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Catégorie :Category: nCreator TI-Nspire
Auteur Author: keith.w07
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.60 Ko KB
Mis en ligne Uploaded: 05/03/2025 - 05:07:33
Uploadeur Uploader: keith.w07 (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4524698
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.60 Ko KB
Mis en ligne Uploaded: 05/03/2025 - 05:07:33
Uploadeur Uploader: keith.w07 (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4524698
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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SAT: Back to Basics Formulas SIGN UP AT ACELY.AI Arithmetic Formulas Arithmetic Properties Rules of Exponents Sum of n n n Consecutive Integers: S = n 2 ( a 1 + a n ) S = frac{n}{2} (a_1 + a_n) S = 2 n ( a 1 + a n ) Where n n n = total number of terms, a 1 a_1 a 1 = first term, a n a_n a n = last term Sum of n n n Consecutive Odd Integers: S = n 2 S = n^2 S = n 2 Sum of Natural Numbers (Starting from 1): S = n ( n + 1 ) 2 S = frac{n(n+1)}{2} S = 2 n ( n + 1 ) Sum/Multiplication of Odd and Even Integers: Odd × Odd = Odd Even × Even = Even Odd × Even = Even Cross-multiplication: a b = c d Ò a d = b c frac{a}{b} = frac{c}{d} Rightarrow ad = bc b a = d c Ò a d = b c https://acely.ai SAT: Algebra Formulas Linear Functions Finding the Slope: m = y 2 y 1 x 2 x 1 m = frac{y_2 - y_1}{x_2 - x_1} m = x 2 x 1 y 2 y 1 Point-Slope Formula: y y 1 = m ( x x 1 ) y - y_1 = m(x - x_1) y y 1 = m ( x x 1 ) Slope-Intercept Form: y = m x + b y = mx + b y = m x + b Parallel Lines: Same slope Perpendicular Lines: Slopes are negative reciprocals Factoring Properties Difference of Two Squares: a 2 b 2 = ( a b ) ( a + b ) a^2 - b^2 = (a - b)(a + b) a 2 b 2 = ( a b ) ( a + b ) Perfect Square Trinomial: a 2 + 2 a b + b 2 = ( a + b ) 2 a^2 + 2ab + b^2 = (a + b)^2 a 2 + 2 ab + b 2 = ( a + b ) 2 a 2 2 a b + b 2 = ( a b ) 2 a^2 - 2ab + b^2 = (a - b)^2 a 2 2 ab + b 2 = ( a b ) 2 Sum & Difference of Cubes: a 3 + b 3 = ( a + b ) ( a 2 a b + b 2 ) a^3 + b^3 = (a + b)(a^2 - ab + b^2) a 3 + b 3 = ( a + b ) ( a 2 ab + b 2 ) a 3 b 3 = ( a b ) ( a 2 + a b + b 2 ) a^3 - b^3 = (a - b)(a^2 + ab + b^2) a 3 b 3 = ( a b ) ( a 2 + ab + b 2 ) Intercepts x-intercept: Set y = 0 y = 0 y = 0 , solve for x x x y-intercept: Set x = 0 x = 0 x = 0 , solve for y y y Interest Rates Simple Interest: A = P ( 1 + r t ) A = P(1 + rt) A = P ( 1 + r t ) Compound Interest: A = P ( 1 + r n ) n t A = P(1 + frac{r}{n})^{nt} A = P ( 1 + n r ) n t Distance Formulas Distance Formula: d = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 d = sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} d = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 Midpoint Formula: M = ( x 1 + x 2 2 , y 1 + y 2 2 ) M = (frac{x_1 + x_2}{2}, frac{y_1 + y_2}{2}) M = ( 2 x 1 + x 2 , 2 y 1 + y 2 ) https://acely.ai SAT: Problem Solving and Data & Analysis Median: Middle value in an ordered set Mean: Average value, values total number of values frac{sum text{values}}{text{total number of values}} total number of values values Mode: Most frequently occurring number Range: Difference between max and min values Rate Problems Distance, Speed, and Time: d = r t d = rt d = r t Percentage Problems: Part = Whole × Percentage Percentage = Part Whole × 100 frac{text{Part}}{text{Whole}} times 100 Whole Part × 100 Probability P ( event ) = desired outcomes total outcomes P(text{event}) = frac{text{desired outcomes}}{text{total outcomes}} P ( event ) = total outcomes desired outcomes Study Tip! Establish a study schedule that allows for consistent practice. Allocate time for each SAT section based on strengths and weaknesses. https://acely.ai SAT: Linear and Quadratic Functions Quadratic Functions Quadratic Formula: x = b ± b 2 4 a c 2 a x = frac{-b pm sqrt{b^2 - 4ac}}{2a} x = 2 a b ± b 2 4 a c Discriminant: b 2 4 a c b^2 - 4ac b 2 4 a c > 0 > 0 > 0 Two real solutions = 0 = 0 = 0 One real solution < 0 < 0 < 0 No real solutions Vertex Formula: ( b 2 a , f ( b 2 a ) ) (-frac{b}{2a}, f(-frac{b}{2a})) ( 2 a b , f ( 2 a b )) https://acely.ai SAT: Geometry & Trigonometry Formulas Angles and Lines Intersecting Lines: Vertical angles are equal Parallel Lines: Corresponding, alternate interior, and alternate exterior angles are equal Sum of Angles in a Triangle: 180 180^circ 18 0 Pythagorean Theorem: a 2 + b 2 = c 2 a^2 + b^2 = c^2 a 2 + b 2 = c 2 Special Right Triangles 30-60-90 Triangle: x , x 3 , 2 x x, xsqrt{3}, 2x x , x 3 , 2 x 45-45-90 Triangle: x , x , x 2 x, x, xsqrt{2} x , x , x 2 Triangle Properties Triangle Inequality Theorem: The sum of any two sides must be greater than the third side Exterior Angle Theorem: An exterior angle equals the sum of the two remote interior angles Similar Triangles: Same shape, proportional sides Circles and Properties Circumference: C = 2 À r C = 2pi r C = 2 À r Area: A = À r 2 A = pi r^2 A = À r 2 Trigonometry SOH CAH TOA sin a ¸ = opposite hypotenuse sin theta = frac{text{opposite}}{text{hypotenuse}} sin ¸ = hypotenuse opposite cos a ¸ = adjacent hypotenuse cos theta = frac{text{adjacent}}{text{hypotenuse}} cos ¸ = hypotenuse adjacent tan a ¸ = opposite adjacent tan theta = frac{text{opposite}}{text{adjacent}} tan ¸ = adjacent opposite Arc Length: L = ¸ 360 × 2 À r L = frac{theta}{360^circ} times 2pi r L = 36 0 ¸ × 2 À r Sector Area: A = ¸ 360 × À r 2
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Compatible OS 3.0 et ultérieurs.
<<
SAT: Back to Basics Formulas SIGN UP AT ACELY.AI Arithmetic Formulas Arithmetic Properties Rules of Exponents Sum of n n n Consecutive Integers: S = n 2 ( a 1 + a n ) S = frac{n}{2} (a_1 + a_n) S = 2 n ( a 1 + a n ) Where n n n = total number of terms, a 1 a_1 a 1 = first term, a n a_n a n = last term Sum of n n n Consecutive Odd Integers: S = n 2 S = n^2 S = n 2 Sum of Natural Numbers (Starting from 1): S = n ( n + 1 ) 2 S = frac{n(n+1)}{2} S = 2 n ( n + 1 ) Sum/Multiplication of Odd and Even Integers: Odd × Odd = Odd Even × Even = Even Odd × Even = Even Cross-multiplication: a b = c d Ò a d = b c frac{a}{b} = frac{c}{d} Rightarrow ad = bc b a = d c Ò a d = b c https://acely.ai SAT: Algebra Formulas Linear Functions Finding the Slope: m = y 2 y 1 x 2 x 1 m = frac{y_2 - y_1}{x_2 - x_1} m = x 2 x 1 y 2 y 1 Point-Slope Formula: y y 1 = m ( x x 1 ) y - y_1 = m(x - x_1) y y 1 = m ( x x 1 ) Slope-Intercept Form: y = m x + b y = mx + b y = m x + b Parallel Lines: Same slope Perpendicular Lines: Slopes are negative reciprocals Factoring Properties Difference of Two Squares: a 2 b 2 = ( a b ) ( a + b ) a^2 - b^2 = (a - b)(a + b) a 2 b 2 = ( a b ) ( a + b ) Perfect Square Trinomial: a 2 + 2 a b + b 2 = ( a + b ) 2 a^2 + 2ab + b^2 = (a + b)^2 a 2 + 2 ab + b 2 = ( a + b ) 2 a 2 2 a b + b 2 = ( a b ) 2 a^2 - 2ab + b^2 = (a - b)^2 a 2 2 ab + b 2 = ( a b ) 2 Sum & Difference of Cubes: a 3 + b 3 = ( a + b ) ( a 2 a b + b 2 ) a^3 + b^3 = (a + b)(a^2 - ab + b^2) a 3 + b 3 = ( a + b ) ( a 2 ab + b 2 ) a 3 b 3 = ( a b ) ( a 2 + a b + b 2 ) a^3 - b^3 = (a - b)(a^2 + ab + b^2) a 3 b 3 = ( a b ) ( a 2 + ab + b 2 ) Intercepts x-intercept: Set y = 0 y = 0 y = 0 , solve for x x x y-intercept: Set x = 0 x = 0 x = 0 , solve for y y y Interest Rates Simple Interest: A = P ( 1 + r t ) A = P(1 + rt) A = P ( 1 + r t ) Compound Interest: A = P ( 1 + r n ) n t A = P(1 + frac{r}{n})^{nt} A = P ( 1 + n r ) n t Distance Formulas Distance Formula: d = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 d = sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} d = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 Midpoint Formula: M = ( x 1 + x 2 2 , y 1 + y 2 2 ) M = (frac{x_1 + x_2}{2}, frac{y_1 + y_2}{2}) M = ( 2 x 1 + x 2 , 2 y 1 + y 2 ) https://acely.ai SAT: Problem Solving and Data & Analysis Median: Middle value in an ordered set Mean: Average value, values total number of values frac{sum text{values}}{text{total number of values}} total number of values values Mode: Most frequently occurring number Range: Difference between max and min values Rate Problems Distance, Speed, and Time: d = r t d = rt d = r t Percentage Problems: Part = Whole × Percentage Percentage = Part Whole × 100 frac{text{Part}}{text{Whole}} times 100 Whole Part × 100 Probability P ( event ) = desired outcomes total outcomes P(text{event}) = frac{text{desired outcomes}}{text{total outcomes}} P ( event ) = total outcomes desired outcomes Study Tip! Establish a study schedule that allows for consistent practice. Allocate time for each SAT section based on strengths and weaknesses. https://acely.ai SAT: Linear and Quadratic Functions Quadratic Functions Quadratic Formula: x = b ± b 2 4 a c 2 a x = frac{-b pm sqrt{b^2 - 4ac}}{2a} x = 2 a b ± b 2 4 a c Discriminant: b 2 4 a c b^2 - 4ac b 2 4 a c > 0 > 0 > 0 Two real solutions = 0 = 0 = 0 One real solution < 0 < 0 < 0 No real solutions Vertex Formula: ( b 2 a , f ( b 2 a ) ) (-frac{b}{2a}, f(-frac{b}{2a})) ( 2 a b , f ( 2 a b )) https://acely.ai SAT: Geometry & Trigonometry Formulas Angles and Lines Intersecting Lines: Vertical angles are equal Parallel Lines: Corresponding, alternate interior, and alternate exterior angles are equal Sum of Angles in a Triangle: 180 180^circ 18 0 Pythagorean Theorem: a 2 + b 2 = c 2 a^2 + b^2 = c^2 a 2 + b 2 = c 2 Special Right Triangles 30-60-90 Triangle: x , x 3 , 2 x x, xsqrt{3}, 2x x , x 3 , 2 x 45-45-90 Triangle: x , x , x 2 x, x, xsqrt{2} x , x , x 2 Triangle Properties Triangle Inequality Theorem: The sum of any two sides must be greater than the third side Exterior Angle Theorem: An exterior angle equals the sum of the two remote interior angles Similar Triangles: Same shape, proportional sides Circles and Properties Circumference: C = 2 À r C = 2pi r C = 2 À r Area: A = À r 2 A = pi r^2 A = À r 2 Trigonometry SOH CAH TOA sin a ¸ = opposite hypotenuse sin theta = frac{text{opposite}}{text{hypotenuse}} sin ¸ = hypotenuse opposite cos a ¸ = adjacent hypotenuse cos theta = frac{text{adjacent}}{text{hypotenuse}} cos ¸ = hypotenuse adjacent tan a ¸ = opposite adjacent tan theta = frac{text{opposite}}{text{adjacent}} tan ¸ = adjacent opposite Arc Length: L = ¸ 360 × 2 À r L = frac{theta}{360^circ} times 2pi r L = 36 0 ¸ × 2 À r Sector Area: A = ¸ 360 × À r 2
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