MTH 209 WEEK 1 QUIZ



MTH 209 WEEK 4

Name

1. Use the product rule to simplify. (All variables represent non negative real numbers.)

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= sqrt(4x^4 * 5xy)

= sqrt(4x^4)*sqrt(5xy)

= 2x^2 * sqrt(5xy)

2. Evaluate:

253/2

= sqrt(25)^3

= 5^3

= 125

3. Simplify

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= 27w / w^-2

= 27w^3

4. Simplify

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= 3x * sqrt(8x^4)

= 3x * sqrt(4x^4 * 2)

= 6x^3 * sqrt(2)

5. Multiply

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It’s a difference of squares:

(5sqrt2)^2 – 3^2

= 50 – 9

= 41

6. Add

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= 11/sqrt(11)

= 11*sqrt(11)/11

= sqrt(11)

7. Solve and check for extraneous solutions

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Square both sides:

5x+2 = 3x+8

x = 3

Check: sqrt(17) = sqrt(17), yes!

8. Solve by completing the square:

x2 + 10 x – 9 = 0

x^2 + 10x = 9

x^2 + 10x + 25 = 9+25

(x+5)^2 = 34

x+5 = +/- sqrt(34)

x = -5+sqrt(34), -5-sqrt(34)

9. Solve using quadratic formula

3x2 - 6x = 24

3x^2 – 6x – 24= 0

x = (6 +/- sqrt(6^2 -4*3*-24))/6

x = (6 +/- sqrt(324))/6

x = (6 +/- 18)/6

x = 1 +/- 3

x = 4 or -2

10. What are the length and the width of a metal plate which has a length that is 4 cm less than twice its width and which has an area of 96 cm.

A = LW

L = 2W-4

96 = W(2W-4)

96 = 2W^2 – 4W

2W^2 – 4W – 96 = 0

Divide by 2:

W^2 – 2W – 48 = 0

Factor:

(W-8)(W+6) = 0

W = 8 or -6

Can’t be negative.

W = 8 cm

L = 2W-4 = 2*8-4 = 16-4 = 12 cm

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