Math ACT PrepAVID

Math Prep

Make sure you write down each example and the steps to solving them This will be part of your overall grade on

this set of notes

Math Basics

60 minutes -> 60 questions Each question has 5 answer choices

(different than every other section)

Math Question Breakdown Refer to description handout▪ 24 Pre-algebra/elementary algebra ▪ 14 plane geometry▪ 10 intermediate algebra▪ 8 coordinate geometry▪ 4 trigonometry

Use of Calculators

You do NOT need a calculator to solve any of the problems on the ACT▪ If you find yourself doing lengthy calculations,

you probably missed a short cut.▪ Relying on the calculator will waste time

Make sure you use a calculator your are familiar with on test day

Calculators are good for trig calculations.

Lesson 8 – Percents

Some percent questions will be disguised as word problems. Make sure to read the problem and

understand what it is asking you to do. Most Common Types of Percent

Questions: Percent taken off Percent change Combined percents

Percent Taken Off

Example: A jacket regularly priced at $135 is discounted by 10%. What is the discounted price of the jacket?

Step 1 – Subtract the percent from 100Step 2 – Convert the percent to a decimalStep 3 – Multiply the decimal by the original whole.

Percent Change

This types involves a percent increase or percent decrease.

Percent Change Formula:

Percent Change

Example:A sweater that originally cost $100 is discounted to $70. What percent discount was applied to the sweater?

Use the formula from the previous slide

What is the given information

Combined Percents

These are more difficult because they require more steps and manipulation Usually a percent is taken off the original

twice, consecutively There is no formula to apply directly,

you must break the problems down to make them easier.

Combined Percents

Example:A television set originally costs $250. It is discounted 20% one day and another 15% the next. What is the total percent discount applied to the television set?

Percent Tips

If you see the words -> discount or sale Be ready to use the percent change

formula

Golden Rule of combining percents= NEVER JUST ADD PERCENTS ACT will have these as answer choices to

trick you

Lesson 9 – Proportions/Probability

Proportion and Probability problems include the following: Ratios▪ Comparison of two quantities by division▪ Written in fraction form or with a colon▪ Ratios are always written in lowest terms▪ They are part-to-part, not a fraction (part-to-whole)

Example – One term ratiosThe ratio of dogs to cats is 4:7. If there are 12 dogs, how many cats are there?

Example – Two Term RatiosThe ratio of dogs to cats is 4:7, and the ratio of cats to hamsters is 1:2. What is the ratio of dogs to hamsters?

Proportions▪ Two equal ratios, usually written as two

fractions set equal to each other ▪ Simplest way to answer them is to cross

multiply

Example:3/12 = x/36

Averages▪ Involve a simple 3-part formula▪ Average = sum of terms/number of terms

▪ Most problems will give you two parts of the formula and ask for the third

Example:Julie drove 15 miles on Monday, 23 miles on Tuesday, and 13 miles on Wednesday. What was the average number of miles Julie drove per day?

Rates▪ Is “any something PER something”▪ Rate formula -> rate = x/y▪ Most common rate is distance/time (rate =d/t)▪ Example: miles per hour

Example:Fred needed to drive 250 mile to get back to college. For the first 225 miles, he drove 60 miles per hour, and for the last 25 miles, he drove 50miles/hour. What was his average speed during this trip?

Probability▪ Probability formula -> three part formula▪ Probability = # of desired outcomes/# of possible outcomes

▪ In probability questions figure out what is the “outcome,” then use the formula

ExampleThere are 35 eighth-grade students, 22 seventh-grade students, and 43 sixth-grade students. If a student is randomly chosen to be a principle for a day, what is the probability the chosen student will be in eighth grade?

Lesson 10 – Variable Manipulation

Variables follow the same rules and order of operations of numbers

Trap Doors: Common answer traps involve details,

such as: negative signs, reversal of inequality signs.

Remember the order of operations: PEMDAS

Remember when working with equations, you must do the same thing to both sides.

Key Rules

Simplifying Expressions Follow the order of operations Rules for exponents▪ When dividing exponents with the same base,

subtract the exponent on the bottom with the one from the top.

Equations and Inequalities Follow order of operations With inequalities, when multiplying by

a negative number, you must flip the inequality sign

Systems of Equations Can be solved two ways: Substitution or

Combination▪ Substitution = solve the first equation, then

plug that value in the second▪ Combination = involves adding or subtracting

the equations, usually getting rid of one of the variables

The method usually depends on the problem, one method will be easier than the other.

Be sure to do what the question asks you to

Quadratic Equations –> ax2 + bx + c Classic quadratic equations▪ (x+y)2 = x2 + 2xy + y2

▪ (x-y)2 = x2 – 2xy + y2

▪ (x+y)(x-y) = x2 – y2

When given factors and asked to find the quadratic equation, you must use the FOIL method (first, outside, inside, last).

When given a quadratic equation and asked to find two factors, you must find two numbers that add up to “b” and multiply to produce “c”

Lesson 11 – Translating Word Problems

Trap Doors: Order of terms – make sure you read

carefully and order the terms correctly Variables – ▪ Variable stand for missing numbers▪ Follow the same rules for numbers▪ Don’t get confused if there is an extra “x” instead of

a number

Variable Names – ▪ If the problem asks you to make up your own

variable, be consistent and don’t get confused

Key Steps

Step 1 Read through the entire problem first

Step 2 Identify the type of problem▪ Percents, proportions, variable manipulation, etc.

Step 3 Look for key words or phrases▪ Words that signify operations

Step 4 Translate the problem into math▪ Use appropriate variables when necessary

Answer Key

LESSON 9

1. B2. J3. C4. H5. D6. G7. C8. J9. A10. H

LESSON 11

1. D2. F3. E4. H5. D6. K7. E8. J9. B10. J

Lesson 12 – Plane Geometry

Common Plane Geometry Traps Mistake 1 – misusing information

Make sure to identify the given info and use the correct formula

If an object is not given, make sure to draw the figure with the info in the correct spots

Mistake 2 – Assuming incorrectly Don’t assume a figure is a certain way

because of the way it looks, pay attention to the info given

Mistake 3 – incorrectly using formulas Make sure to use the correct formula▪ Most common mistake is the formula for the

area of a triangle▪ A = ½ bh

Key Rules

Circles Everything depends on the radius▪ Always identify the radii

Key formulas

Triangles All angles add up to 180° A = ½ bh Isosceles = two sides are equal in length Right triangle rules:▪ c2 = a2 + b2 - Pythagorean theorem

Rectangles and Squares Area = base x height

Parallelograms Opposite sides are equal

Isosceles Trapezoid Left and right sides are the same length

Multiple Figures Properties of figures don’t change when

figures are combined May have to draw in lines to complete

figures

Lesson 13 – Coordinate Geometry and Trigonometry

Key Rules Coordinate Geometry Formulas

Circle on the Coordinate Plane Formula (x-h)2 + (y-k)2 = r2

Trigonometry functions SohCahToa

Inverse Trig Functions