Download MA 180 Pretest

MA 180/PRECALCULUS PRETEST
SHOW ALL WORK.
CIRCLE YOUR ANSWERS.
WRITE YOUR EXACT ANSWERS UNLESS OTHERWISE INSTRUCTED.
1. Solve for x.
a. 8 x  (2 x  1)  3x  10
b. ( x  7)( x  1)  ( x  1) 2
c. 1  Ax  B  0
d. 8  4(2  x)  2 x
e.
x6  x
f.
3
5
x2
2. Given 2 x  3 y  6
a. Graph the equation.
b. Determine the slope and y-intercept.
c. Select two points on the line and use them to confirm, algebraically, that the slope you calculated
from part (b) is correct.
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g(x)
Graph of function g
3. Answer these questions about
the function g that is graphed at the
right.
7
6
5
a. g(4) = _____
4
3
2
b. If g(a) = 3, then a = _____
1
0
c. The zero of function g is ____
-6
-4
-2
0
2
-1
-2
x
2 x  11y  9
4. Solve the system of equations by any algebraic method. 
 4x  8 y  0
x
5. Each of parts to this question should be answered
without the aid of a calculator.
f(x)
0
a. Complete the table on the right for f  x   3
x
1
2
b. For the same function f,
determine the exact values of these:
f  1  _____,
3
f  2  __________,
f  3  __________
6. Without the aid of a calculator determine the exact values of the following
a.
 169 
1
e. log3 81  _____
b.
 169 
3
2
8
c.
f. log3 1  _____
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3
d.
8
1
3
4
6
7. Simplify without the aid of a calculator:
a. 5 6

24

b.
900
c.
   2x 
5 x3
8. Simplify and write with positive exponents:
9. Solve:
Solve by Factoring:
a. 6m2  26m  20
7  49  120
4
2
4 3
b. 3x3  27 x  0
c. Solve using the Quadratic Formula: x 2  13  6 x
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10. Given g ( x)   x 2  9 :
a. Find g(0)
c. Find f  0 
e. Solve for x:
b. Find g  4
d. g  x   5
g(x) = 0.
f. g  x  5
11. Given h( x)  0.5x 3  4.5 x  2.8 , use your graphing calculator to find the following in the standard
window. Round your answers to the nearest thousandth.
a. relative minimum
b. relative maximum
c. each zero of h(x)
6
 8 and h  x   5  x
x
a. State the domain of the function f.
12. Given f ( x)  3 x 2 
b. State the domain of the function h.
13. Graph the quadratic function f  x   x2  8x  7 and find the vertex.
Number your axes
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Trigonometry [administer mid-semester]:
14. Use your calculator to find the following. Round your answers to 3 decimal places.
a. sin 35
b. tan 81
c. cos 128
d. csc 75
15. Find b and .
3
3 2

b
16. Find two values of , 0    2 , that satisfy the given trigonometric equation.
3
a. sin  
b. csc  2
c. tan  1
2
17. A 12-foot ladder is resting against a wall and makes an angle of 52 with the ground. Find the height
to which the ladder will reach the wall.
18. Convert the measure of each angle to exact radian measure.
a. 15
b. -225
c. 315
19. Convert the radian measure of each angle to degree measure.
a.
3
8
b. 1.5
c. 5.25
20. Find the six trigonometric functions for the angle  whose terminal side passes through the point
 8,  5
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Answers to MA 180/PRECALCULUS PRETEST
1. a. 
11
3
4. a.
c.
2
3
b=2
b. 0
c. 4
2. b. m 
3. a. 6
b. 2
1 B
A
d. x  8
e. 3
f.

7
5
6 5 , 35 
1
5. a. 3
b.
1
3
,
1
9
,
1
512
,
1
27
9
27
6. a. – d.
16
9
,
27
64
7. a. 60
, 2
b. 30i
e. 4
f. 0
c. –5, +3/2
5
8x 6
8.
9. a. m  2 ,  5
3
b. x  0,  3
c. x  3  2i or x  3  2i . These solutions are not real numbers.
10. a. 9
b. -7
11. a. -2.396
b. 7.996
12. a.
x0
c. undefined
 x +14
2
d.
c. x = 3.273, 0.653, 2.620
b. x  5
13. vertex: (4, -9)
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e.
x  3
f.  x 2  10 x  16
14. a. 0.574
 2
3
c. -0.616
d. 1.035
  45
15. b = 3
16 .a.
b. 6.314
,
b.
3
17.
 5
6
,
c.
6
9.5 feet

18. a.
12
b. 
19.a.
67.5
b. 85.94
20.
sin   
5 89
89
csc  
89
5
cos  
8 89
89
sec  
89
8
tan  
5
8
5
4
c.
3 7
,
4 4
7
4
c. 300.80
cot  
8
5
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d.
5 7
,
6 6