pre-calc practice exam
MATH-1150 130
PRACTICE Exam #2
Instructor: Eric Harshbarger
Student Name: ____________________________
Student ID #: ______________________
Show all relevant work (use back of pages for scratch paper, if needed). CIRCLE FINAL ANSWERS.
1. [3 pts each] Evaluate each expression; write answer as a single complex number of the form a + bi.
a)
5−3 i 42 i
b)
7−2i−9−3 i
c)
8−3 i126i
d)
3−−4 6− −5
e)
4−i
75i
2. [4 pts each] Find all solutions of each equation and express them in the form a + bi.
a)
x2 - 3x + 3 = 0
b)
4x2 - 16x + 19 = 0
3. [3 pts each] Use a calculator to evaluate the function f(x) = 5·2x for the given input values of x.
Express your answer rounded to three decimal places.
a)
f 6.1 =
b)
f 3 =
c)
f −0.4 =
4. [3 pts each] Find the exact value (do not use a calculator or decimal places) of each expression:
a)
log63 + log612
b)
log32 - log354
c)
ln e4
5. [4 pts each] Combine each expression into a single logarithm and simplify, if possible:
a)
b)
log7(x2 - 5x + 6) - log7(x - 3)
ln 2ln x1−4 ln 3 x7
6. [4 pts] Use a calculator to evaluate this logarithm, rounded to three decimal places: log7168
7. [10 pts] For g(x) = 2x, complete the chart below: x g(x)
3
2
1
0
-1
-2
-3
8. [4 pts] Plot the points and sketch the graph of g from #7 above using the chart as a guide.
9. [4 pts] Now, on the same grid above, sketch the graph of h x =4−2 x2
10. [3 pts each] Find the solution to each equation; you may leave the answer in exact form, or rounded to three decimal places:
a)
3 x2=17
b)
e 3−5 x =16
11. [4 pts each] In each equation, solve for x; you may leave the answer in exact form, or rounded to three decimal places:
a)
b)
e 4 x 2 e 2 x −15=0
log3(x + 15) - log3(x - 1) = 2
12. [10 pts] A sum of $1000 is invested at an interest rate of 7% per year. Find the
PRACTICE Exam #2
Instructor: Eric Harshbarger
Student Name: ____________________________
Student ID #: ______________________
Show all relevant work (use back of pages for scratch paper, if needed). CIRCLE FINAL ANSWERS.
1. [3 pts each] Evaluate each expression; write answer as a single complex number of the form a + bi.
a)
5−3 i 42 i
b)
7−2i−9−3 i
c)
8−3 i126i
d)
3−−4 6− −5
e)
4−i
75i
2. [4 pts each] Find all solutions of each equation and express them in the form a + bi.
a)
x2 - 3x + 3 = 0
b)
4x2 - 16x + 19 = 0
3. [3 pts each] Use a calculator to evaluate the function f(x) = 5·2x for the given input values of x.
Express your answer rounded to three decimal places.
a)
f 6.1 =
b)
f 3 =
c)
f −0.4 =
4. [3 pts each] Find the exact value (do not use a calculator or decimal places) of each expression:
a)
log63 + log612
b)
log32 - log354
c)
ln e4
5. [4 pts each] Combine each expression into a single logarithm and simplify, if possible:
a)
b)
log7(x2 - 5x + 6) - log7(x - 3)
ln 2ln x1−4 ln 3 x7
6. [4 pts] Use a calculator to evaluate this logarithm, rounded to three decimal places: log7168
7. [10 pts] For g(x) = 2x, complete the chart below: x g(x)
3
2
1
0
-1
-2
-3
8. [4 pts] Plot the points and sketch the graph of g from #7 above using the chart as a guide.
9. [4 pts] Now, on the same grid above, sketch the graph of h x =4−2 x2
10. [3 pts each] Find the solution to each equation; you may leave the answer in exact form, or rounded to three decimal places:
a)
3 x2=17
b)
e 3−5 x =16
11. [4 pts each] In each equation, solve for x; you may leave the answer in exact form, or rounded to three decimal places:
a)
b)
e 4 x 2 e 2 x −15=0
log3(x + 15) - log3(x - 1) = 2
12. [10 pts] A sum of $1000 is invested at an interest rate of 7% per year. Find the