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Exam 4 Review Name___________________________ Sections 6.1 โ 6.6 Math 100C
- Simplify. Your answer should not contain any negative exponents, any numbers raised to a power should be computed, and any fractions need to be simplified.
a. (^2 b
โ 5
c
โ 2
3
( 3 b
4
c
โ 6
โ 2 b. 10 215 2216 5213 c. ( 16 b^8 c โ^4 ) 1 4 ( (^25) b โ^6 c^4 ) 3 2
d. โ^125 x
15
y
21
- Perform the indicated operation. a. (โ^7 x 3 + 5 x 2 โ 9 )^ +(^2 x 3 โ 8 x 2 + 3 x ) b. (^5 a 3 b โ 2 a 2 b 2 + 9 ab (^3) ) โ(^8 a 3 b + 4 a 2 b 2 โ ab (^3) ) c. (โ^7 x 3 + 5 x 2 โ 9 )^ โ( 2 x 3 โ 8 x 2 + 3 x )
d. (^5 a 3 b โ 2 a 2 b 2
- 9 ab (^3) ) +(^8 a 3 b + 4 a 2 b 2 โ ab (^3) ) e. 8 a 2 b (^ โ 5 a 3 b 5
- 2 ab )
f. (^3 x +^7 y^ )
2 g. (^4 x^ โ^3 )^ (^5 x 2 โ 2 x + 4 )
- Factor when possible. a. x 2 โ 25 b. โ^11 x โ^24 +^ x 2 c.
2 ax โ 10 ay โ 3 bx + 15 by
d. 5 r 2 t + 30 rt 2
b. 3 x^ (^ x^ +^10 )=^6 x
3 c. m 2 2
7 m 6
d. x 3 โ 4 x = 12 โ 3 x 2 e. 64 t 2 = 9
6. Find all x-intercepts of f^ ( x^ )=^3 x
3
+ 3 x
2
โ 18 x .
7. Use the graphs of y = x
3
โ 3 x
2
+ 1 and y = x โ^2 to solve the given equations or
system.
a. x 3 โ 3 x 2
- 1 =โ 3 b. x 3 โ 3 x 2
- 1 = x โ 2 c. x 3 โ 3 x 2
- 1 =โ 1 d. y = x 3 โ 3 x 2
- 1 y = x โ 2
8. Solve by referring to values of the function f^ (^ x^ )=^3 x
2
โ 6 x + 1 shown in the table.
x f(x) -2 25 -1 10 0 1 1 - 2 1 3 10 4 25 a. 3 x 2 โ 6 x + 1 = 25 b. 3 x 2 โ 6 x + 1 =โ 3 c. 3 x 2 โ 6 x + 1 = 1 d. 3 x 2 โ 6 x + 1 =โ 2
- A rectangular painting (not including the frame) has a width of 9 inches and a length of 15 inches. If the area of the frame (of uniform width) is 112 sq. inches, what is the width of the frame?
- Give an example of a graph of a quadratic function with two x-intercepts, 1 x-intercept, and no x-intercepts. Label the vertex and draw in the axis of symmetry.
c. Predict the average money each African will receive from foreign aid in 2010 using the function provided. d. Predict when Africans will receive an average of $58 per person from foreign aid using your graph.
