒ‬
ܵ − 6ߨ‫ ݒ‬ଶ
݀=
6ߨ‫ݒ‬
5ܾ ଶ − 26ܾ − 24 = 0
ሺ5ܾ + 4ሻሺܾ − 6ሻ = 0
4
ܾ=− , ܾ=6
5
5
‫‪ − 3 = 12‬ݔ‪ ଶ + 2‬ݔ‬
‫‪ − 15 = 0‬ݔ‪ ଶ + 2‬ݔ‬
‫‪ − 3ሻ = 0‬ݔ‪ + 5ሻሺ‬ݔ‪ሺ‬‬
‫‪ = −5,‬ݔ‬
‫‪=3‬ݔ‬
‫‪ + 3ሻ = 12‬ݔ‪ − 1ሻሺ‬ݔ‪39) ሺ‬‬
‫‪ − 54 = 0‬ݒ‪ ଶ + 3‬ݒ )‪40‬‬
‫‪(v – 6)(v + 9) = 0‬‬
‫‪v = 6, v = -9‬‬
‫‪=1‬‬
‫‪6‬‬
‫‪24‬‬
‫‪−‬‬
‫‪=1‬‬
‫‪ − 2ሻ‬ݕ‪ + 2ሻሺ‬ݕ‪ − 2 ሺ‬ݕ‬
‫‪24‬‬
‫‪6‬‬
‫‪ − 2ሻ ൤‬ݕ‪ + 2ሻሺ‬ݕ‪ሺ‬‬
‫‪−‬‬
‫‪ − 2ሻ‬ݕ‪ + 2ሻሺ‬ݕ‪൨ = 1ሺ‬‬
‫‪ − 2ሻ‬ݕ‪ + 2ሻሺ‬ݕ‪ − 2 ሺ‬ݕ‬
‫‪ ଶ − 4‬ݕ = ‪ + 2ሻ − 24‬ݕ‪6ሺ‬‬
‫‪ ଶ − 4‬ݕ = ‪ + 12 − 24‬ݕ‪6‬‬
‫‪ ଶ − 4‬ݕ = ‪ − 12‬ݕ‪6‬‬
‫‪ + 8‬ݕ‪ ଶ − 6‬ݕ = ‪0‬‬
‫‪ − 4ሻ‬ݕ‪ − 2ሻሺ‬ݕ‪0 = ሺ‬‬
‫‪ = 4‬ݕ ‪ = 2,‬ݕ‬
‫‪݊.‬݋݅ݐݑ݈݋ݏ ݕ݈݊݋ ݏ݅ ‪ = 4‬ݕ ‪,‬ݏݑ݋݁݊ܽݎݐݔ݁ ݏ݅ ‪ = 2‬ݕ‬
‫‪6‬‬
‫‪ଶସ‬‬
‫‪௬ మ ିସ‬‬
‫‪−‬‬
‫଺‬
‫‪௬ିଶ‬‬
‫)‪41‬‬