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MAC 1105 College Algebra Test #1 - Review
Section P-5: Factoring Polynomials
Factor completely the following:
1.
2. 16 x 3  250
1
5
3. ( x  2 ) 4  ( x  2 ) 4
Section 1.1: Graphs and Graphing Utilities
4. Graph y = - x2 + 3. Let x = -3, -2, -1, 0, 1, 2, 3
x
y
-3
-2
-1
0
1
2
3
MAC1105 review T1 (sections: P-5, 1.1, 1.5, 1.6 and 1.7)
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5. This table of values was generated by a graphing utility with a TABLE feature. Use the
table to solve exercise 3a-3d.
X
-3
-2
-1
0
1
2
3
X=3
Y1
-2
-1
0
1
2
3
4
Y2
-7
-5
-3
-1
1
3
5
a. Does the graph of either equation pass through the origin? __________________
b. At which point does the graph of Y1 cross the x-axis? ______________________
c. At which point does the graph of Y 2 cross the y-axis? _____________________
d. At which points do the graphs intersect? ________________________________
Section 1.5: Quadratic Equations
6. Solve the equation by the square root properties:
2( x  3) 2  64
7. Solve the equation by completing the square:
3x 2  9 x  2  0
MAC1105 review T1 (sections: P-5, 1.1, 1.5, 1.6 and 1.7)
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8. Solve the equation using the quadratic formula.
2x 2  x  5
9. Find all values of x satisfying the given condition.
y1 = x - 1, y2 = x - 5
and
y1 × y2 = 4
10. A 5-meters ladder is leaning against a building. How far from the building is the bottom
of the ladder when the top of the ladder touches the building 4 meters above the ground?
5m
4m
?
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11. A ball is thrown vertically upward from the ground with an initial velocity of 80 feet per
second. Using the position formula, determine when the ball will be 96 feet above
ground?
Position formula: s  16 t 2  v0t  s0 , where v0  initial velocity , s0  initial position ,
t  time
12. Use a graphing utility and round x 
 6  66
 6  66
 _______________
8
8
to 3 decimal places.
 6  66
 _________________
8
Section 1.6: Other Types of Equations
13. Solve the radical equation:
x  2  3x  7  1
MAC1105 review T1 (sections: P-5, 1.1, 1.5, 1.6 and 1.7)
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14. Solve equation with radical exponents.
3
(t  1) 2  8
15. Solve the equation by making substitution and check the solution on the calculator.
2
1
( x  2) 3  ( x  2) 3  2  0
MAC1105 review T1 (sections: P-5, 1.1, 1.5, 1.6 and 1.7)
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Section 1.7: Linear Inequalities
16. Solve and graph each absolute value inequality:
a.
Interval notation: _______________________________________
Graph:
b.
Interval notation: _______________________________________
Graph:
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