The document is a math review from Colegio San Patricio for the 3rd period of the 2009-2010 school year. It contains 20 practice problems across 5 sections - comparing ratios, central tendency measures, numerical sequences, linear equations, and graphing linear equations. The student is asked to show their work and provide the answers.

1. Colegio San Patricio
3rd Period Math Review WITH ANSWERS
School Year 2009 – 2010
Name ___________________________________________________List No._________8th_________
Teacher_________________________________________________ Date_______________________
I. Comparing Ratios
1. You need to buy a bottle of catsup. As you look at the bottles on the shelf, you notice that
you can pay $2.70 for an 18 oz. bottle, or you can pay $1.68 for a 12 oz. bottle. Which bottle is
the better buy?
$2.70/ 18 = $0.15 ¢ $1.68/ 12 = $0.14 ¢
So the 12oz. is the cheapest bottle, and the better buy.
2. In a major city, 8% of the potential work force, which consists of 550,000 people, are
unemployed. How many people are unemployed?
550,000 people - 100% (550,000 * 8)/100 = 44,000
_______ - 80% So 44,000 represent the 8% of unemployed people.
3.) A large university employs 275 work study students. The 150 men that are employed take
home a total of $6,000 per week, and the 125 women earn $5,625 per week. Who, on the
average, makes more, a man or a woman?
Men = $6000/150 = $40 per week
Women = $5625 /125 = $45 per week So women earn $5 more dollars per week.
4.) If you have 3 dogs out of 10 pets, which is the dog’s ratio?
a) 0.7 b) 0.3 c) 0.75 d) 0.45
3/10 = 0.3
II. Central Tendency Measures (Mean, median, mode)
5.) In the following exercises find the mean, median and mode.
a) 6, 7, 12, 14, 12, 11, 10, 12, 9, 10
Mean = (6 + 7 + 12 + 14 + 12 + 11 + 10 + 12 + 9 + 10)/10 = 10.3
Median = 10.5
6, 7, 9, 10, 10, 11, 12, 12, 12, 14 so (10 + 11)/2 = 10.5 is the median.
Mode = 12
b) 10, 12, 12, 14, 20, 16, 12, 14, 11
Mean = 13.4 Median = 12 Mode = 12
c) 4, 8, 3, 4, 9, 7, 8, 3, 2, 4, 3
Mean = 5 Median = 4 Mode = 3 and 4

2. III. Numerical Sequences
6.) What is the rule for the next sequence: 3, 5, 7, 9, …?
The difference between each integer is +2, so the first part of the rule is 2n. Now you do
a quick check just so see if you need to add or subtract so the rule is “complete”.
(Remember n = position of the integer in the sequence.)
2n = 2(1) = 3 (it should give us the first number of the sequence). We notice that we
should add +1 so that statement is correct. Then our rule is complete.
2(1) = 2 +1 = 3. Now we have the rule: 2n + 1.
7.) What is the next number in the following sequence: 1, 4, 7, 10 …?
10 + 3 = 13. (Just in case you want the rule: 3n -2.)
8.) From the following numerical sequence -2, 3, 8, 13, …, what is the number on the
7th.position?
Rule: 5n – 7 when n= 7, we substitute: 5(7) – 7 = 35 – 7 = 28
9.) Being 3n - 5 the rule for a numerical sequence, which is the corresponding number for n
= -4? Rule: 3n – 5 substitute n = -4 3(-4) – 5 = - 12 – 5 = -17
IV. Linear Equations
10.) The Tri-State car rental agency charges a flat fee of $25 plus $0.17 per mile to rent a
subcompact car on weekends. Write a linear model for the cost in terms of the number of
miles driven. How much would you pay if you rented the car for 3 days and you traveled 50
miles each day?
Cost = $25 + $0.17x x = miles used
3 days * 50miles per day = 150 miles
Substitute: Cost = $25 + $0.17(150 miles) = $50.5
11.) What is the solution for the following equation: 5x - 3x + 15 = x + 16?
Simplify first: 2x + 15 = x + 16
Variables on one side: 2x – x = 16 - 15
Simplify: x=1
12.) What is the solution for the following equation: 2(x - 1) = x + 1?
2(x - 1) = x + 1
2x - 2 = x + 1
2x – x = 1 +2
x=3
13.) According to the following chart, which value should be the accumulated one by the
8th.month?
y = b + ax
y = $ 750 + (1) ($50)
y = $ 750 + (2) ($50)
y = $ 750 + (3) ($50)
y=…?
Just substitute:
y= $750 +(8) ($50) = 750 + 400 = $1150

3. 14.) Solve: -2(x + 3) = x + 6
-2x – 6 = x + 6
-2x – x = 6 + 6
-3x = 12
x = 12 / -3 (Remember: it’s INVERSE OPERATION, so the number moves WITH the sign.)
x = -4
V. Graphing Linear Equations
15.) Use a table to graph the equation: 16.) Use x and y intercepts to graph the
2y – 10x = 20 equation: 8y + 4x = 24
x -2 -1 0 1 2
Y 0 5 10 15 20
1. Isolate “y”: * When you read “Quick graph” or “Intercepts”
2y -10x = 20 it means you should let x= 0 and y=0.
2y = 20 + 10x x=0 y=0
y = (20 + 10x)/2 y= 3 x=6
y = 10 + 5x 8y + 4(0) =24 8(0) +4x=24
2. Substitute for EACH “x” value 8y = 24 4x=24
y = 10 + 5(-2) y = 10 + 5(-1) y= 24/8 = 3 x=24/4= 6
= 10 – 10 = 10 -5
=0 =5 * Now you can graph because you have
y = 10 + 5(0) y = 10 + 5(1) 2 coordinates to plot in the
“Cartesian Plane”.
= 10 = 10 + 5 (0, 3) and (6, 0)
= 15
y = 10 + 5(2)
= 10 + 10
= 20
3. Graph

4. Slope of a Line:
17.) Find the slope of the line 18.) Find the slope of the line passing
through points (9, 2) (-5, -2).
m = y2 – y1
X2 – x 1
x1 y1 x2 y2
(9, 2) (-5, -2)
Substitute in the formula:
-2-2 = - 4
-5-9 -14
So the slope is 2
7
Slope = ____-1_______________________ Slope = ___2/7___________________
*Remember: If the line is FALLING it
has a negative slope.
*Choose 2 points that ARE whole numbers.
* Then, just get rise and run.
* Rise= the “height” = 1
* Run= the “length” = 1
So 1/1 =1, and because it’s falling is -1.
19.) Determine whether the line passing through the points (-9, -4) (6, -1) rises, falls, is horizontal
or vertical line.
m = -1 –(-4) = -1+4 = 3 = 1
6 –(-9) 6+9 15 5
So the slope rises.
20.) Find the slope of the line passing through points (3, -2) (5, 5).
m = y 2 – y1
X2 – x1
x1 y1 x2 y2
(3, -2) (5, 5)
Substitute in the formula:
5-(-2) = 5+2 = 7
5–3 2 2
So the slope is 7
2