Download Algebra 2 - Formulas for Chapter 12

Algebra 2 Midterm Review ANSWER KEY
Chapter 9 Review: Sequences and Series
1.
Arithmetic ( d  0.5 )
2.
Neither
3.
Geometric ( r  0.5 )
4.
4, 1, 2,5
5.
5, 2,1, 4
6.
an  12   n 1 40
7.
an  4  5 
8.
an  127   n 1 5
n 1
9.
an  6  4 
n 1
a10  1,572,864
10. 360
11. huge number: 1,741,425,868
12. 157,305, 453
13. 52, 26
a10  348
14. 2585
a10  7,812,500
15. 364
a10  82
16. 7.5
17. 16,598
Chapter 1 Review: Solving Eqs & Ineqs
1. a) a  6
b) x  2, x  
2. a) x  7
(graph below should have open circle)
b) 87 2  x  2
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
c) x  7 or x  3
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
3. C
5
4. C   F  32 
9
5. a.
b.
c.
d.
Distributive Property
Commutative Property of Multiplication
Symmetric Property
Inverse Property of Addition
6. 26
9
8
3
y
6
5
4
3
2
1
-9 -8-1
-2-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-3
-4
9 y
-5
8
-6
7
-7
6
-8
5
-9
4
3
2
1
-1
-9 -8-2-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-3
-4
-5
-6
-7
-8
-9
1
3
d)   x 
2
2
7. Given
Addition Property
Multiplication Property
Substitution Property
Addition Property
Addition Property
Division Property
Symmetric Property
8. B, C, D, E
9
8
7
6
5
4
3
2
1
-1
-2
-3
-4
9
-5
8
-6
7
-7
6
-8
5
-9
4
3
2
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
y
y
Algebra 2 Midterm Review ANSWER KEY
Chapter 2 Review: Linear Functions
2
1. a) y   x  4
b) f  x   3x
3
2
Slope = 
Slope = 3
3
y-int: -4
y-int: 0
y
c) x  2
Slope: undefined
y-int: none
y
x
x
d) 2 x  5 y  10
2
Slope:
5
y-int: -2
e) 6 y  3 x  18
1
Slope: 
2
y-int: -3
y
y
x
2. x-intercept: - 4
x
y-intercept: 2
3. a) Not a function, x-values repeat
b) Function, passes Vertical Line Test
4. a) y 
y
2
x 3
3
5. y  3x  56
1
x  0.35
4
b) 15 ounces
6. a) y 
7. shift left 2, shift up 4
b) y  4 x  15
x
8. a)
y   x4
b) y  2 x  5
y
y
x
9. a) g  x   f  x  2  3
Shift left 2, shift down 3
x
b) g  x    f  x 
Reflect in x-axis (or flip graph upside down)
y
y
x
10.
a)
b)
c)
d)
x
Positive
y  1.71x  53.57
87.77
3.76
11. a) y  .375 x  722.25
b) 31.5 million
12. a) 5,1
3
 7
b)  , 2, 
2
 2
13. a) Yes, function; Domain: all real numbers; Range: y  0
b) Yes, function ; Domain: all real numbers; Range: y  0
c) Not a function; Domain: 1  x  3
Range: 0  y  4
Algebra 2 Midterm Review ANSWER KEY
Chapter 4 Review: Quadratics
1. a) y  x 2  6 x  7
V : 1,3
axis : x  3
x  int : 1 and 7
y  int : 7
axis : x  1
x  int : .22 and 2.22
y  int :1
D : x |   x  
D : x |   x  
R :  y | 16  y  
R :  y |   y  3
-9 -8 -7 -6 -5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-12
-14
-16
-18
y
y
x
x
1 2 3 4 5 6 7 8 9
 x 14 x  2
b) 2  2 x  3 3x  4 
d) can’t be factored
e)
c) 9  4 x  3 4 x  3
 4x  5 x  9
b) x  4, x 
3. a) x  4, x  5
4.
2
V :  3, 16 
18
16
14
12
10
8
6
4
2
2. a)
b) f  x   2  x  1  3
 2, 6
1
3
5. y  x 2  3x  18
6. y  .004 x 2  .352 x  .369
7. a) x 
1 5
2
b) x  2
c) x  5  38
d) x 
3  233
16
d) x 
4  i 26
7
8. B
9. a)  i
b) 1
10. a) 2  5i
b) 14  2i
11. a) x  9i
12.
 1, 10 and  4,30
13.
 7, 6 and  2,12
c) i
c)
d) 1
1 7
 i
4 4
b) x  i 26
c) x  2  i 6
14. B and D
15. a) 6.94 seconds
b) 236 meters
c) 13.9 seconds
Algebra 2 Midterm Review ANSWER KEY
Chapter 5 Review (Sections 5.1 & 5.2): Polynomial Functions
1. Standard form: 4𝑥 3 + 2𝑥 2 − 3, degree = 3, cubic trinomial
2. Standard form: −𝑥 5 + 9𝑥 2 − 2𝑥 + 8, degree = 5, quantic polynomial of 4 terms
3. Standard form: 2𝑥 4 + 6𝑥 − 2, degree = 4, quartic trinomial
4. Standard form: 24𝑥 2 + 3, degree = 2, quadratic binomial
5. Left: As 𝑥 → −∞, 𝑓(𝑥) → −∞.
Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞.
6. Left: As 𝑥 → −∞, 𝑓(𝑥) → ∞.
Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞.
7. Left: As 𝑥 → −∞, 𝑓(𝑥) → −∞.
Right: As 𝑥 → ∞, 𝑓(𝑥) → −∞.
8. Left: As 𝑥 → −∞, 𝑓(𝑥) → ∞.
Right: As 𝑥 → ∞, 𝑓(𝑥) → −∞.
9. Left: As 𝑥 → −∞, 𝑓(𝑥) → −∞.
Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞.
10. Left: As 𝑥 → −∞, 𝑓(𝑥) → ∞.
Right: As 𝑥 → ∞, 𝑓(𝑥) → −∞.
11. zeros: -2, -3
y-int: (0, 6)
12. zeros: 0, 1, -3
y-int: (0,0)
End Behavior:
Left: As 𝑥 → −∞, 𝑓(𝑥) → ∞.
Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞.
End Behavior:
Left: As 𝑥 → −∞, 𝑓(𝑥) → −∞.
Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞.
13. rel. min = (-.27, -3.83), rel. max = (2.49, 27.63), Increasing: (-.27, 2.49), Decreasing:
(−∞, −.27) and (2.49, ∞)
14. rel. min = (.12, .94), rel. max = (-2.79, 13.21), Increasing: (−∞, −2.79) and (. 12, ∞),
Decreasing: (−2.79, .12)
15. Positive coefficient and odd degree
16. Negative coefficient and odd degree