Download College Algebra MAT-121-TE

TECEP® Test Description
College Algebra MAT-121-TE
This TECEP® tests algebraic concepts, processes, and practical applications. Topics include: linear equations and
inequalities; quadratic equations; systems of equations and inequalities; complex numbers; exponential and
logarithmic expressions and functions; basic probability. (3 s.h.)
•
•
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Test format: 64 multiple choice questions (1 point each)
Passing score: 70% (45/64 points). Your grade will be reported as CR (credit) or NC (no credit).
Time limit: 3 hours
You may use a scientific calculator (non-graphing, non-programmable) during testing.
Topics on the test and their approximate distribution
1.
Review of basic concepts (15%)
A. Real numbers and their properties
B. Polynomials – exponents, addition, subtraction, multiplication, division
C. Polynomials - factoring
D. Polynomials – fractions (simplification, multiplication, division)
E.Radicals
2.
Equations and inequalities (20%)
A. Linear equations, simple interest
B. Word problems
C. Complex numbers – multiplication, division
D. Quadratic equations
E. Factoring method, formula method
F. Application of quadratic equations
G. Equations with radicals
H.Inequalities
I. Absolute value equations
3.
Graphs and functions (15%)
A. Graphing – straight line, distance, midpoint
B. Graphing – circle
C. Graphing – domain, range
D. Graphing – slope
E. Graphing – parallel and perpendicular lines
4.
Polynomial and rational functions (10%)
A. Parabola – domain, range, vertex, intercepts
B. Synthetic division
C. Zeros of polynomial functions
D. Graphs of polynomial functions
E.Variations
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5.
Exponential and logarithmic functions (25%)
A. Inverse functions, one-to-one functions, symmetry
B. Exponential functions, application of exponential functions
C. Logarithms – log, log functions
D. Logarithms – common log, natural log
E. Solving exponential equations with log, log equations
F. Applications of exponential functions
6.
Systems of equations, parabolas, and further topics
A. Systems of linear equations
B. Systems of nonlinear equations
C. Analytic geometry
D. Binomial theorem
E. Counting theory – permutation, combination
F. Basic probability
(15%)
Outcomes assessed on the test
• Solving problems involving linear and quadratic equations
• Solving systems of linear and nonlinear equations and inequalities
• Solving exponential and logarithmic functions
• Applying algebraic concepts and processes to the solution of real-world problems
• Solving basic probability problems
Study materials
College Algebra. Margaret Lial, John Hornsby, and David Schneider.
Current edition. Boston: Pearson/Addison Wesley.
Sample questions
1.
Perform the indicated operation.
20a-50b
3a-7b
a.
+
58b-22a
3a-7b
2a-8b
7b-3a
b.
18a-58b
3a-7b
c.
6
d.
22a-58b
3a-7b
2. Factor completely. 12t2 + 40t – 7
a. (2t + 7)(6t – 1)
b. (3t + 7)(2t – 1)
c. (3t – 7)(2t + 1)
d. (2t – 7)(6t +1)
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3. Perform the indicated operation.
1 - 2
x+3 3
2 - 1
x+33
a.
3+2x
x-3
b.
c.
-1
-3-2x
1+x
d.
6
x+3
4. Solve the equation.
3 1 5 (2x-3) - 2x =
(x+3)
4
2
8
a. {7}
b. {-9}
c.
}3715}
d. {37}
5. Simplify the following so that there are no negative exponents. Assume that all variables represent
positive real numbers.
}
a.
}
18
x 5/3 y -3/2
x1/6 y 5/3 z -5/6
x27 y57
z15
b.
x27 z15
y57
c.
x33 y3
z15
d.
z15
x33 y3
6. Two cars leave the same point at the same time traveling in opposite directions. One car travels 8 mph
slower than the other. After 4 hours they are 368 miles apart. Find the speed of the faster car.
a. 42 mph
b. 50 mph
c. 60 mph
d. 68 mph
7. The number y of people attending the Ozark Mountain Bluegrass Festival between 1989 and 1996 can
be approximated by the model y = 69.75x2 – 328.7x + 1283, where x = 0 corresponds to 1989. Based on
this model, in what year was the festival attendance about 1800?
a. 1991
b. 1993
c. 1995
d. 1996
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8. Solve the inequality. Give the answer using interval notation.
2x-1
5
<
3
3
a. (-2, 3)
b. (-3, -2)
c. (-3,2)
d. [-2,3]
9. Solve the equation.
2 _
1
x - 36
x- 6
2
a. { -1 }
=
1
x+ 6
} }
b. _ 12
5
c. {1}
d.
} }
3
2
10. Solve the equation.
2x+3 a. { -3, -11}
x-2=2
b. {3, -11}
c. {-3, 11}
d. {3,11}
11. Perform the operation. Give the answer in standard form.
6 - 9i
4 + 2i
a.
21 12
i
+
5
5
b. 1
+ 2i
4
c. 7
+ 2i
2
12. Which of the following is the domain of f (x) =
d.
2 - x
3
12
i
10
5
?
a. [0, 2]
b. (−∞, 2]
c. [2, ∞)
d. (−∞, ∞)
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13. What is the slope of the line passing through (-7,-4) and (3,-2)?
y
s
s
.
b. _ 1
5
c.
1
5
d.
x
s
.
1
0
s
1
0
a.
(3, -2)
5
(-7, -4)
14. Identify the vertex of the parabola.
f(x) = (x + 4)2 + 10
a.
b.
c.
d.
(10,0)
(0, -4)
(-4, 10)
(10, -4)
15. Write an equivalent statement in exponential form.
log99 = 1
a.
b.
c.
d.
99 = 1
91 = 9
1*9 = 9
19 = 9
16. Solve:
3y3 – 5y2 + 5y – 5
y−1
a.
b.
c.
d.
–3y2 – 2y + 3 R2
3y2 − 2y + 3 R − 2
3y2 − 5y − R0
3y2 + 2y − 3 R5
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17. Factor f(x) into linear factors given that k is a zero of f(x).
f(x) = x3 – 2x2 – 36x + 72; k = 6
a.
b.
c.
d.
(x – 6)(x – 2)(x + 2)
(x – 6)(x + 2)(x + 6)
x(x – 6)(x – 2)
(x – 6)(x – 2)(x + 6)
18. Graph the polynomial function.
f(x) = x(x – 3)(x + 2)(x – 2)
y
23
x
s
-25
▲
25
s
-25
x
-3 -2 0
s
23
-25
▲
▲
0
x
y
d.
▲
25
-2
23
-25
y
c.
-2 0
s
▲
0
▲
s 25
▲
-2
y
b.
▲
s 25
2
x
s
a.
s
19. The power a windmill obtains from the wind varies directly as the cube of the wind velocity. If a
10 km/hr wind produces 10,000 units of power, how much power is produced by a wind of 15 km/hr?
a.
b.
c.
d.
2,963 units
3,375 units
15,000 units
33,750 units
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20. Pick the linear function f(x) that has this line as its graph.
y
s
s
0
-2,-1
a. f(x) =
.
1
5
x3 3
x
s
-4,-3
s
.
b. f(x) = -3x - 5
3
c. f(x) =
1
1
x+
3
3
d. f(x) = 3x -
5
3
21. Solve the equation.
1
x
2– = 8
a.
b.
c.
d.
{-3}
{1/4}
{1/3}
{3}
22. Find the equation of a circle where the center is (3,1) and the radius is 5.
a. (x + 1)2 + (y + 3)2 = 25
b. (x − 3)2+(y − 1)2 = 25
c. (x − 1)2 +(y − 3)2 = 5
d. (x − 3)2- (y − 1)2 = 25
23. Solve the equation and express the solution in exact form.
log (x + 10) = 1 + log(4x – 3)
a.
b.
c.
d.
{40/39}
{40/39, 1}
{13/3}
{1}
24. Solve the system.
x – 4y = 16
9x – 5y = 51
a.
b.
c.
d.
{(4, −3)}
O
{(−4, −2)}
{(3, −2)}
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25. Solve the nonlinear system of equations.
x2 – y2 = 39
x – y = 3
a.
b.
c.
d.
{(–8, 5)}
{(8, 5)}
{(8, –5)}
{(–8, –5)}
26. Match the equation of the parabola with the appropriate description.
y = 4 + 3x – x2
a.
b.
c.
d.
Opens right
Opens down
Opens up
Opens left
27. How many ways can a president, vice president and secretary be chosen from a club with 12 members?
Assume that no member can hold more than one office.
a.
b.
c.
d.
6
36
220
1320
28. Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 4?
a.
b.
c.
d.
1/12
11/12
1/6
2/6
29. Write the indicated term of the binomial expansion.
(x – 2y)13 ; 5th term
a.
b.
c.
d.
–5720x4y9
–5720x9y5
11,440x4y9
11,440x9y4
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TECEP® Test Description
30. ln510
a.
b.
c.
d.
2.0775
2.7075
6.2344
6.33244
31. The population of Twin Lakes is given by the function P(x) = 3250e.02x where x is the number of years after
1970. What was the population in the year 2000?
a.
b.
c.
d.
3316
5805
5922
1,311,144
Answers to sample questions
1. c
2. a
3. a
4. a
5. b
6. b
7. c
8. a
9. c
10. d
11. d
12. b
13. c
14. c
15. b
16. b
17. d
18. b
19. d
20. a
21. d
22. b
23. a
24. a
25. b
26. b
27. d
28. a
29. d
30. c
31. c
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