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 Writing1. Exponents, Roots and Work

2. Identifying Sentence Errors

3. Improving Sentences

4. ACT Prompt: Thesis Sentence, Details, Conclusion

5. Math and Readingd) Sentence Competion

e) Geometry

f) Essay – SAT prompt

6. Math and Writing1. Functions and more Geometry

2. Multiple Choice Writing SAT

7. Math and Writing3. Word Problems

4. 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• Radius Diameter

– Squares Side– Exponents and Roots

• Geometry– Volumes Cubes– Cylinder– Triangles

• Area Base Height• 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 ---------------0---------------

• Absolute Value-a = a

• Inequalities– Greater than >– Less Than <

Averages

• Average = Sum

Total

Tip 1: The variable is in the SUM

87 + 95 + 85 + 92 + 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 1 whole 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 = 2• 10 9 5 3 15

Combinations

A x B x C = number of combinations

Exponents

ADDING AND SUBTRACTING:THINK “LIKE TERMS”

X4 + X4 = 2X4 NOT X 8

X4 + X3 = X4 + X3 NOT X 7

MULTIPLYING AND DIVIDING:(62)(64) VISUALIZE: 6x6 x 6x6x6x6  = 62+4 = 66 = 46,656 x5 VISUALIZE: X X X X X x3 X X X  = x5-3 = x2

EXPONENT PRACTICE

Medium :

x6y-3

x-3y9

= x6-(-3) = x9

y9-(-3) y12

Exponents

6-5 = 1 Term: Inverse/Reciprocal

65

 

x6y-4 = x6 TIP: Make everything +

y4

Exponents

Rule: When Bases are the same, the exponents are equal

 EXAMPLE: 2x = 8, x = ?

2x = 8

2x = 23 x=3

RootsTo add or subtract Roots, the radican must be the same

___ ___ 300 +27 Visualize :

1.Common FACTOR (3)2. Perfect Square (100 and

9) _____ ___ 3. Like terms 10x + 3x = 100x3 + 9x3 __ __ = 103 + 33 __ = 133

Exponents – MEDIUM Difficulty

• If 3x+1 = 92 , what is the value of x2 ?• TIP: Get bases the same• Solution:• 3x+1 = (32 ) 2 = 34 • So, x+1 = 4 and x = 4-1 or 3.

Roots and Fractional Exponents

__

a1 = a1/2

 

Example 1: __4a2 = a2/4 = a1/2

Example 2: __4a8 = a8/4 = a2

 

Root Power becomes denominator of fractional exponent

Power inside the radican () becomes numerator of fractional exponent

 Work

Two people working together

1 + 1 = 1

xt yt T(x+y)

Algebraic Expressions

FactoringGreatest Common Factor / Distribute

3x + 3 = 3(x+1)12x2 y2 + 3xy = 3xy (4xy +1) FOIL/ UNFOIL

(x+3 ) (x+ 4)F: x2

O: 4xI: 3xL: 12X2 + 3X+ 4X + 12 = x2 + 7x + 12

(collect like terms)

Expand (a+b)2:

( a + b ) 2

( a + b ) 2

( a + b ) 2

Algebraic ExpressionsCommon 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/x bottom

Simplify or Collect Like Terms 2x + 3y + 4x – 6y 2x + 4x +3y – 6y 6x – 3y

Solve for y Easy: 3 + 3y = 4y NO: 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) = x2 – 5, and f(6) – f(4) = f(y) What is y?

• Remember this is HARD! REREAD before you answer!!

Cont

• f(x) = x2 – 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) = y2 – 5• SO f(y) = 20, WHAT IS just “y?”• 20 = y2 – 5• y =√ (20+5) = √ 25 = +5, -5

Functions

• EASY (but they say is HARD)• f(x) = 2x2 -4x -16 and g(x) = x2 – 3x – 4• What is f(x) / g (x), in terms of x?• Solution

• 2x2 -4x -16 = 2(x2 -2x -8) = 2 [(x-4)(x+2)]• x2 – 3x – 4 x2 – 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 = -36 +6 = -

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

CirclesQuadrilaterals SquaresCubesTrianglesTrapezoidCylinder

Plane Geometry - Quadrilaterals

Area = Base x Height(units squared)

Perimeter = 2 x Base + 2 x Side (units not squared)

hb

bh

Area / Perimeter Problems

• 2010 SAT Princeton Review #16, page 330

The Square

• Square – Area = S2 (units squared)– Perimeter= S+S+S+S = 4S(units not squared)– Also, Area = d2/2

• Do you see pythagorean?

s

s

d

Triangles

Area = ½ Base x Height (Altitude)

Plane Geometry – Triangles• Special Rights

– 30-60-90 x, x√3, 2x– 45-45-90 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

30

60

45

45

Trapezoid (no formula given)

Area = ½ (B1+B2)HOr B1+B2 x H

2

B1

B2

H

Plane Geometry - Circles

Area = r2 (units squared)

Circumference= 2r (units not squared)

 

r

R

3/4r2

Solid Geometry - Volume

• CUBE– Volume = S3 (units cubed)– Surface Area = 6 S2

– SAT Twist:• Length of Side = Length of Edge

• Cylinder– Volume = r2h h

S2

edge

Geometry – Coordinate

• Lines – y= mx + b– Slope = y2 –y1

x2-x1Parallel = mPerpendicular = -1/m

• Distance Formula– think PYTHAGOREAN __________________ __________

D = (Y2– Y1) 2 + (X2-X1)

= Y2 + X2

(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

HHypotenuse(H) 

Cosine = AFor angle A, adjacent (A)For angle B, opposite (O)A

H Tangent = Sine = O

Cosine A 

SOH CAH TOA  

Sine x Cosecant = 1Cosine x Secant = 1Tangent x Cotangent = 1

Conics

Logs

Log a b = x EXAMPLE: logx 8 = 3

ax = b x3 = 8

x = 2

Change of Base EXAMPLE: log 4 3 = log 3 = 0.4771

log u v = log v log 4 0.6021

log u

Expand or condense EXAMPLE: log 3 x2 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