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?