SAT/ACT Prep

Test TakingTips Use your time wisely Make good decisions quickly Use the choices to your advantage Penalty for Wrong but POINTS for correct

Schedule 1.Pretest 2.Parent Meeting and Intro to course 3. Reading and Math a)Reading of Long Passages b)Numbers, Averages, Ratios and Proportions and Percentages c)Writing Multiple Choice 4. Math and Writing 1.Exponents, Roots and Work 2.Identifying Sentence Errors 3.Improving Sentences 4. ACT Prompt: Thesis Sentence, Details, Conclusion 5. Math and Reading a)Sentence Competion b)Geometry c)Essay – SAT prompt 6. Math and Writing 1.Functions and more Geometry 2.Multiple Choice Writing SAT 7. Math and Writing 1.Word Problems 2.Long Passages 8. ACT Review a) Logs b) Trig c) Science

Math Easy MediumHard

MATH PreAlgebra –Numbers –Operations –Percentages –Fractions –Probability Algebra 1 –Equations of a Line Slope:Parallel Perpendicular –Quadrilaterals Perimeter and Area –Circles Perimeter and Area RadiusDiameter –SquaresSide –Exponents and Roots Geometry –VolumesCubes –Cylinder –Triangles AreaBaseHeight Isoceles and Equilateral Algebra 2 –Systems of Equations –Functions –Word Problems Sequences Logs Trig

Don’t Be Afraid

SAT: MATH Read the question carefully. Ask “What math skill do I need to use on this? Algebra, Geometry, Pre-Algebra, … Look at answers to see how far you need to calculate? Can you eliminate any? Do the answers give a clue how to do the problem? (If there is a , then that suggests circle area or circumference)

SAT: Math continued… Reread the question: –a. You get additional information to help you continue if you get stumped b. You get “x” but the question asked for “y” Start Calculations Finish to the Answer whether by calculation or estimating to the answer

Math Table of Contents Numbers –Signs –Integers, Absolute Value, Inequalities Averages Ratios, Probability and Percentages Formulas Exponents and Roots Algebraic Expressions Geometry Word Problems –Combinations –Work

Whole Numbers Odd / Even Prime and Composite Factor/ Multiple Integers Sum / Difference Product SAT Twist Words –Consecutive –Distinct

Numbers - Signs Integers   Absolute Value  -a  = a Inequalities –Greater than > –Less Than <

Averages Average = Sum Total Tip 1: The variable is in the SUM x =90 5 Tip 2: The variable/answer is large!!!

Q1: The average (arithmetic mean) of five positive even integers is 60. If p is the greatest of these integers, what is the greatest possible value of p? Q2: The average (arithmetic mean) of 6 distinct numbers is 71. One of these numbers is –24, and the rest of the numbers are positive. If all of the numbers are even integers with at least two digits, what is the greatest possible value of any of the 6 numbers.

Ratios, Probability and Percentages Probability = Ratio = Fraction Part or part 1=part 2 Whole whole 1whole 2 Cross multiply: a = c Solve for c: a x d = c x b b d

Multiple Probabilities Multiply each 4 green marbles, 3 red, 3 blue What is probability of drawing 2 green? Step 1 : First “draw” = 4 out of 10 4/10 Step 2: Second “draw” = 3 out of 9 3/9 Multiply 4 x 3 = 2 x 1 =

Combinations A x B x C = number of combinations

Exponents ADDING AND SUBTRACTING: THINK “LIKE TERMS” X 4 + X 4 = 2X 4 NOT X 8 X 4 + X 3 = X 4 + X 3 NOT X 7 MULTIPLYING AND DIVIDING: (6 2 )(6 4 ) VISUALIZE: 6x6 x 6x6x6x6 = = 6 6 = 46,656 x 5 VISUALIZE: X X X X X x 3 X X X =x 5-3 = x 2

EXPONENT PRACTICE Medium : x 6 y -3 x -3 y 9 = x 6-(-3) = x 9 y 9-(-3) y 12

Exponents 6 -5 = 1Term: Inverse/Reciprocal 6 5 x 6 y -4 = x 6 TIP: Make everything + y 4

Exponents Rule: When Bases are the same, the exponents are equal EXAMPLE: 2 x = 8, x = ? 2 x = 8 2 x = 2 3 x=3

Roots To add or subtract Roots, the radican must be the same ___ ___   27 Visualize : 1.Common FACTOR (3) 2. Perfect Square (100 and 9) _____ ___ 3. Like terms 10x + 3x =  100x3 +  9x3 __ __ = 10   3 __ = 13  3

Exponents – MEDIUM Difficulty If 3 x+1 = 9 2, what is the value of x 2 ? TIP: Get bases the same Solution: 3 x+1 = (3 2 ) 2 = 3 4 So, x+1 = 4 and x = 4-1 or 3.

Roots and Fractional Exponents __  a 1 = a 1/2 Example 1: __ 4  a 2 = a 2/4 = a 1/2 Example 2: __ 4  a 8 = a 8/4 = a 2 Root Power becomes denominator of fractional exponent Power inside the radican (  ) becomes numerator of fractional exponent

Work Two people working together = 1 x t y t T (x+y)

Algebraic Expressions Factoring Greatest Common Factor / Distribute 3x + 3 = 3(x+1) 12x 2 y 2 + 3xy = 3xy (4xy +1) FOIL/ UNFOIL (x+3 ) (x+ 4) F: x 2 O: 4x I: 3x L: 12 X 2 + 3X+ 4X + 12 = x 2 + 7x + 12 (collect like terms) Expand (a+b) 2: ( a + b ) 2

Algebraic Expressions Common Denominator Easy: 1/5 +2/3 = 3/15+10/15 = 13/15 Hard 1/x +1 Tip: Clean up the top, Clean up the bottom, merge top and 1- 1/xbottom Simplify or Collect Like Terms 2x + 3y + 4x – 6y 2x + 4x +3y – 6y 6x – 3y Solve for y Easy: 3 + 3y = 4yNO: 3 + 3y = 6y 3 = 1 y 3= y Hard: Solve for t in terms of a and b a + bt = 8 bt = 8-a t = (8-a)/b

Algebraic Expressions - Functions Problem: f(x)= x/2 and g(x) = 3x. Find f(g(x)) if x = 2 Option 1 : Solve algebraically f(g(x)) = f(3x) = 3x / 2 If x=2, then 3(2) / 2 = 3 Option 2: Make the replacement first f(g(2)) g(2) = 3(2) = 6 f(6) = 6/2 = 3 Therefore, f(g(2) = 3

Functions HARD IF f(x) = x 2 – 5, and f(6) – f(4) = f(y) What is y? Remember this is HARD! REREAD before you answer!!

Cont f(x) = x 2 – 5, f(6) – f(4) = f(y).What is “y?” f(6) = (6) 2 – 5 = 31 and f(4) = (4) 2 – 5 = 11 SO, f(6) – f(4) = 20 NOW WHAT? REREAD f(y) = y 2 – 5 SO f(y) = 20, WHAT IS just “y?” 20 = y 2 – 5 y =√ (20+5) = √ 25 = +5, -5

Functions EASY (but they say is HARD) f(x) = 2x 2 -4x -16 and g(x) = x 2 – 3x – 4 What is f(x) / g (x), in terms of x? Solution 2x 2 -4x -16 = 2(x 2 -2x -8) = 2 [(x-4)(x+2)] x 2 – 3x – 4 x 2 – 3x – 4 [(x-4)(x+1)] Answer = 2(x+2) (x+1)

Absolute Value Medium -- REREAD!!! Before you answer IF │3x-6│= 36, what is one possible value of x? Choices: -30, -14, -10, 0, 10 Solution: 3x-6 = 36 AND 3x- 6 = -36 3x = 36+6 = 42 AND 3x = = -30 x = 42/3 = 14 AND x = -10

ABSOLUTE VALUE - HARD Let the function f(x) be defined by f(x) = │2x-3│. If p is a real number, what is one possible value of p for which f(p) < p? TIP – Choose values IF p = 1, the f(p) is │2-3│ = 1, –no f(p) = p. If p= 2, then f(p) is │2(2)-3│= 1, –yes f(p) < p

Geometry Plane Geometry –2 dimensional Solid Geometry –3 dimensional

Formulas Circles Quadrilaterals Squares Cubes Triangles Trapezoid Cylinder

Plane Geometry - Quadrilaterals Area = Base x Height(units squared) Perimeter = 2 x Base + 2 x Side (units not squared) h b b h

Area / Perimeter Problems 2010 SAT Princeton Review #16, page 330

The Square Square –Area = S 2 (units squared) –Perimeter= S+S+S+S = 4S(units not squared) –Also, Area = d 2 /2 Do you see pythagorean? s s d

Triangles Area = ½ Base x Height (Altitude)

Plane Geometry – Triangles Special Rights – x, x√3, 2x – x, x, x√2 Types –Equilateral – each angle is 60 (180/3) –Isosoceles – 2 sides (therefore, angles) equal, like the “45” 180= middle angle + 2 base angles

Trapezoid (no formula given) Area = ½ (B1+B2)H Or B1+B2x H 2 B1 B2 H

Plane Geometry - Circles Area =  r 2 (units squared) Circumference= 2  r (units not squared) r R 3/4  r 2

Solid Geometry - Volume CUBE –Volume = S 3 (units cubed) –Surface Area = 6 S 2 –SAT Twist: Length of Side = Length of Edge Cylinder –Volume =  r 2 h h S2S2 edge

Geometry – Coordinate Lines –y= mx + b –Slope = y2 –y1 x2-x1 Parallel = m Perpendicular = -1/m Distance Formula –think PYTHAGOREAN __________________ __________ D =  (Y 2 – Y 1 ) 2 + (X 2 -X 1 ) =   Y 2 +  X 2 (x2, y2) (x1, y1)

Geometry – Multiple Figures A – a = Shaded Area

Trigonometry For angle A, opposite (O) For angle B, adjacent (A) Sine B = O H Hypotenuse (H) Cosine = A For angle A, adjacent (A) For angle B, opposite (O) A H Tangent = Sine = O Cosine A SOH CAH TOA Sine x Cosecant = 1 Cosine x Secant = 1 Tangent x Cotangent = 1

Conics

Logs Log a b = x EXAMPLE: log x 8 = 3 a x = b x 3 = 8 x = 2 Change of Base EXAMPLE: log 4 3 = log 3 = log u v = log v log log u Expand or condense EXAMPLE: log 3 x 2 y log a x y = log a x + log a y z log a x = log a x – log a y = log 3 (x 2 y) – log 3 z y = log 3 x 2 + log 3 y – log 3 z log a x n = n log a x = 2 log 3 x + log 3 y – log 3 z

Word Problems