Math 152
Study Guide for Exam 2
Instructor: G. Rodriguez
You may use both sides of a 3" × 5" note card (index card/piece of paper) and a scientific
calculator. You are expected to know (or have written on your note card) any formulas you
may need. Think about any formulas you needed for homework (e.g. formula for sum of
cubes).
For some items I have only listed one sample problem BUT I expect you to be able to do any
of the homework problems.
1. Linear function applications: given some data, find a linear function that fits the data and
then use the function to answer some questions. 2.5
Number of U.S. lawsuits by
smartphone companies for patent
infringement
The scatter plot shows the number of U.S. lawsuits by smartphone companies for patent
infringement from 2004 to 2010.
(6, 97) 97 100 80 (3,49) 60 49 72 57 38 40 26 26 20 0 0 1 2 3 4 5 6 Number of Years after 2004
a. Let x represent the number of years
after 2004. Let y represent the number
lawsuits. Use the coordinates of the
points shown to write the line’s
equation in point-slope form and slopeintercept form. (The points for the
years 2007 and 2010.)
b. Use the slope-intercept form of the
equation from part (a) to project the
number of lawsuits by smartphone
companies for patent infringement in
2016.
2. Write the point-slope form of the line’s equation satisfying the conditions. Then use the
point-slope form of the equation to write the slope-intercept form of the equation in
function notation. 2.5
passing through (4, 2) and (6,−2)
3. Use the given conditions to write an equation for each line in point-slope form and in
slope-intercept form. 2.5
a. Passing through (8, −3) and parallel to line whose equation is 3x + 4y = 6
b. Passing through (3, 2) and perpendicular to line whose equation is y = 3x+5
4. Solve a linear inequality in one variable, including those with fractions, no solution or an
infinite number of solutions. If the inequality has solutions, I expect you to graph the
solution set and write it in interval notation. If the inequality has no solution, then write ∅.
(
)
(
a) 3x − 5 x − 4 > 4 x + 8
b)
x+4
2x − 1
+ 3 ≤
6
4
)
4.1
( )
8 − 5 ( x + 2 ) > 4x − 7 − 9x + 2
c) 8 − 5 x + 2 < 4x − 7 − 9x + 2
d)
e) Let f (x) = 2(x − 4) + 5 and g(x) = −5x + 8 + 7x . Find all values of x for which f(x)≥g(x).
5. Solve an application by setting up a linear inequality. Be sure to answer the question
asked; that is to write the inequality as a sentece. 4.1
a) The percentage, P, of U.S. voters who use punch cards or lever machines national
elections can be modeled by the formula P = −2.5x + 63.1, where x is the number
of years after 1994. In which years will fewer than 38.1% of U.S. voters use punch
cards or lever machines?
b) A salesperson earns $500 a month plus a commission of 20% of sales. Describe the
sales needed to receive a total income that exceeds $3200 per month.
6. Solve a compound inequality that: uses ‘and’; uses ‘or’; is of the form a < bx + c < d; or
is written using function notation. Expect at least one of each type to be on the exam. 4.2
a) x − 1 ≤ 8 and 4x + 1 ≤ 9
b) x − 1 ≤ 8 or 4x + 1 ≤ 9
c) 2x − 1 ≤ 9 or 3x − 2 > 4
d) 2x − 1 ≤ 9 and 3x − 2 > 4
e) 3 < 2x + 4 < 8
f) Let f(x)= x—2 and g(x) = 2x+1. Find all values of x for which f(x)≥5 or g(x)<3.
7. Solve an absolute value equation. Remember to isolate the absolute value expression
BEFORE rewriting as two equations. 4.3
a)
2x − 5 − 4 = 12
b)
4 3x + 2 = 18
8. Solve an absolute value inequality. Graph the solution set and write the solution in interval
notation. If the inequality has no solution or an infinite number of solutions, use
appropriate notation. 4.3
a)
2x − 4 ≥ 6
c)
2x + 5 + 8 < 6
b)
2x − 4 ≤ 6
d)
2x + 5 + 8 > 6
9. Graph a linear inequality. 4.4
x + 2y > 6
10. Graph the solution set of a system of linear inequalities. 4.4
x—y ≤ 1
x>2
11. Add or subtract polynomials. If only one variable in poly, write the answer in descending
order. Remember that when you combine terms, the variable part stays the same; only
the coefficient changes. 5.1
a) (9x3 — 3x2 — 2) + (2x2 — 9x — 5)
b) (6x 4 y 2 − 2x 3 y − 4 y) − (4x 4 y 2 + 5x 3 y − 3y + 9x)
12. Multiply two poly’s. If only one variable in poly, write the answer in descending order.
Problem may be given using functions, i.e., find (fg)(x). 5.2
a)
b)
c)
( 3x + 2 ) ( 5x − 4 x − 8 )
( 3x − 5 y )
Let f ( x ) = x − 4 and g ( x ) = 3x + 2 . Find ( fg ) ( x ) .
2
2
2
13. Factor completely any given polynomial. Expect SEVERAL factoring problems. My only
instructions for these will be to factor completely or state the poly is prime. There are
SEVERAL methods to factor. It is up to you to decide which method/tool to use. I won’t
give you any formulas so write any you need on your index card. ONLY 5.3, 5.4
a) 3x3 − 15x2 + 7x – 35
b) 3x2 − 18xy − 48y2
c) 3x2 + 2x – 21
d) 4x2 + 5xy − 6y2
e) 4x2 + 16xy + 15y2
f) 10y5 – 28y4 + 16y3
g) 2y10 + 5y5 – 3