Algebra 101

simple algebra questions, make it pdf

Math-UA.009. Written Homework
MATH-UA-009 — Algebra, Trigonometry and Functions
Professor Ross Flek
Name:
NetID:
Homework Assignment #9
Due Date: December 4th, 2023, 11:59 PM
• This homework should be submitted via Gradescope by 23:59 on the date
listed above. You can find instructions on how to submit to Gradescope on
our Campuswire channel.
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uploaded.
• You must show all work. You may receive zero or reduced points for
insufficient work. Your work must be neatly organised and written.
You may receive zero or reduced points for incoherent work.
• If you are writing your answers on anything other than this sheet, you should
only have one question per page. You can have parts a), b) and c) on the
page for example, but problems 1) and 2) should be on separate pages.
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page that your answer appears on. If you do not you will be docked a
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• When appropriate put a box or circle around your final answer.
• The problems on this assignment will be graded on correctness and completeness.
• These problems are designed to be done without a calculator. Whilst there is
nothing stopping you using a calculator when working through this assignment,
be aware of the fact that you are not permitted to use calculators on exams
so you might want to practice without one.
1
Math-UA.009. Written Homework
1. (6 points) Evaluate the following.
(a) (1 point) log7 (710 ) =

(b) (1 point) log3
1
27

=
 
1
(c) (1 point) log4
=
2
(d) (1 point) log4 (8) =
(e) (1 point) 5log5 (27)
(f) (1 point) eln(1/π)
2
Math-UA.009. Written Homework
2. (10 points) Expand the following completely. Your final results should have
no exponents or radicals.
(a) (2 points) ln (x2 y)
(b) (2 points) log7
 2 !
x
y
 3 2
xy
(c) (2 points) log2
z
(d) (2 points) log5
!
√ p
x 3 y2
z4
r
(e) (2 points) log4
3 2
4 x y
z4
!
3
Math-UA.009. Written Homework
3. (9 points) Combine the following into a single logarithm.
(a) (2 points) log2 (A) + log2 (B) − 2 log2 (C)
(b) (2 points) 4 log6 (y) −
1
log6 (z)
4
(c) (2 points) 4 log2 (x) −
1
log2 (x2 + 1)
3
(d) (3 points) log10 (5) + 2 log10 (x) + 3 log10 (x2 + 5)
4
Math-UA.009. Written Homework
4. (4 points) Solve the following basic equations for x.
(a) (1 point) log4 (x) = 3
(b) (1 point) ln (x) = −1
(c) (1 point) logx (16) = 4
(d) (1 point) log8 (x) =
1
3
5
Math-UA.009. Written Homework
5. (12 points) Solve the following equations for x
(a) (3 points) log5 (x) + log5 (x + 1) = log5 (20)
(b) (3 points) log13 (x) + log13 (x − 1) = log13 (4x)
(c) (3 points) log10 (x) + log10 (x − 3) = 1
(d) (3 points) log3 (x + 15) − log3 (x − 1) = 2
6
Math-UA.009. Written Homework
6. (4 points) Solve the following for x.
2
(a) (1 point) 8x = 83x+10
(b) (1 point) 51−x = 25
(c) (2 points) 9x = 272+x
7
Math-UA.009. Written Homework
7. (6 points) Graph the oriented angle in standard position. Classify each angle
according to which Quadrant its terminal side lies in.
(a) (1 point)
π
3
(b) (1 point) −
(c) (1 point)
π
6
7π
6
8
Math-UA.009. Written Homework
(d) (1 point) −
(e) (1 point)
11π
3
7π
2
(f) (1 point) −
15π
4
9
Math-UA.009. Written Homework
8. (12 points) Find the terminal point on the unit circle determined by the following real numbers t:
(a) (2 points) t =
5π
4
(b) (2 points) t =
4π
3
(c) (2 points) t =
5π
6
(d) (2 points) t = −
π
4
(e) (2 points) t = −
π
2
(f) (2 points) t = −π
10
Math-UA.009. Written Homework
9. (2 points) Find the area of a sector of a circle with central angle of 45◦ if the
radius of the circle is 4 m. Leave your answer in terms of π.
11