Download Midterm Exam Review

Intermediate Algebra
Name
Period
Date
Midterm Exam Review


4 12
1) Let the set S   5, 9,7, ,0, , 16, 8,2.5,10 . List the elements that belong in each of
3
4


the following sets.
a) Rational Numbers
b) Integers
c) Whole Numbers
d) Real Numbers
2) Perform the indicated operations to completely simplify the expression
a) –6 + 14 + (–11) – (–3)
b) 10 – 43 + 6(–4)
c) 7 – 42 + 2(6) + (–4)3
1
 8  24  (6)
d) 2
2
 6  16(5)
3
e)
2 3  (1  2)  2 
4
 9  (2)
3
g) |7-15| + |6-2|
478154593
f)
8  4  32  5  2(1)
3  23  1
h) | 21 – 6 | – | 14 – 18 |
p. 1
3) Use properties of real numbers to simplify each expression
a) –3y + 6 – 5 + 4y
b) 2a + 3 – a – 1 –a – 2
c) –2(k – 1) + 3k – k
d) –3(4m – 2) + 2(3m – 1) – 4(3m + 1)
e) 6(2x – 4) + 4[–5x + 3(4x – 7)]
f) –(–p + 6q) – (2p – 3q)
4) Evaluate the following expressions when k = –4, m = –3, n = 16, and r = 25
a) 4k – 7m
b) 3 n  m  5k
8k  2m2
c)
r2
d) 4 mr  7k n
5) Rewrite these sentences as equations
a) 5 less than 6 times a number equals 2
times the number
b) 9 less than 3 times a number equals 8 less
than 5 times the number
6) Rewrite the following equations as English language sentences.
a) 3 + 4x = 4x – 11
b) 7 – 3x = 2x
478154593
p. 2
7) Write each set in interval notation and graph on a number line
a) {x | x > –5
b) { x | –2 < x < 3 }
8) Find the distance between the given points on the number line.
a) x = 14 and x = –5
b) x = –35 and x = –12
9) Solve each equation for the unknown variable
a) 2x + 4 – x = 4x – 5
c) 4(m+2) – 8m – 5 = –3m + 9 – 2(m + 6)
b) –2k – 3(4 – 2k) = 2(k – 3) + 2
d)
2x  5
1
2 x
2
2
e)
3x 5x

 13
4
2
f)
8y 2 y

 13
3
4
g)
2x  1 x  1

3
4
h)
2x  3 5x  2

2
5
478154593
p. 3
10) Solve each formula for the specified variable
PV
a)
 n ; for T
RT
c) V= LWH; for H
h
b) A  (B  b) ; for b
2
9
d) F  C  32 ; for C
5
11) Solve each absolute value equation. Be sure to check to see if the answer is “no solution.”
a) |z – 4| = –12
c)
478154593
1
3x  4  3
2
b) |4a + 2| = 4
d) |–3a + 1| –8 = 2
p. 4
Solve each inequality, show the solution in interval notation and graph on a number line
b) –5x – 4 ≥ 11
2
a)  x  6
3
c) 8 ≤ 3x – 1 < 14
d) –16 ≤ 3x + 2 < –10
e) –4x + 1 ≥ –15 and 3x – 4 ≤ 8
f) 2x – 6 ≤ –18 and 2x ≥ –18
g) x + 1 > 3 or x + 4 < 2
h) –4x + 1 > 5 or x + 12 < 3x
i) |x + 1| ≥ –3
j) |5r – 1| > 9
k) |11x – 3| ≤ –2
l) |4x – 7| < 3
478154593
p. 5
2) Find the x-intercept and y-intercept for each equation and graph the line.
a)
2x + 5y = 20
b)
7x + 7y = 28
3) Graph the lines associated with these equations
a)
y = 2x + 3
b)
3x + 4y = 18
c)
x=5
d)
y=3
478154593
p. 6
4) Write the equations of the lines that pass through the two given points. Your answers should be in
slope-intercept form.
a) ( –1, 2 ) and (4, –5)
b) ( 2, –3 ) and (4, –2)
5) In each case, determine if the two given lines are parallel, perpendicular, or neither
a) 2x + 3y = 7 and 4y = 6x + 3
b) y = –3x + 9 and –2y = 6x + 7
c) 4x – 12y = 8 and 12x + 4y = 16
d) 2x + 3y = 7 and 4y = 6x + 3
6) Write the equation of the line that passes through the given point and is parallel to the given line
a) Through (7, 2) and parallel to 3x – y = 8
b) Through (–1, 3) & parallel to –x + 3y = 12
478154593
p. 7
7) Write the equation of the line that through the given point and perpendicular to the given line
a) Through (8, 5) and perpendicular to
b) Through (–2, 7) and perpendicular to
2x – y = 7
5x + 2y = 18
8) Graph the solution set to each of these inequalities
a)
4x – y < 4
b)
–3x + 2y ≥ 6
c)
x ≤ –1
d)
y≥4
478154593
p. 8
9) Simplify the following exponential expressions. When you are completed, each variable base
should be used only once and there should be no negative exponents. Numerical bases must be
completely simplified.
a) 80 =
b) –80 =
c) 5–2 =
d) (9x2)(–2x5) =
2
2
e)   
 3
g)
49x 2 y10

7x 3 y 12
f)
12x 3 y 6 z10

6xy 5 z11
h)
36x 5 y10

24xy 3
10) Perform any indicated operations and simplify these polynomial expressions
a) (9x – 3)(3x + 6)
b) (2x + 6)2=
c) (6x – 3) – (5x + 7)
d) (12x2 + 3x – 6) – (9x2 +6x – 5)
478154593
p. 9
Solve these word problems. The following items must be shown:
a)
b)
c)
d)
e)
Define the unknown variable you will use to solve this problem. Make sure the definition is specific.
Write the appropriate equations using the variable you defined
Solve for the indicated value(s)
Check your solutions against the original problem statement
Write each solution using a descriptive sentence. Be sure to give everything that is requested.
Formulas: for interest: p r t = I
for travel: r  t = d
11) Jack wants to invest $20,000. He invests part into an account that earns 7% interest and the
remaining into an account that earns 3% interest. If the total interest earned after 1 year is $1,100 ,
how much did Jack invest into each account?
12) Let x be the measure of the first angle of a triangle. The measure of the second angle is 10 less
than the first angle. The measure of the third angle is 35 less than 10 times the first angle. Find the
measure of each angle in the triangle
13) Steve’s yard is in the shape of a rectangle. The perimeter of his yard is 310 meters. The length of
his yard is forty yards less than twice the width. What are the length and width of his yard?
14) Find three consecutive odd integers such that the sum of the smallest and four times the largest is
61
15) At 3 pm, Marty leaves Hackensack and travels East at 45 miles/hour. At 5 pm, Artie leaves
Hackensack and also travels East, but he is going 65 miles/hour. At what time will Artie catch up
to Marty?
478154593
p. 10