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
1
3
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) .
9 1
2 4
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
.
6
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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