Pre calculus review

MAC 1147 TEST 3 REVIEW

lessons 5, 6, 7

1. Show synthetic division, factor, and solve

A. f(x) = x3 –x2 -9x + 9 given x=1 a solution

B. f(x) = x3 – x – 6 given x=2 a solution

c. f(x)= x3 -7x2 + 36 given x = 3 a solution

2. Graph. State the multiplicity of each solution

A. f(x)= x(x+4)2

B. f(x) = x4 -7x2 +10

C. f(x) = (x – 3)(x +1)(x +5)

D. f(x) = (x-4)2(x +2)2

3. Write a polynomial function with the given zeros x= - 6, 2, - 4

4. Is x 3 a factor of the function F(X) = x3 -4x2 +9

5. Graph the following

y = ex +2 y = log x + 2

y = 2x +2 y = ln(1 – x)

y= -2x +5 y = ln(x + 3)

y= - ( 1

2 )

𝑥

+ 5 y = log (x – 2)

y = ( .5)x -2 y = ( 1

3 )x +3

6. Evaluate

log3 81 log5 1

625 log .001 log212

e.06 41.4

7. Convert to exponential form log5 x = 2

8. Convert to log form x3 = 5

9. Expand

log x2(x – 7)3 ln 3x √𝑥 + 4

ln x √𝑥 + 2 3

log (𝑥+5)2

√𝑥

ln √ 𝑥+1

𝑥−1 log √

𝑥

𝑦3 4

10. Write as a single log

2lnx + 4ln(x + 2)

ln x + ln(x2 -81) –ln(x+9)

3logx + 2logy -3log z

5log(x - 1) - 2logx

11. Solve. Must round to 4 decimal places

e2x = 5 e2x + ex – 6 = 0

4x = 17 52x – 5x - 12 = 0

5x + 1 = 3125 5x +2 = 23x

log4 (5x – 1 )= 4 log2 x + log2 (x – 2) =3

log x = - 3 log2 (x – 1) – log2 (x – 2) = 3

3(1.075)x = 375 log (8x ) = 5

ln x = 4 ln √𝑥 + 4 = 2

ln (3x) = 2 ln (x +3) = 2

12. Suppose you invest $20000 at 6% rate for 4 years. Calculate the interest earned if

invested

semi-annually

quarterly

continuously

13. How long will it take for $4000 to grow to 5800 at 6.5% rate if invested

quarterly

monthly

continuously

14. How long will it take to double a $2000 at 6% rate if compounded

continuously

semi annually

quarterly

15. You bought a computer for $600 in 2014. It is worth $475 in 2018.

find the depreciation rate

write a function in terms of years

find the value of the computer in 2020

16. How much should be invested to have $8000 in 5 years at 9.2 percent rate compounded

quarterly

semiannually

continuously

17. Suppose you buy a car in 2018 for $23500. If your car depreciate at a rate of 15.5% per

year, how long will it take for your to reach half of its worth?

18. How many half life does it take for 200 gram of an element to decompose to 25 grams?