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____ 1.____ 2.____ 3.=1does not exist.=0d.Use a geometric series to find the rational number represented by the decimal . r =.01.181.81If 10 people apply for 3 jobs, in how many ways can people be chosen for the job if the jobs are all different? a.b. c. d.Find the solution set of this equation:32612
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Course Name: Precalculus: Analytic Geometry and
Algebra
Student: Kwinda Netshitangani
Course ID:
MTHH043059
ID: J47865775
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.
a.
b.
c.
d.
____ 2.
Use a geometric series to find the rational number represented by the decimal
a.
b.
c.
d.
____ 3.
=1
does not exist.
=0
.01
.1
81
.81
If 10 people apply for 3 jobs, in how many ways can people be chosen for the job if the jobs are all different?
a.
b.
c.
d.
____ 4.
.r=
Find the solution set of this equation:
a.
b.
c.
d.
3
2
6
12
____ 5.
Let z1 = 2 + 3i and z2 = 1 – i. Find z1 + z2.
a.
b.
c.
d.
____ 6.
1 + 2i
1 + 4i
3 + 2i
3 + 4i
Use a geometric series to find the rational number represented by the decimal
. What does the rational
number equal?
a.
b.
c.
d.
____ 7.
Use the elimination method to find the solution for x:
a.
b.
c.
d.
____ 8.
3
2
1
0
Given: logb2 = .4, logb3 = .6, logb5 = .7. Use properties of logarithms to find the following value: logb18 =
a.
b.
c.
d.
____ 9.
.
.76
1.6
.144
.48
Find the solution set of this linear system:
a.
b.
c.
d.
(2, 0)
(0, 2)
no solution
(0, −2)
____ 10. The sum of three numbers is 35. The second number is twice the first, and the third number is twice the
second. If the three numbers are x, y, and z in that order, then two equations can be written as
a.
b.
c.
d.
x = 2y and z = 2x.
y = 2x and z = 2y.
x = 2y and z = 4x.
y = 2x and z = 2x.
____ 11.
Solve the system:
. What is one solution?
a.
b.
c.
d.
____ 12. 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.
____ 13.
5, 10, 20
5, 12, 18
7, 14, 28
10, 15, 20
Solve the system:
a.
b.
c.
d.
. What is one solution?
(–2, 4)
(2, –4)
(–2, –4)
(2, 4)
____ 14. Solve this system by using a matrix.
a.
b.
c.
d.
x= −1, y = 1
x = 1, y = −1
x = −1, y = 0
x = 0, y = −1
____ 15. Find the sum of this series:
a.
b.
c.
d.
____ 16. Let z1 = −1 – 3i and z2 = 4 + 5i. Find
.
a.
b.
c.
d.
____ 17.
−1 + 3i
1 – 3i
1 + 3i
Use this system to find the value of the y:
a.
b.
c.
d.
.
−6
6
4
−4
____ 18. Find the value of a for this series:
a.
b.
c.
d.
____ 19.
3
Use this system to find the value of the x:
a.
b.
c.
d.
.
–3
–4
3
4
____ 20. Use the elimination method to find the solution for z:
a.
b.
c.
d.
4
3
2
1
____ 21. 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
____ 22. 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
the same?
a.
b.
c.
d.
____ 23.
a.
b.
c.
d.
does not exist.
=1
=0
____ 24. Evaluate the given expression:
a.
b.
c.
d.
.
6
30
24
2
____ 25. Find the value of r for this series:
a.
b.
c.
3
d.
____ 26. Find the first 5 terms of this sequence:
a.
b.
c.
d.
1, 2, 3, 4, 5
−2, 1, 6, 13, 22
−2. 1, 3, 5, 7
−3, −2, 1, 5, 10
____ 27. Write f(x) = x3 + 25x in factored form. f(x) =
a.
b.
c.
d.
x (x + 5) (x – 5)
x (x + 5i) (x – 5i)
(x + 25) (x + i) (x – i)
(x + 25i) (x + 1) (x – 1)
____ 28.
Evaluate the determinant
a.
b.
c.
d.
.
66
6
–66
–6
____ 29. Find the common difference in the arithmetic sequence:
3, 1, -1, -3, -5, …
a.
b.
c.
d.
−1
3
−2
2
____ 30. Write log5
– log5
as a single logarithm.
a.
b.
c.
d.
____ 31.
Let z1 = 2 + 3i and z2 = 1 – i. Find
a.
+
b.
c.
i
+
+
.
i
i
d.
____ 32. Use the Binomial Theorem to expand the expression (x – 2y)4.
a.
x4 + 8x3y + 24x2y + 32xy3 + 16y4
b.
x4 – 8x3y + 24x2y2 – 32xy3 + 16y4
c.
x4 – 4x3y + 24x2y – 16xy3 + 2y4
d.
x4 – 8x3y + 32x2y – 32xy3 + 8y4
____ 33.
Find the value of the sum
a.
b.
c.
d.
.
35
750
150
30
____ 34. 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
____ 35. 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
____ 36. Find the value of log3
a.
b.
c.
.
−2
2
d.
____ 37.
Use this system to find the value of the determinant:
a.
b.
c.
d.
–7
5
7
−5
____ 38. Use the elimination method to find the solution for y:
a.
b.
c.
d.
1
no solution
infinite solutions
2
.
____ 39. Use the Binomial Theorem to find the coefficient of the third term: (x + 2)6.
a.
b.
c.
d.
C (6, 4)
C (6, 3)
C (5, 3)
C (6, 2)
____ 40. Find a polynomial function with real coefficients that has –2 and 3i as its roots.
a.
b.
c.
d.
x³ – 2x² + 9x – 18
x³ – 2x² – 9x + 18
x³ + 2x² – 9x – 18
x³ + 2x² + 9x + 18
____ 41. Given g(x) = (2)2x + 1; find g(2).
a.
b.
c.
d.
16
32
8
10
____ 42. Solve for x: 9x = 3x + 6
a.
b.
c.
d.
–4
–3
6
3
____ 43. What are the roots of f(x) = x4 – 81?
a.
b.
c.
d.
3, 3i
3i, −3i
3, −3, 3i, −3i
−3, 3
____ 44. Let z1 = 3 – 4i and z2 = −1 – i. Find | z2 |.
a.
b.
c.
1+i
–1+i
d.
1–i
____ 45. Solve for x: log7(2x – 7) = 2
a.
b.
c.
d.
28
10.5
21
56
____ 46.
Which is the graph of the system:
a.
b.
c.
d.
____ 47. Solve for x: logx
a.
b.
c.
d.
1
6
−6
−1
= −1
?
____ 48.
Which shows the graphs of the equations:
a.
b.
c.
d.
?
____ 49.
Use this system to find the determinant:
.
a.
b.
c.
d.
____ 50.
Solve for x:
a.
b.
c.
d.
30
–30
–6
6
Carefully review your answers on this progress test and make any corrections you feel are necessary. When