sat/act prep test takingtips use your time wisely make good decisions quickly use the choices to...
TRANSCRIPT
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• 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
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
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
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
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
Plane Geometry - Quadrilaterals
Area = Base x Height(units squared)
Perimeter = 2 x Base + 2 x Side (units not squared)
hb
bh
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
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
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)
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
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