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SAT/ACT Prep

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. Pretest Parent Meeting and Intro to course 3. Reading and Math Reading of Long Passages

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SAT/ACT Prep

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  1. SAT/ACT Prep

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

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

  4. Math Easy Medium Hard

  5. 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 MATH

  6. Don’t Be Afraid

  7. 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)

  8. SAT: Math continued… • Start Calculations •  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” •  Finish to the Answer whether by calculation or • estimating to the answer

  9. 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

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

  11. Numbers - Signs • Integers ---------------0--------------- • Absolute Value -a = a • Inequalities • Greater than > • Less Than <

  12. 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!!!

  13. 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.

  14. 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

  15. 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

  16. Combinations A x B x C = number of combinations

  17. 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

  18. EXPONENT PRACTICE Medium : x6y-3 x-3y9 = x6-(-3) = x9 y9-(-3) y12

  19. Exponents 6-5 = 1 Term: Inverse/Reciprocal 65 x6y-4 = x6 TIP: Make everything + y4

  20. ExponentsRule: When Bases are the same, the exponents are equal  EXAMPLE: 2x = 8, x = ? 2x = 8 2x = 23 x=3

  21. 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 __ __ = 103 + 33 __ = 133

  22. 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.

  23. Roots and Fractional Exponents __ a1 = a1/2 Example 1: __ 4a2 = a2/4 = a1/2 Example 2: __ 4a8 = a8/4 = a2 Root Power becomes denominator of fractional exponent Power inside the radican () becomes numerator of fractional exponent

  24.  Work Two people working together 1 + 1 = 1 xt yt T(x+y)

  25. Algebraic Expressions Factoring Greatest Common Factor / Distribute 3x + 3 = 3(x+1) 12x2 y2 + 3xy = 3xy (4xy +1) FOIL/ UNFOIL (x+3 ) (x+ 4) F: x2 O: 4x I: 3x L: 12 X2 + 3X+ 4X + 12 = x2 + 7x + 12 (collect like terms) Expand (a+b)2: ( a + b ) 2 ( a + b ) 2 ( a + b ) 2

  26. 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/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

  27. 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

  28. 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!!

  29. 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

  30. 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)

  31. 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

  32. 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

  33. Geometry • Plane Geometry • 2 dimensional • Solid Geometry • 3 dimensional

  34. Formulas Circles Quadrilaterals Squares Cubes Triangles Trapezoid Cylinder

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

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

  37. The Square • Square • Area = S2 (units squared) • Perimeter= S+S+S+S = 4S(units not squared) • Also, Area = d2/2 • Do you see pythagorean? d s s

  38. Triangles Area = ½ Base x Height (Altitude)

  39. 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 45 45 60

  40. Trapezoid (no formula given) Area = ½ (B1+B2)H Or B1+B2 x H 2 B1 H B2

  41. Plane Geometry - Circles Area = r2 (units squared) Circumference= 2r (units not squared) 3/4r2 r R

  42. Solid Geometry - Volume • CUBE • Volume = S3 (units cubed) • Surface Area = 6 S2 • SAT Twist: • Length of Side = Length of Edge • Cylinder • Volume = r2h S2 edge h

  43. Geometry – Coordinate • Lines • y= mx + b • Slope = y2 –y1 x2-x1 Parallel = m Perpendicular = -1/m • Distance Formula • think PYTHAGOREAN __________________ __________ D =  (Y2– Y1) 2 + (X2-X1) = Y2 + X2 (x2, y2) (x1, y1)

  44. Geometry – Multiple Figures • A – a = Shaded Area

  45. 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

  46. Conics

  47. 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

  48. Word Problems

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