Review for Test IV – Sections 7.5,7.6,8.1-8.4
MAT135
1. Solve for x:
Spring 2010
4 y  4  3 y  7  0 , where x is a real number.
2. Multiply and simplify: (6  8i)(3  9i) .
3. Solve: (3k  1) 2  9  1 .
4. Find the value of t such that z 2  8z  t is a perfect square.
5. If f ( x)  x 2  8 and g ( x)  8 x  11 find all value(s) of x such that f(x)=g(x).
6. Solve: x2  10x  4  0 .
7. Write the quadratic equation that has x  2, x  10 as solutions.
2
3
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8. Solve for z: z  2 z  3  0 .
9. Use the discriminant to find the number and type of solutions for 4 x2  x  5 .
10. Find the vertex and domain and range of: f ( x)  3 x 2  18 x  5.
11. The temperature, t, in degrees Farenheit, of a chemical reaction is approximated by
the function t ( s )  3s 2  36s  70 where s is the number of seconds after the reaction
begins. What is the lowest temperature attained by the reaction, and when will it occur?
12. Consider the function f ( x)   x 2  9 x  20. Which statement(s) is/ are true?
a. The roots occur at (4,0) and (5,0) .
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b. The vertex is at ( , ) .
c. The y-intercept is at (-20,0).
d. The domain is (, ) .
e. The graph is a parabola that opens upward.
13. Simplify: 5 
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MAT135
Review for Test IV – Sections 7.5,7.6,8.1-8.4
Spring 2010
14. Solve: 2 x2  16  0 .
15. What is the range, in interval notation, of the function below? You may assume that
each tick mark represents one unit.
y
x
16. Simplify:
18  72
.
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17. Evaluate and simplify: (2  3i ) 2 .
18. Evaluate:
16( 5  16) .
19. Solve by completing the square: x2  6x  7  0 .
20. What is the vertex of the graph of the quadratic function f ( x)  2 x 2  4 x  1 ?
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Review for Test IV – Sections 7.5,7.6,8.1-8.4
MAT135
Spring 2010
Answer Key
1) y = 3
2) 90 – 30i
3) k 
1  2i 2
3
4) t = 16
5)
x  4  13
6)
x  5  21
7)
8)
9)
10)
x 2  8 x  20  0
z = 27, z = – 1
2 complex numbers solutions
( 3, 22) , D ( , ) , R[22, )
11) Lowest temp: – 38 ° occurs at 6 seconds
12) a) F
b) T
c) F
d) T
e) F
13) i
14) x  2i 2
15) (, 6]
16) 3  i 2
17) 12i – 5
18) 4 5  16
19) x  3  2
20) (1, 3)
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