University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2012
Views:

124

Pages:

121
Author:

illettemuxb

Ratio a comparison of any two quantities SET A to SET B 4 to 3 to all of set A to 3:5 set B to set A 9 to 7 or 9:7 Page 1 Absolute Value -6 -5 |5| = 5 |-5| = 5 5 units 5 units -4 -3 -2 -1 0 1 2 3 4 5 6 distance a number is from zero Page 2 Fraction Multiplication How much is of ? 3 8 x 2 3 = 6 24 Page 3 Fraction Division How many halves are in three-fourths? one “whole” half half There are 1 halves in three-fourths. Page 4 Fraction Division How many halves are in three-fourths? three-fourths one-half 1 “whole” one-half one-half There are 1 halves in three-fourths. Page 5 Percent Per hundred 56% = = = 0.56 Page 6 Equivalent Relationships Fraction: Decimal: 0.4 Percent: 40% Page 7 Exponential Form exponent 2 =2 2 2 3 base n =n n n n 4 factors Page 8 Perfect Squares 0 =0 2 1 =1 2 2 =2 2 3 =3 2 4 =4 2 5 =5 2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 0=0 1=1 2=4 3=9 4 = 16 5 = 25 16 = 4 ⋅ 4 = 4 perfect square Page 9 Powers of Ten Meaning Value 10 10 10 10 10,000 102 ⋅ ⋅ ⋅ 10 ⋅ 10 ⋅ 10 10 ⋅ 10 101 10 10 100 1 1 104 103 10-1 10-2 10-3 10-4 1000 100 0.1 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = 0.01 = 0.001 = 0.0001 Page 10 Scientific Notation a x 10 n a = number greater than or equal to 1 and less than 10 n = integer 17,500,000 = 1.75 x 10 0.0000026 = 2.6 x 10 7 -6 Page 11 Natural Numbers The set of numbers 1, 2, 3, 4… Rational Numbers Rational Numbers Integers Integers Irrational Irrational Numbers Numbers Whole Numbers Numbers Whole Natural Numbers Page 12 Whole Numbers The set of numbers 0, 1, 2, 3, 4… RationalNumbers Numbers Rational Integers Integers Irrational Irrational Numbers Numbers Whole Numbers Natural Numbers Page 13 Integers The set of numbers …-3, -2, -1, 0, 1, 2, 3… Rational Numbers Integers Irrational Numbers Whole Numbers Natural Numbers Page 14 Rational Numbers Rational Numbers Integers Irrational Numbers Whole Numbers Natural Numbers A number that can be written as the quotient of two integers 2 -5 Page 15 Irrational Numbers Rational Numbers Integers Irrational Numbers Whole Numbers Natural Numbers Natural Numbers A number that cannot be expressed as the quotient of two integers -0.23223222322223… Page 16 Real Numbers Rational Numbers Irrational Numbers Integers Whole Numbers Natural Numbers The set of all rational and irrational numbers Page 17 Comparing Integers -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 < 1 or 1> -5 -4 > -5 or -5 < -4 Page 18 6 Order of Operations Grouping Symbols () {} [] |abs| Fraction bar Exponents Multiplication Division Left to right Addition Subtraction Left to right Page 19 Integer Operations Addition -5 + 6 = 1 -6 -5 -4 -3 -2 -1 0 1 2 -5 -4 -3 -2 -1 0 1 2 Subtraction 1 – 6 = -5 -6 Page 20 Integer Operations Addition -5 + 6 = 1 Subtraction 1 – 6 = -5 Page 21 Integer Operations Multiplication 3 (-4) = -12 Division -12 -4 = 3 How many tiles are in 3 groups of -4 tiles? How many groups of -4 tiles are in -12 tiles? Page 22 Proportion a c = b d a:b = c:d a is to b as c is to d Page 23 Scale Factor Figures A and B are similar. 2 4 A B 1 2 What is the scale factor from A to B? Scale factor = 2 What is the scale factor from B to A? Scale factor = Page 24 Unit Rate $4 per gallon = 70 miles per hour = Page 25 Percent of Increase Percent of change = new – original original What is the percent of increase? Was $3.25 per gallon 3.85 – 3.25 3.25 Now $3.85 per gallon increase of 18% Page 26 Percent of Decrease Percent of change = new – original original What is the percent of decrease? Was $1200 Now only $900 900 – 1200 1200 decrease of 25% Page 27 Square Root radical symbol =6 = = =6 Squaring a number and taking a square root are inverse operations. = -6 2 (-6) = -6 ∙ -6 = 36 Page 28 Square Root 0 between 3 4 and Page 29 Ballpark Comparisons Length 1 inch or 2.5 centimeter 1 yard < 1 meter Page 30 Ballpark Comparisons Weight/Mass ≈ ≈ ≈ Page 31 Ballpark Comparisons Volume ≈ Page 32 Ballpark Comparisons Temperature Fahrenheit Celsius Water freezes Water boils 32°F 0°C 212°F 100°C Body Temperature 98°F 37°C Room Temperature 70°F 20°C Page 33 Perimeter the measure of the distance around a figure b a c d P=a+b+c+d r s u t P=r+s+t+u e f g P=e+f+g Page 34 Area the number of square units needed to cover a surface or figure Area = 12 Square Units Page 35 Pi π ≈ 3.14159… diameter π= Page 36 Circumference radius C = 2πr C = perimeter of a circle Page 37 Area of a Circle A = πr 2 Page 38 Volume of a Prism height width length Volume = length x width x height V = lwh measured in cubic units Page 39 Surface Area h l w back left side top right side front bottom Surface Area (S.A.) = sum of areas of faces Page 40 Vertex vertex vertices Page 41 Face and Base Face Face Base Face Base Page 42 Pyramid h l h B = area of base p = perimeter of base V = Bh l B = area of base p = perimeter of base S.A. = lp + B Page 43 Prism h B = area of base p = perimeter of base V = Bh h B = area of base p = perimeter of base S.A. = hp + 2B Page 44 Cone l h r V = π r 2h S.A. = π r + π r l 2 Page 45 Cylinder h r V = π r 2h S.A. = 2π r 2 + 2π r h Page 46 Volume Changing one attribute 3 2 8 Height increases to 6 3 6 3 8 2 What happens to the volume? Page 47 Complementary Angles 1 2 1 2 Fig 1 Fig 2 m∠1 + m∠2 = 90° in each figure Page 48 Supplementary Angles 1 2 Fig 1 1 2 Fig 2 m∠1 + m∠2 = 180° in each figure Page 49 Vertical Angles 1 2 4 3 ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles. ∠1 ≅ ∠3 and ∠2 ≅ ∠4 Page 50 Adjacent Angles ∠1 is adjacent to ∠2 in each figure 1 2 1 2 Fig 1 Fig 2 1 2 Fig 3 Share a common side and a common vertex Page 51 Similar Figures C B 4 A 12 F G D H 6 E 2 ABCD ∼ HGFE Angles ∠A corresponds to ∠H ∠B corresponds to ∠G ∠C corresponds to ∠F ∠D corresponds to ∠E Sides corresponds to corresponds to corresponds to corresponds to Corresponding angles are congruent. Corresponding sides are proportional. Page 52 Similar Figures and Proportions C B 4 A 12 F G D H x E 2 ABCD ∼ HGFE = = Page 53 Congruent Figures have exactly the same shape and size B P ≅ A B Q A G H B ABCD ≅ P C E D A C HGFE F R Q ∠BAC ≅ ∠PQR Page 54 Triangles Page 55 Quadrilaterals parallelogram rhombus rectangle kite square trapezoid Page 56 Quadrilaterals Relationships Quadrilateral Kite Parallelogram Rhombus Trapezoid Rectangle Square Page 57 Parallelogram • opposite angles are congruent • 2 pairs of parallel sides • 2 pairs of opposite sides congruent Page 58 Rhombus • opposite angles are congruent • 2 pairs of parallel sides • 4 congruent sides Page 59 Rectangle • 4 right angles • 2 pairs of parallel sides • 2 pairs of opposite sides congruent Page 60 Square • 4 right angles • 2 pairs of parallel sides • 4 congruent sides Page 61 Trapezoid • may have zero or two right angles • exactly one pair of parallel sides • may have one pair of congruent sides Page 62 Kite • one pair of opposite congruent angles • 2 pairs of adjacent congruent sides Page 63 Composite Figures 20 cm 14 cm Subdivide into other figures then determine the perimeter. 5′ 22.5′ 5′ 5′ 10′ 25′ Subdivide into other figures then determine the area. Page 64 Right Triangle C leg b leg a B c hypotenuse A Page 65 Pythagorean Theorem b c a a +b =c 2 2 2 Page 66 Three Dimensional Models front front side side top top Page 67 Coordinate Plane y axis Quadrant II Quadrant I 4 (4,3) 3 2 1 -4 -3 -2 (-2,-1) -1 1 2 3 x axis 4 -1 -2 -3 (0,-3) Quadrant III -4 Quadrant IV ordered pair (x,y) Page 68 Rotation y B A C A′ B′ D′ C′ D x center of rotation Preimage A(-3,0) B(-3,3) C(-1,3) D(-1,0) Image A′(0,3) B′(3,3) C′(3,1) D′(0,1) Page 69 Reflection y F′ F x E′ D′ D E Preimage Image D(1,-2) D′(-1,-2) E(3,-2) E′(-3,-2) F(3,2) F′(-3,2) Page 70 Translation y E D C A B x E′ D′ C′ A′ Preimage A(1,2) B(3,2) C(4,3) D(3,4) E(1,4) B′ Image A′(-2,-3) B′(0,-3) C′(1,-2) D′(0,-1) E′(-2,-1) Page 71 y Dilation center of dilation = (0,0) 1 scale factor = 2 A A′ C C′ B′ B x Preimage A(0,4) B(4,0) C(0,0) Image A′(0,2) B′(2,0) C′(0,0) y center of dilation = (0,0) scale factor = 2 Preimage G(0,-2) H(0,0) J(1,0) K(2, -1) L(1, -2) Image G′(0,-4) H′(0,0) J′(2,0) K′(4,-2) L′(2,-4) H H J G L G′ J x K K′ L′ Page 72 Probability A B A B A C C P(A) = unlikely 0 impossible likely 1 certain Page 73 Probability of Independent Events What is the probability of landing on green on the first spin and then landing on yellow on the second spin? P(green and yellow) = P(green) P(yellow) = = Page 74 Probability of Dependent Events What is the probability of getting a red jelly bean on first pick and then without replacing it, getting a green jelly bean on the second pick? P(red) ∙ P(green after red) = Page 75 Fundamental Counting Principle If there are m ways for one event to occur and n ways for a second event to occur, then there are m n ways for both events to occur. Page 76 Tree Diagram Joe has two pairs of pants (blue and tan). He also has three shirts (red, green and white). List the possible outfits that Joe can make. PANTS SHIRTS blue tan red green white red green white POSSIBLE OUTCOMES blue pants with red shirt blue pants with green shirt blue pants with white shirt tan pants with red shirt tan pants with green shirt tan pants with white shirt 2 3 or 6 possible outcomes Page 77 Mean a measure of central tendency 2, 3, 4, 7 Balance Point 2 3 1 -1 0 1 2 3 4 5 6 7 Numerical Average 2 + 3 + 4 + 7 16 = =4 4 4 Page 78 Median a measure of central tendency 6, 7, 8, 9, 9 8 = median 5, 6, 8, 9, 11, 12 8.5 = median Page 79 Mode a measure of central tendency Data Sets Mode 2, 3, 3, 3, 5, 5, 9, 10 3 5.2, 5.4, 5.5, 5.6, 5.8, 5.9, 6.0 none 1, 1, 2, 5, 6, 7, 7, 9, 11, 12 1, 7 bimodal Page 80 Range Data set 2 , 3, 3 , 3 , 5, 5 , 9 , 10 , 15 , 20 20 – 2 = 17 Range = 17 Page 81 Bar Graph Page 82 Line Graph Page 83 Stem-and-Leaf Plot Math Test Scores 56, 65, 98, 82, 64, 71, 78, 86, 95, 91, 59, 70, 80, 92, 76, 82, 85, 91, 92, 73 STEM 5 6 7 8 9 LEAF 69 45 01368 02256 112258 Key: 5|6 means 56 Page 84 Circle Graph Favorite Ice Cream Page 85 Histogram Page 86 Scatterplot illustrates the relationship between two sets of data. y x Page 87 Positive Correlation y-coordinates increase as x-coordinates increase y x Page 88 Negative Correlation y-coordinates decrease as x-coordinates increase y x Page 89 Constant Correlation y-coordinates remain about the same as x-coordinates increase y x Page 90 No Correlation no pattern exists between the x- and y-coordinates y x Page 91 Arithmetic Sequences What is the next term? +6 +6 +6 4, 10, 16, 22 ... common difference + 3, + + , 4, + ,5… Page 92 Geometric Sequences What is the next term? x3 x3 x3 9, 27, 81, 243 … common ratio x x x x 7, 0.7, 0.07, 0.007, 0.0007 … Page 93 Additive Identity Property 0.3 + 0 = 0.3 0 + (-7) = -7 =0+ w+0=w Page 94 Additive Inverse Property 1.4 + (-1.4) = 0 (-9) + 9 = 0 0 = + (- ) x + (-x) = 0 Page 95 Associative Property Addition: (4 + 2) + 8 = 4 + (2 + 8) x + (3x + ) = (x + 3x) + Multiplication: (3 ∙ 1.5) ∙ 6 = 3 ∙ (1.5 ∙ 6) 2(3x) = (2 ∙ 3)x Page 96 Commutative Property Addition: 2.76 + 3 = 3 + 2.76 (a + 5) + 7 = (5 + a) + 7 Multiplication: -8 = (-8) y ∙ 9 = 9y Page 97 Multiplicative Identity Property 9 1=9 1 (-10) = -10 = 1 Page 98 Multiplicative Inverse Property 2∙ 1= x =1 ∙ -9 = 1 (x ≠ 0) Page 99 Multiplicative Property of Zero 0=8 0(-13) = 0 x 0=0 Page 100 Distributive Property -4(2 + 3) = -4(2) + -4(3) 5 ∙ (y – 7) = (5 ∙ y) – (5 ∙ 7) (2 ∙ ) + (2 ∙ 5) = 2( + 5) Page 101 Equation 6 + 2x = 10 A mathematical sentence stating that two expressions are equal. 2.76 + 3 = 3 + 2.76 3x = 6.9 Page 102 Expression x 2x + 3 4 3(y + 3.9) – Page 103 Variable 2(y + 3) 3 + x = 2.08 A = πr 2 Page 104 Coefficient (-4) + 2x -7y 2 ab – Page 105 Term 3x + 2y – 8 3 terms -5x + (-2x) 2 2 terms ab 1 term Page 106 Constant 4x – 12 -12 7 – 2y + x – 6x 2 3(x + 3.9) + Page 107 Inequality y<4 0 1 2 3 4 5 0 1 3r ≥ -7.5 -4 -3 -2 -1 -3(n – 4) < 0 0 1 2 3 4 5 Page 108 Like Terms 4x – 3y + 6x – 7 2y – 3y + 7y 2 2 -5r – 6 + 2r + 2 2 Page 109 Relations {(2,3), (4,1), (2,5)} x 2 -3 5 0 1 y 2 4 -1 4 -6 {(0,4), (0,3), (0,2), (0,1)} Page 110 Functions {(2,4), (3,2), (0,2), (-1,2)} x 3 2 0 -1 y 2 4 2 2 y x Page 111 Table of Values a b 1 x y 0 1 1 2 2 5 3 10 4 17 2 3 4 22,500 22,000 21,500 21,000 Page 112 Domain {(-2,0), (-1,1), (0,2), (1,3)} x -2 -1 0 1 y 0 1 2 3 {-2,-1, 0, 1} Page 113 Range {(-2,0), (-1,1), (0,2), (1,3)} x y -2 -1 0 1 0 1 2 3 {0, 1, 2, 3} Page 114 Dependent/ Independent Variable Determine the distance a car will travel going 55 mph. independent d = 55h h d 0 0 1 55 2 110 3 165 dependent Page 115 Independent Variable y = 2x + 7 x represents the independent variable (input values or domain) Page 116 Dependent Variable y = 2x + 7 y represents the dependent variable (output values or range) Page 117 Connecting Representations The total distance Sam walks depends on how long he walks. If he walks at 2.1 mph, show multiple representations of the relationship. d t t 0 1 2 4 d 0 2.1 4.2 8.4 d = 2.1t Page 118 Multistep Equations 2x – 5.7 = -3.4x + 11.04 (n + 9) = - n 25 = Page 119 Multistep Equation 3x + 5 = -3 – x Page 120 Unit Rate as Slope A student walks 2 miles per hour miles 2 miles 1 hour 2 1 2 1 hours Page 121