Course Name: Advanced Algebra 1 (2nd Year
Algebra 1)
Student: Devin Vega
Course ID:
MTHH039058
ID: H56683935
Submittal:
59
Progress Test 3
Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book test. It is
important that you do your own work. Select the response that best completes the statement or answers the question.
For some questions, you will be solving systems by either graphing, substitution, or linear combinations. You are free to
decide which method you would like to use if one is not specified. Your graphing calculator may be used on this progress
test. You may also use scratch paper to work out the solutions.
____ 1.
____ 2.
Find f-1 if f(x) =
a.
f-1 = x2 + 9
b.
f-1 =
c.
f-1 = x2 − 16; x ≥ 0
d.
f-1 = x − 9
The function d = 16t2 models the distance d in feet that an object falls in t seconds. Express t in terms of d.
a.
b.
c.
d.
____ 3.
Write this polynomial in standard form: 5c 2 – 6 + 4c + 12
a.
5c 2 + 4c + 6
b.
5c 2 + 4c + 18
c.
9c 2 + 6
c + 18
d.
____ 4.
Write this expression in simplest from:
a.
b.
c.
d.
____ 5.
Let f(x) = x3 and g(x) = 3x – 1. Evaluate
a.
b.
c.
d.
____ 6.
Identify this function by type: y = x + 3
a.
b.
c.
d.
____ 7.
____ 8.
linear
quadratic
cubic
constant
Find the roots of this equation: 3x4 – x3 – 22x2 + 24x = 0.
a.
–3i, 2i, i, 0
b.
±3, ±
c.
d.
–3, 0, 2, 4
–3, 0, 2,
Solve this equation and check for extraneous solutions:
a.
b.
c.
d.
____ 9.
512
23
125
400
x = 1, 3
x = -1, -3
x = -1, 3
x = 1, -3
Solve this equation: x 2 = –6.
a.
b.
c.
d.
There is no solution.
-3, -2
.
____ 10. Divide (x3 + 3x2 − 7x − 21) ÷ (x + 4).
a.
x2 + 7
b.
x2 – 3x + 7
c.
x2 – 7
d.
x2 – 4
____ 11. Multiply and simplify:
a.
b.
9
c.
d.
____ 12. What is the discriminant of this equation? 3x2 = 8x – 4
a.
b.
c.
d.
112
16
-16
-48
____ 13. Factor this expression: 3x 2 − 5x + 2.
a.
b.
c.
d.
(3x – 2)(x – 1)
(3x – 1)(x – 2)
(3x + 1)(x + 2)
(3x – 2)(x + 1)
____ 14. Evaluate 8P4.
a.
b.
c.
d.
32
720
210
1680
____ 15. Solve this equation and check for extraneous solutions:
a.
b.
c.
d.
.
x=5
x = 10
x = 10, -1
x = 2, 5
____ 16. The lengths of the sides of a right triangle are x, x + 2, and x + 4 inches. What is the value of x?
a.
b.
c.
d.
x
x
x
x
=5
=6
=7
=8
____ 17. Given these zeros, write a polynomial function in standard form for: x = -2, 1, 2, 2.
a.
y = x 4 – 3x 3 – 2x 2 + 12x – 8
b.
y = x 4 – 2x 2 + 12x – 8
c.
y = x 4 + 3x 3 + 2x 2 – 12x + 8
d.
y = x4 – 8
____ 18. Solve this expression: x 2 − 11x + 24 = 0.
a.
b.
c.
d.
x = 3, 8
x = -3, -8
x = 3, -8
x = -3, 8
____ 19. Divide (x 3 + 12x + 11) ÷ (x + 2).
a.
x 2 + 4x – 8, R 13
b.
x 2 – 2x + 16, R 43
c.
x 2 – 2x + 16 R -21
d.
x 2 – 8, R 12
____ 20. Identify this function by type: 3x + 2y = 1.
a.
b.
c.
d.
linear
quadratic
cubic
quartic
____ 21. Factor this expression: x 2 – 36.
a.
b.
c.
d.
(x – 6)(x – 6)
(x + 6)(x + 6)
(x – 6)(x + 6)
(x – 9)(x + 4)
____ 22. Solve w4 – 136w2 + 3600 = 0.
a.
b.
c.
d.
±6i, ±10i
6, 10, 6i, 10i
±6, ±10
6, 10
____ 23. Write this polynomial in standard form: 4n2 + 3n3 – 2 + 5n + 6n2
a.
3n3 + 10n2 + 5n – 2
b.
13n3 + 5n – 2
18n – 2
c.
d.
3n3 + 15n2 – 2
____ 24. Simplify this expression: (2 − 4i) − (7 − 3i).
a.
b.
c.
d.
-5 – i
5–i
-5 – 7i
9 – 7i
____ 25. Simplify this expression: (8 – 6i) + (1 – 2i).
a.
b.
c.
d.
7 – 4i
9 – 8i
9 + 8i
9 – 4i
____ 26. Hal’s sister is 6 years older than Hal. The product of their ages is 475. How old are Hal and his sister?
a.
b.
c.
d.
Hal is 5, his sister is 95
Hal is 19, his sister is 25
Hal is 15, his sister is 21
Hal is 13, his sister is 19
____ 27. Evaluate 6C2.
a.
b.
c.
d.
15
12
4
8
____ 28. Let f(x) = x 2 and g(x) = 3x + 1. Evaluate
a.
b.
c.
d.
29
76
256
32
____ 29. Solve this expression: 4x 2 – 64 = 0.
a.
b.
c.
d.
x = ±4
x=8
x = ±8
x = 2, 32
____ 30. Expand this binomial: (x – 1)3.
a.
x3 – 3x2
b.
x3 – 1
c.
x3 + 3x2 − 3x + 1
d.
x3 − 3x2 + 3x − 1
____ 31.
Divide and simplify:
a.
b.
c.
d.
____ 32. Simplify
a.
b.
c.
d.
+
.
15
____ 33. Solve by completing the square: x 2 – 14x – 44 = 0.
a.
b.
-4, 10
7±
c.
d.
4, -10
–7 ±
____ 34. Expand this binomial: (3x – 2)4.
a.
81x4 + 16
b.
81x4 + 216x3 – 216x2 + 96x – 16
c.
27x4 + 54x3 – 54x2 + 18x – 16
d.
81x4 – 216x3 + 216x2 – 96x + 16
____ 35. A total of 10 students will be coming to the end-of-the-year picnic. In how many ways can the teacher select
3 students for the clean-up crew?
a.
b.
c.
d.
120 ways
720 ways
30 ways
90 ways
____ 36. Given these zeros, write a polynomial function in standard form: x = 0, 2, -3,
a.
y = x 3 + 2x 2 – 3x + 6
b.
y = x 3 + x 2 – 6x
c.
y = x 3 + 5x + 6
d.
y = x2 + x – 6
____ 37. Factor this expression: x 2 − 3x – 28.
a.
b.
c.
d.
(x – 2)(x + 14)
(x – 4)(x + 7)
(x + 4)(x – 7)
(x + 2)(x – 14)
____ 38. Find the roots of this equation: x3 + 3x2– 2x – 6 = 0.
a.
-3, ±i
b.
c.
-3, ±3i
3, ±i
d.
-3, ±
____ 39. Simplify
+
.
a.
b.
c.
d.
____ 40. You must answer exactly 12 out of 15 questions on a test. How many different ways can you select the
questions to answer?
a.
b.
c.
d.
455 ways
2000 ways
180 ways
27 ways
____ 41. Factor this expression: 25x 2 + 70x + 49.
a.
b.
c.
d.
(5x – 7)(5x + 7)
(5x + 7)(5x + 7)
(5x – 7)(5x – 7)
(25x + 49)(x + 1)
____ 42. Find f-1 if f(x) = 2 – x2.
a.
f-1 = x2 – 2
b.
f-1 = 2 – x
c.
f-1 = ±
d.
f-1 =
;x≥2
____ 43. What is the discriminant of this equation? x2 – 16x + 4 = 0
a.
b.
c.
d.
240
0
-272
27
____ 44.
Write this expression in simplest form:
a.
b.
c.
d.
____ 45. Simplify this radical:
a.
64x7
b.
64x36
c.
4|x36|
d.
4|x7|
.
____ 46. Evaluate 3!4!.
a.
b.
c.
d.
288
144
36
12
____ 47. Simplify this radical:
.
a.
-3k 3
b.
3k 3
c.
-81k 10
This radical does not simplify.
d.
____ 48. How many ways are there to choose six shirts out of nine to take to camp?
a.
b.
c.
d.
144
54
84
60,480
____ 49. Let f(x) = 3x – 1 and g(x) = x3. Evaluate
a.
b.
c.
d.
12
16
2
8
____ 50. Solve this equation: x 2 + 81 = 0.
a.
b.
c.
d.
±9i
±81i
±9
no solution
Carefully review your answers on this progress test and make any corrections you feel are necessary. When
you are satisfied that you have answered the questions to the best of your ability, transfer your answers to the
online test submission page in the presence of your proctor.
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