AVID

 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

 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

 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.

 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

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

 This types involves a percent increase or percent decrease.  Percent Change Formula:

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

 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.

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?

 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

 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 ratios The ratio of dogs to cats is 4:7. If there are 12 dogs, how many cats are there?

Example – Two Term Ratios The 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 Example There 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?

 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.

 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 –> ax 2 + bx + c  Classic quadratic equations ▪ (x+y) 2 = x 2 + 2xy + y 2 ▪ (x-y) 2 = x 2 – 2xy + y 2 ▪ (x+y)(x-y) = x 2 – y 2  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”

 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

 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

LESSON 9 1. B 2. J 3. C 4. H 5. D 6. G 7. C 8. J 9. A 10. H LESSON D 2. F 3. E 4. H 5. D 6. K 7. E 8. J 9. B 10. J

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

 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: ▪ c 2 = a 2 + b 2 - 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

 Key Rules  Coordinate Geometry Formulas

 Circle on the Coordinate Plane Formula  (x-h) 2 + (y-k) 2 = r 2  Trigonometry functions  SohCahToa Inverse Trig Functions