This test contains 50 multiple choice questions based on Precalculus: Analytic Geometry and Algebra, please get me a good grade!The test is attached below.
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Course Name: Precalculus: Analytic Geometry and
Algebra
Student: Aryash Chauhan
Course ID:
MTHH043059
ID: F68560331
Submittal:
59
Progress Test 3
Progress Test 3 (Evaluation 59) covers the course materials that were assigned in Units 5 and 6. Although the progress
test is similar in style to the unit evaluations, the progress test is a closed-book, proctored test. You may not have
access to notes or any of the course materials while you are taking the test. You may use your graphing
calculator on this test.
____ 1.
Find the sum of this series:
a.
b.
c.
108
4
d.
____ 2.
Find the solution set of this linear system:
a.
b.
c.
d.
____ 3.
Given: logb2 = .4, logb3 = .6, logb5 = .7. Use properties of logarithms to find the following value: logb18 =
a.
b.
c.
d.
____ 4.
(2, 0)
(0, 2)
no solution
(0, −2)
.76
1.6
.144
.48
Let z1 = 2 + 3i and z2 = 1 – i. Find
a.
+
b.
c.
d.
i
+
+
i
i
.
____ 5.
Solve for x:
a.
b.
c.
d.
____ 6.
The sum of three numbers is 84. If the first is three times the second, and the third is twenty-one more than
the first, what are two of the equations?
a.
b.
c.
d.
____ 7.
1
–1
z = 3y and y = 21 + x.
z = 3y and x = 21 + y.
x = 3y and z = 21 + x.
x = 3y and y = 21 + x.
Solve the system:
a.
b.
c.
d.
____ 8.
a.
b.
c.
d.
does not exist.
=3
=1
=0
. What is one solution?
____ 9.
Which shows the graphs of the equations:
a.
b.
c.
d.
____ 10. Solve for x: 162x = 8x + 1
a.
b.
c.
5
3
d.
____ 11.
Solve the system:
a.
b.
c.
(0, 0)
d.
(0, 3)
. What is one solution?
?
____ 12. Find the first 5 terms of this sequence: an = n + 3.
a.
b.
c.
d.
−2, −1, 0, 1, 2
1, 2, 3, 4, 5
4, 5, 6, 7, 8
3, 4, 5, 6, 7
____ 13. Let z1 = 3 – 4i and z2 = −1 – i. Find
a.
b.
c.
d.
.
–3 + 4i
3 + 4i
5
–3 – 4i
____ 14. Let z1 = −1 – 3i and z2 = 4 + 5i. Find | z2 |.
a.
b.
c.
d.
4 – 5i
–4 – 5i
–4 + 5i
____ 15. Find the common difference in the arithmetic sequence:
3, 1, -1, -3, -5, …
a.
b.
c.
d.
−1
3
−2
2
____ 16.
Use the elimination method to find the solution for x:
a.
b.
c.
d.
3
2
1
0
a.
b.
c.
=1
does not exist.
d.
=0
____ 17.
.
____ 18.
Find the value of r for this series:
a.
b.
c.
d.
3
____ 19. Let z1 = 2 + 3i and z2 = 1 – i. Find z1 + z2.
a.
b.
c.
d.
1 + 2i
1 + 4i
3 + 2i
3 + 4i
____ 20. Find the solution set of this equation:
a.
b.
c.
d.
1
2
2, -1
-2, 1
____ 21. Use the Binomial Theorem to find the third term of the expression (x + 2)6.
a.
128×6
b.
60×4
c.
–60×6
d.
32×4
____ 22. In how many ways can a committee of 3 be chosen from 10 people?
a.
b.
c.
d.
____ 23. Solve for x: logx
a.
b.
c.
d.
1
6
−6
−1
= −1
____ 24.
Use this system to find the value of the y:
a.
b.
c.
d.
.
4
3
–3
–4
____ 25. Write f(x) = x4 – 16 in factored form. f(x) =
a.
b.
(x + 2) (x – 2) (x + 2i) (x – 2i)
c.
(x + 2i)2 (x – 2i)2
d.
(x − 2)2 (x – 2i)2
(x + 2)2 (x – 2)2
____ 26. Find the value of a for this series:
a.
b.
c.
d.
3
____ 27. Use a geometric series to find the rational number represented by the decimal
a.
b.
c.
d.
.01
.1
48
.48
.r=
____ 28.
Which is the graph of the system:
?
a.
b.
c.
d.
____ 29. Use a geometric series to find the rational number represented by the decimal
number equal?
a.
b.
c.
d.
. What does the rational
____ 30. Write log5
– log5
as a single logarithm.
a.
b.
c.
d.
____ 31.
Use this system to find the determinant:
.
a.
b.
c.
d.
____ 32. The perimeter of a triangle is 26 inches. If the longest side is twice as long as the shortest side, and the third
side is 2 inches longer than the shortest side. Which algebraic equation would best represent the side
lengths of the triangle?
a.
b.
c.
d.
x + 2y + z + 2 = 26
x + x + 2 + 2x = 26
x + 2y + 2z = 26
x + 2x + 3x = 26
____ 33. Find the value of log48.
a.
____ 34.
b.
c.
6
d.
–6
Find the value of the sum
a.
b.
c.
d.
20
1024
30
384
.
____ 35. Use the elimination method to find the solution for z:
a.
b.
c.
d.
−1
no solution
infinite solutions
0
____ 36. Solve this system by using a matrix.
a.
b.
c.
d.
x = 4, y = −5
x = 5, y = −4
x = −5, y = 4
x = 5, y = 4
____ 37. What are the roots of f(x) = x4 – 81?
a.
b.
c.
d.
3, 3i
3i, −3i
3, −3, 3i, −3i
−3, 3
____ 38. Use the Binomial Theorem to expand the expression (y2 – 1)5.
a.
y10 + 5y8 – 10y6 + 10y4 – 5y2 + 1
b.
y10 + 5y8 – 20y6 + 20y4 – 5y2 + 1
c.
y10 – 5y8 + 10y6 – 10y4 + 5y2 – 1
d.
y10 – 5y8 + 20y6 – 20y4 + 5y2 – 1
____ 39. Use the Binomial Theorem to find the coefficient of the fifth term: (2x + 1)7.
a.
b.
c.
d.
C (7, 4)
C (7, 5)
C (7, 3)
C (6, 5)
____ 40. Evaluate the given expression:
a.
b.
c.
d.
1,030,200
103,020
102
303
____ 41. Solve for x: log3(x + 2) = 2
a.
b.
c.
d.
10
11
6
7
.
____ 42. If you have 8 friends and 4 gifts to give, in how many ways can you give the gifts to friends if the gifts are all
different?
a.
b.
c.
d.
____ 43.
Use this system to find the value of the determinant:
a.
b.
c.
d.
____ 44.
−18
18
6
−6
Use this system to find the value of the x:
a.
b.
c.
d.
.
.
–3
–4
3
4
____ 45.
Use the elimination method to find the solution for y:
a.
b.
c.
d.
0
1
2
3
____ 46. Find a polynomial function with real coefficients that has 3 and –2i as its roots.
a.
b.
c.
d.
x³ – 3x² + 4x – 12
x³ + 3x² + 4x + 12
x³ + 3x² – 4x – 12
x³ – 3x² – 4x + 12
____ 47. The sum of three numbers is 35. The second number is twice the first, and the third number is twice the
second. What are the three numbers?
a.
b.
c.
d.
5, 10, 20
5, 12, 18
7, 14, 28
10, 15, 20
____ 48. Given: logb2 = .4, logb3 = .6, logb5 = .7. Use properties of logarithms to find the following value: logb0.6 =
a.
b.
c.
d.
–0.1
1.0
–.06
–.76
____ 49.
Evaluate the determinant
a.
b.
c.
d.
.
0
36
138
−36
____ 50. Given g(x) = (2)2x + 1; find g(2).
a.
b.
c.
d.
16
32
8
10
Carefully review your answers on this progress test and make any corrections you feel are necessary. When