Compass Review

January 2014

Math Section Consist of 5 parts.

Pre-Algebra

Algebra

College AlgebraGeometry

Trigonmetry

Pre-Algebra Concepts

•Mean, median, and mode•Fractions, decimals, and percentages• Integers, exponents, square roots, and scientific notation

Mean, Median, Mode

Mean

This is the average of the set of data. You simply add up the data and then hit enter to find the sum. Divide the sum by the number of data in the list.

MedianPut the set of data in order and then find the number located in the middle position. If there are two, find the average of the two.

Mode

This is the easiest! It is simply the number or piece of data that is most frequent in the set.

Let’s Practice…. • Find the mean, median, mode, and range for the following list of values:• 13, 16, 14, 14, 13, 16, 15, 21, 13, 20Step 1 – put the data in order….. (13,13, 13, 14, 14, 15, 16, 16, 20, 21)Remember this test isn’t timed, so don’t rush. To find the mean, add the data. The sum is 155 and there were 10 pieces of data so 155/10 = 15.5 The mode you can see is 13. There can be more than 1 mode. The median is the middle two numbers in the set. Since there are two numbers in the middle we find the middle or average of those. 14 and 15 are in the middle of the list. They add up to 29/2 is 14.5.

Calculate the mean of the number set (26, 12, 26, 8, 26, 26, 23).

a. 26 b. 24 c. 23 d. 21e. 20

What is the median?

What is the mode?

26

26

A company selling televisions instituted a price increase at the end of the year. One unit’s selling price of $720 was increased to $900. By what percentage was the price increased?

a. 20% b. 15% c. 25% d. 18% e. 22%

Fractions, Decimals, and Percents• It is best to know basic conversions like these• ½ = .5 = 50% 1/3=.3 R = 33.3 R % ¼ = .25=25%• 1/5= .2 = 20% 1/6 = .16 R = 16.6R% 1/8 = .125 = 12.5%• 1/10 = .10 = 10% 2/3 = .6 R = 66.6R % 1/20 = .05 = 5%When in doubt you can divide the numerator by the denominator to get the decimal. Zoom also converts these with the mode button. When changing a decimal to a percent move decimal 2 places right. When changing a percent to a decimal move decimal 2 places to the left. There will be basic computation and word problems using all 3 forms of these numbers. Use common sense to see if answer is practical.

Basic calculation of fractions… remember to follow order of ops.

If not using zoom remember we don’t divide fractions like 3/2 by 1/4. We multiply by the reciprocal.

Series of fractions is pre-algebra too.

What will be the eighth element of the series beginning 1, -1/2, 2, -1/4, 4, -1/8?

a. ¼ b. 6 c. -1/16 d. 16 e. 8

There will be many types of word problems with these concepts.

Yossi gets a 20% discount at the bicycle store because he works there. How much will he have to pay for gear that normally sells for $150? a. $140 b. $130 c. $120 d. $110 e. $100

Martine gets an auto service bill charging her $350 for labor and $150 for parts.

What percentage of the total bill is for parts? a. 30% b. 15% c. 150% d. 75% e. 45%

Bartholomew buys 12 gallons of gasoline for his car at a price of $2.40 per gallon.

He hands the attendant two $20 bills. How much change should he receive?

a. $16 b. $12.20 c. $11.40 d. $11.20 e. $10.80

Half the students taking a math test receive an average grade of 66%. The other half receives an average grade of 86%. What is the average grade overall?

a. 70% b. 74% c. 76% d. 78% e. 82%

A man drives 350 miles in 7 hours. If he continues at the same average speed, how long will it take him to complete a 400 mile trip?

a. 8 hours b. 9 hours c. 8.5 hours d. 9.5 hours e. 7.5 hours

You will have to be able to use integers by adding, subtracting, multiplying, and dividing.

John works for four hours at $15/hour. He then buys two CDs at $13.25 each. How much money does he have left? a. $33.50 b. $1.75 c. $26.50 d. $15 e. $30

There will be word problems with integers as well.

A cell phone company offers two plans. Plan A customers pay $3 for every hour of phone usage. Plan B customers pay a flat fee of $35 per month. If Melanie signs up for plan B and uses her phone for 16 hours the first month, how much does she save compared to if she had selected plan A? a. $8 b. $48 c. $35 d. $13 e. $17

If 25 pounds of potatoes costs $30, how much will 30 pounds cost?

a. $25 b. $32 c. $36 d. $38 e. $42

You must use exponents and square roots.

Which expression is equivalent to This one takes some thinking….

And use scientific notation. Solve 4.5 × 107

1.5 × 10-3

Do this first mentally with exponent rules and take time to check on zoom. a. 3×104

b. 3×10−4

c. 3×1010

d. 3×10−10

e. 3×1021

If simplifying scientific notation, move decimal left with negative exponents and right with positive exponents.

Algebra• Basic operations/factoring polynomials• Setting up equations and substitution• Linear equations with one or two variables• Radicals and rational expressions

What is the value of y if y = 2x2 − 4 and x = 3?

a. 16 b. 9 c. 18 d. 14 e. 2

The area A of a triangle is calculated as A = 1/2hB. If the height h is 12 feet and the base B is 4 feet long, what is the area, in square feet?

a. 24 b. 12 c. 36 d. 48 e. 8

Mrs. Park is organizing a class trip to the aquarium, and has raised $900 to help pay for it. Adult tickets are $45, and student tickets are $30. If she has 25 students and needs to take one adult for every five students, how much will each student have to pay so that the adults who agree to chaperone will have to pay nothing?

a. $5 b. $6 c. $4 d. $3 e. $2

A 210 ft. long rope is cut into 3 pieces. The first piece of rope is 3 times as long as the second piece of rope. The third piece of rope is 2 times as long as the second piece of rope. What is the length of the longest piece of rope?

a. 70 ft. b. 90 ft. c. 105 ft. d. 110 ft. e. 140 ft.

Linear equations with one or two variables.