NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Final Exam Multiple Choice Review
Chapter 5
Write the letter for the correct answer in the blank at the right of each question.
1. Simplify (3𝑥 0 )2(2𝑥 4 ).
A 𝑥4
B 12𝑥 4
C 18𝑥 6
D 18𝑥 4
1. _________________
3𝑦 2 𝑧
2. Simplify 15𝑦5 . Assume that no variable equals 0.
𝑧
F 5𝑦 3
G
𝑦3𝑧
5
H 5𝑦 3 z
J
𝑦7𝑧
5
2. _________________
3. Shen is simplifying the expression (3𝑥 4 + 4𝑥 2 )( 𝑥 3 – 2𝑥 2 – 1). Which of the following
shows the correct product?
A 3𝑥 12 – 6𝑥 8 + 4𝑥 6 – 11𝑥 4 – 4𝑥 2
C 3𝑥 7 + 6𝑥 6 – 4𝑥 5 + 11𝑥 4 + 4𝑥 2
7
6
5
4
2
B 3𝑥 – 6𝑥 + 4𝑥 – 11𝑥 – 4𝑥
D 3𝑥 12 – 6𝑥 8 – 11𝑥 4 + 4𝑥 6 – 4𝑥 2
3. _________________
4. Simplify (5m – 9) + (4m + 2).
F 9m – 11
G m – 11
H 9m – 7
J 20𝑚2 – 18
4. _________________
5. Simplify 3x(2𝑥 2 – y).
A 5𝑥 3 + 3xy
B 12x – y
C 6𝑥 2 – 3y
D 6𝑥 3 – 3xy
5. _________________
6. Simplify (𝑥 2 – 2x – 35) ÷ (x + 5).
F 𝑥 2 – x – 30
Gx+5
Hx–7
J 𝑥 3 + 3𝑥 2 – 45x – 175
6. _________________
7. Which represents the correct synthetic division of (𝑥 2 – 4x + 7) ÷ (x – 2)?
A
C
7. _________________
B
D
8. _________________
2
8. Factor 𝑚 + 9m + 14 completely.
F m(m + 23)
G (m + 7)(m + 2)
H (m + 14)(m + 1)
J m(m + 9) + 14
9. _________________
9. Simplify
At–5
Chapter 5
𝑡2
+𝑡−6
.
𝑡−2
Assume that the denominator is not equal to 0.
Bt–2
Ct–3
61
Dt+3
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
10. Find p(–3) if p(x) = 4 – x.
F 12
G4
10. _________________
H1
J7
11. _________________
11. State the number of real zeros for the function
whose graph is shown at the right.
A0
C2
B1
D3
For Questions 12 and 13, use the graph shown at the right.
12. Determine the values of x between which
a real zero is located.
F between –1 and 0
G between 6 and 7
H between –2 and –1
J between 2 and 3
12. _________________
13. Estimate the x-coordinate at which a relative minimum occurs.
A3
B2
C0
13. _________________
D –1
14. Write the expression 𝑥 4 + 5𝑥 2 – 8 in quadratic form, if possible.
F (𝑥 2 )2 + 5(𝑥 2 ) – 8
H (𝑥 4 )2 + 5(𝑥 4 ) – 8
2 2
2
G (𝑥 ) – 5(𝑥 ) – 8
J not possible
15. Solve 𝑥 4 – 13𝑥 2 + 36 = 0.
A –3, –2, 2, 3
B –9, –4, 4, 9
14. _________________
15. _________________
C 2, 3, 2i, 3i
16. Use synthetic substitution to find f(3) for f(x) = 𝑥 2 – 9x + 5.
F –23
G –16
H –13
D –2, –3, 2i, 3i
16. _________________
J 41
17. One factor of 𝑥 3 + 4𝑥 2 – 11x – 30 is x + 2. Find the remaining factors.
A x – 5, x + 3
B x – 3, x + 5
C x – 6, x + 5
D x – 5, x + 6
17. _________________
18. Which describes the number and type of roots of the equation 4x + 7 = 0?
F 1 imaginary root
H 1 real root and 1 imaginary root
G 2 real roots
J 1 real root
18. _________________
19. Which is not a root of the equation 𝑥 3 – 𝑥 2 – 10x – 8 = 0?
A1
B4
C –2
D –1
20. _________________
20. Find all the rational zeros of p(x) = 𝑥 3 – 12x – 16.
F –2, 4
G 2, –4
H4
Chapter 5
19. _________________
J –2
62
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Chapter 6
Write the letter for the correct answer in the blank at the right of each question.
1. ______________
For Questions 1 and 2, use f(x) = x + 5 and g(x) = 2x.
1. Find (f + g)(x).
A 3x + 5
Bx+5
C 2x + 10
D 2𝑥 2 + 5
2. Find (f ⋅ g)(x).
F 2𝑥 2 + 5
G 3𝑥 2 + 10x
H 2𝑥 2 + 10x
J 2x + 10
2. ______________
3. ______________
3. If f(x) = 3x + 7 and g(x) = 2x – 5, find g[f(–3)].
A –26
B –9
C –1
D 10
4. ______________
4. If f(x) = 𝑥 2 and g(x) = 3x – 1 find [ g ◦ f](x).
F 𝑥 2 + 3x – 1
H 9𝑥 2 – 1
G 9𝑥 2 – 6x + 1
J 3𝑥 2 – 1
5. ______________
5. Find the inverse of g(x) = –3x.
A 𝑔−1 (x) = x + 1
C 𝑔−1 (x) = x – 1
B 𝑔−1 (x) = –3x – 3
D 𝑔−1 (x) = – 3x
1
6. Determine which pair of functions are inverse functions.
F f(x) = x – 4
g(x) = x + 4
H f(x) = x – 4
g(x) = 4x – 1
G f(x) = x – 4
J f(x) = 4x – 1
g(x) =
𝑥–4
4
6. ______________
g(x) = 4x + 1
7. State the domain and range of the function graphed.
A D = {x │ x > 2}, R = {y │ y > 0}
7. ______________
B D = {x │ x < 2}, R = {y │ y > 0}
C D = {x │ x ≥ 2}, R = {y │ y < 0}
D D = {x │ x ≥ 2}, R = {y │ y ≥ 0}
8. Which inequality is graphed?
F y ≤ √4𝑥 + 8
8. ______________
G y > √4𝑥 + 8
H y < √4𝑥 + 8
J y ≥ √4𝑥 + 8
9. Simplify √121.
A 11
Chapter 5
9. ______________
B –11
D √11
C ±11
62
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
10. Use a calculator to approximate √224 to three decimal places.
F 15.0
G 14.97
H 14.966
J 14.967
C –1 + √5
D –1 – √5
H 10√3
J 7√3
10. _____________
11. Simplify (2 + √5)(3 – √5).
A 1 + √5
B 1 – √5
11. _____________
12. Simplify √75 + √12.
F 21
G √87
12. _____________
1
13. Write the expression 57 in radical form.
7
A √51
7
5
C √5
B 35
2
D √7
13. _____________
1
14. Simplify the expression 𝑚5 • 𝑚5 .
5
3
2
2
F 𝑚3
G 𝑚5
H 𝑚25
J 𝑚5
B7
C 21
D
Hx<2
Jx>2
14. _____________
15. Solve √3𝑥 + 4 = 5.
A –7
25
3
15. _____________
16. Solve 2 + √5𝑥 − 1 > 5.
Fx>5
G x > –2
17. Gilda used the formula f(x) =
Find the inverse of 𝑓 −1 (x).
A 𝑓 −1 (x) = 12x
𝑥
144
to convert square inches to square feet.
B 𝑓 −1(x) = 144x
5
16. _____________
C𝑓 −1(x) =
144
𝑥
D 𝑓 −1(x) = (12𝑥 2 )
17. _____________
1
18. If x is a positive number, then √𝑥 ÷ 𝑥 5 = ?
A 𝑥5
1
5
B x
C1
D
1
5
18. _____________
19. If 28 • y = 25 , then y = ?
F –2−3
Chapter 5
G –23
19. _____________
1
J 2−3
H 23
62
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Chapter 7
Write the letter for the correct answer in the blank at the right of each question.
1. Find the domain and range of the function whose
graph is shown.
A D = {x | x > 0}; R = {y | y > 0}
1. ____________
B D = {all real numbers}; R = {y | y > 0}
C D = {x | x > 0}; R = {all real numbers}
2. ____________
D D = {all real numbers}; R = {y | y < 0}
2. Which function represents exponential growth?
1 𝑥
3
G y = 4𝑥 4
F y = 9( )
1 𝑥
5
H y = 12( )
J y = 10(3)𝑥
3. ____________
3. Solve 8𝑥 + 2 = 322𝑥 + 4 .
F –2
G –1
H0
J1
4. Write the equation 43 = 64 in logarithmic form.
F log 4 3 = 64
G log 3 4 = 64
H log 64 4 = 3
4. ____________
J log 4 64 = 3
5. Write the equation log12 144 = 2 in exponential form.
A 1442 = 12
B 122 = 144
6. Evaluate log 2 8.
F3
7. Solve log 3 𝑛 = 2.
A6
5. ____________
C 212 = 144
D 14412 = 2
6. ____________
G4
H 16
J 64
7. ____________
B5
C8
D9
8. ____________
8. Solve log 2 2m > log 2 (𝑚 + 5).
5
F {𝑥 | 𝑚 > 3}
Chapter 5
G {x | m < 5}
H {x | m > 5}
62
J {x | m > –5}
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
9. __________
9. Use log 5 2 ≈ 0.4307 to approximate the value of log 5 4.
A 0.8614
B 0.8980
C 1.3652
D 0.1855
10. Solve log 6 10 + log 6 𝑥 = log 6 40.
F 180
G4
J 30
10. __________
H5
11. __________
11. Solve 4𝑥 = 20. Round to the nearest ten-thousandth.
A 0.4628
B 1.5214
C 0.6990
D 2.1610
12. Solve 3𝑥 ≥ 21. Round to the nearest ten-thousandth.
F {x | x ≥ 0.8451} G {x | x ≥ 2.7712}
H {x | x ≥ 0.3608}
12. __________
J {x | x ≥ 7.0000}
13. Express log 9 22 in terms of common logarithms.
A log
22
9
14. Solve ln 3𝑥 = 1.
F 20.0855
B log 198
C
13. __________
log 22
log 9
D
log 9
log 22
14. __________
G 0.3333
H 0.9061
J 8.1548
15. AUTOMOBILES Lydia bought a car for $20,000. It is expected to depreciate at a continuous
rate. What will be the value of the car in 2 years? Use k = 0.105 and round to the nearest dollar.
A $16,212
B $16,012
C $19,867
D $18,567
16. ART Martin bought a painting for $5000. It is expected to appreciate at a continuous rate of 4%.
How much will the painting be worth in 6 years? Round to the nearest cent.
F $6200.00
G $5360.38
H $37,647.68
J $6356.25
Chapter 5
62
15. __________
16. __________
Glencoe Algebra 2