Algebra Linear Equations Question

Course Name: Second Year Algebra 1Course ID: MTHH039059
Student: Daimon Gardner
Student ID: G83165467
Generated Date: September 15, 2021
Progress Test 3
This Progress Test covers the course materials that were assigned in Units 5, 6, and 7.
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. Your graphing calculator may
be used on this progress test. You may also use scratch paper to work out the solutions.
____ 1. Solve this equation and check for extraneous solutions
A. x = −1
B. x = –1, −
C. x = −
D. x = 1,
____ 2. Solve w4 – 136w2 + 3600 = 0.
A. ± 6i, ± 10i
B. 6, 10, 6i, 10i
C. ± 6, ± 10
D. 6, 10
____ 3. Expand this binomial (x – 2)3.
A. x3 – 6×2 + 12x – 8
B. x3 + 6×2 – 12x + 8
C. x3 – 8
D. x3 – 6×2
.
____ 4. Find a fourth degree polynomial equation with rational coefficients that has
roots −1 multiplicity of 2 and 1 – 4i.
A. x4 – 18×2 – 32x – 15
B. x4 + 14×2 + 32x + 17
C. x4 + 2×3 + 6×2 + 32x + 40
D. x4 + 4×3 + 2×2 + 12x + 45
____ 5. Simplify this expression
.
A. 6
B. −6
C. 9
D. −12
____ 6. Given these zeros, write a polynomial function in standard form x = 1, 1, 2.
A. y = (x – 1)(x – 1)(x – 2)
B. y = x3 + 5x – 2
C. y = x3 – 4×2 + 5x – 2
D. y = −x3 + 4×2 – 5x + 2
____ 7. Find the difference
–
.
A.
B.
C.
D.
____ 8. Simplify this radical
.
A. −3k3
B. 3k3
C. −81k10
D. This radical does not simplify.
____ 9. What is the remainder when the expression x2 – 6x + 11 is divided by x – 6?
A. 11
B. 13
C. −11
D. 0
____ 10. Find the roots of this equation x3 + 3×2 + 4x + 12 = 0.
A. −3, ± 2i
B. 3, ± 2i
C. −3, ± i
D. 3, ± i
____ 11. State the number of roots for this function 4×6 – x5 – 24 = 0.
A. 3
B. 4
C. 5
D. 6
____ 12. Two hotels in a city are booked for a night. Matrix A shows the number of
single and double rooms for each hotel. Matrix B shows the cost for each type
of room. What is the product AB of these matrices?
Rows are motel 1 and motel 2.Rows are single and double rooms.
Columns are single and double rooms. Column is cost.
A.
B.
C.
D.
____ 13. Margery got a total of 237 points on three tests. The combined scores on the
first and third tests were 67 more than the score on the second test. The
score on the third test was 8 points more than the score on the first test.
Write a matrix equation for this situation.
A.
B.
C.
D.
____ 14. Simplify 3
+6
.
A. 9
B. 18
C. 19
D. 9
____ 15. Write this expression in simplest from
A.
B.
C.
D.
____ 16.
Divide and simplify
A. 2×4
B. 4×4
C. 4×3
D. 2×3
.
.
____ 17. What are the zeros of the polynomial function y = (x + 3)(2x – 1)(x – 1)?
A.
, 1, 3
B. −1, 1, 3
C. − , 1, 3
D. −3,
,1
____ 18. Write this expression in simplest form
.
A. −2×5
B.
C. 2×5
D.
____ 19. State the dimensions of the given matrix.
A. 2 x 4
B. 3 x 5
C. 4 x 2
D. 7 x 2
____ 20. Given these zeros, write a polynomial function in standard form for x = 0, −1,
−2, 2.
A. y = 2×4 – 2×2 – x + 4
B. y = x4 + x3 – 4×2 – 4x
C. y = x4 + x3 + 4x + 4
D. y = x3 – 4×2 – 4x + 1
____ 21. Solve the matrix equation
+X=
A.
B.
C.
D.
.
____ 22. Write this polynomial in standard form 4n2 + 3n3 – 2 + 5n + 6n2.
A. 3n3 + 10n2 + 5n – 2
B. 13n3 + 5n – 2
C. 18n – 2
D. 3n3 + 15n2 – 2
____ 23. Write this polynomial in standard form –4c + 8 – 2c + 7c2.
A. c2 + 8
B. 7c2 + 2c + 8
C. 7c2 – 6c + 8
D. 13c + 8
____ 24. Expand this binomial (3x + 2)4.
A. 81×4 – 216×3 – 216×2 – 96x – 16
B. 12×4 + 6×3 + 6×2 + 6x + 8
C. 81×4 + 216×3 + 216×2 + 96x + 16
D. 81×4 + 16
____ 25. Solve this equation 4×3 – 16×2 + 12x = 0.
A. 3
B. 1, 3
C. 0, −1, −3
D. 0, 1, 3
____ 26. Let f(x) = x3 and g(x) = 3x – 1. Evaluate (f o g)(5).
A. 2744
B. 1750
C. 896
D. 374
____ 27. Multiply and simplify
A. 9
B.
C. 3
D.
•
.
____ 28. A combination lock has 60 numbers on it. How many different 3-digit lock
combinations are possible if no digit can be repeated?
A. 3540 ways
B. 11,406 ways
C. 34,220 ways
D. 205,320 ways
____ 29. Find the domain of this function y = −1 –
.
A. all real numbers
B. y ≤ −1
C. x ≥ –5
D. x ≤ −1
____ 30. You can estimate a tsunami’s speed, s, in meters per second by s = 3.1
,
where d is the depth of the ocean in meters. Express d in terms of s.
A. d =
B. d =
C. d =
D. d =
____ 31. Simplify this expression
.
A. 10
B. 25
C. 5
D. 100
____ 32. You must answer exactly 10 out of 14 questions on a test. How many different
ways can you select the questions to answer?
A. 455 ways
B. 1001 ways
C. 720 ways
D. 140 ways
____ 33. 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
____ 34. How many ways are there to choose five shirts out of seven to take to camp?
A. 21
B. 35
C. 12
D. 2
____ 35. Using
with coordinates A(2, 3), B(−4, 1), and C(5, −6) create a
translation 2 units right and 2 units down. Write the coordinates of each image
in matrix form.
A.
B.
C.
D.
____ 36. Find the range of this function y =
+ 3.
A. x ≥
B. all real numbers
C. y ≥ 3
D. y ≤ −1
____ 37. Simplify this expression
A.
B.
C.
D.
.
____ 38. 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
____ 39. Find the sum
+
.
A.
B.
C.
D.
____ 40. Let f(x) = x2 and g(x) = 3x + 1. Evaluate (f o f)(3).
A. 9
B. 28
C. 81
D. 100
____ 41. Which expression is a cubic polynomial?
A. x3
B. 3x + 3
C. 2×2 + 3x – 1
D. 3x
____ 42. If x represents hotdogs, and y represents hamburgers, use the information in
the following matrix to find out how much each hot dog or hamburger costs.
A. x = 2.00, y = 2.50
B. x = 1.50, y = 2.25
C. x = 1.00, y = 2.00
D. x = 1.75, y = 2.75
____ 43. Simplify this expression
.
A.
B.
C.
D.
____ 44. Identify the indicated element of this matrix
.
A. 3
B. −2
C. 4
D. 8
____ 45. Find all the roots of this equation x3 – 5×2 + 7x – 35 = 0.
A. 5, ± 7i
B. 5, ±
C.
D.
____ 46. Solve this equation and check for extraneous solutions
A. x = 3, −3
B. x = 5, 3
C. x = 5
D. x = 8
____ 47. Divide (x3 + 12x + 11) by (x + 2).
A. x2 + 4x – 8, R 13
B. x2 – 2x + 16, R 43
C. x2 – 2x + 16 R −21
D. x2 – 8, R 12
–2
= 0.
____ 48.
Solve this matrix equation
.
A. x = 63, y = 85, z = 91
B. x = 74, y = 95, z = 70
C. x = 90, y = 87, z = 62
D. x = 87, y = 88, z = 74
____ 49. Simplify this radical
.
A. 4×5
B. 4×16
C. 2×5
D. 2×16
____ 50. Write this expression in simplest form
.
A.
B.
C.
–
D. x8y3
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.
The University of Nebraska is an equal opportunity educator and employer. ©2021, The
Board of Regents of the University of Nebraska. All rights reserved.