Complete SAT Formula List Focus on UNDERSTANDING, not MEMORIZING β Percent Change Formula Use the formula below to find the percent change between two numbers. *zFocus on correctly identifying the final & initial πππππ−πππππππ πππππππ πΏ πππ = % ππππππ → (+) result = % increase → (-) result = % decrease Example . _____________________________. __ The jar came with a total of 27 cookies. One week later, there were 13 pieces left. To the nearest whole number, by what percent did the number of cookies decrease by? A) 14 B) 48 C) 52 (β) D) 57 β‘ X-intercepts, Roots, Zeros Example . _____________________________. ___ Definition: Where the graph crosses the x-axis and makes the y = 0. In a quadratic function, they can be found with factoring or quadratic formula. 3π₯ 2 + 12π₯ + 6 = 0 What are the solutions to the equation above? Factoring [When numbers are simple] Y = x2 + 6x + 5 β y = (x+5)(x+1) C) π₯ = −6 ± 6√2 Quadratic Formula [Numbers are not factorable] Y = x2 + 4x – 4 β −π±√π 2 −4ππ π π Product of the roots = B) π₯ = −6 ± √2 D) π₯ = −2 ± √30 3 *Factor out the 3 to make the math simpler & smaller 2π β’ Sum/Product Of The Roots Sum of the roots = − A) π₯ = −2 ± √2 (β) π Example ___. ___. ________________._________ π¦ = π₯ 2 − 4π₯ + 8 What is the product of the roots for the equation above? π *Trigger – if the question specifically asks to find the sum or product of the roots, use the formula. The equation is probably not factorable. AdmissionHackers.com - All rights reserved. Do not share, copy, reproduce or sell any part of this document unless you have written permission from AdmissionHackers.com. All infringements will be prosecuted. If you are the personal owner of the AdmissionHackers.com End User License then you may use it for your own use but not for any other purpose. Ans = 8 Complete SAT Formula List Focus on UNDERSTANDING, not MEMORIZING β£ Vertex Formula Vertex Formula _. The maximum/minimum point of the parabola (h,k), which can be found in two ways. 1) Vertex formula: x-coordinate = β = − π Roots 2π 2) Midpoint method – Vertex is always located in the middle of the two x-intercepts. π₯1 +π₯2 Midpoint = ( 2 ) Vertex β€ Vertex form & Standard form If the function π(π₯) = π₯ 2 + π΄π₯ + 8 has a vertex at (-2,0), what is the value of A? A) 4 (β) B) 5 C) 6 D) 7 Midpoint Formula ___. _._________ ________ If the roots of the parabola is located at 3 & -5, what is the x-coordinate of the vertex A) 3 B) -5 C) -2 D) -1 (β) Vertex Form ___. 2 Vertex form: π¦ = π(π₯ − π) + π - Shows the location of the vertex (maximum/minimum) as constant or coefficients (h,k) _.______________________ _.______________________ π(π₯) = (π₯ − 2)(π₯ + 6) Which of the following is an equivalent form of the function g above in which the minimum value of the function is shown as constant or coefficient? A) π¦ = π₯ 2 + 4π₯ − 12 B) π¦ = (π₯ − 2)(π₯ + 6) C) π¦ π₯+6 = π₯−2 D) π¦ = (π₯ + 2)2 − 16 (β) β₯ Discriminants Formula (π = π 2 − πππ) serves two purposes: Identifying the number of roots (intersections) in a parabola (parabola and a line) Understanding results d < 0 → No root (intersection) d = 0 → One root (intersection) d > 0 → Two roots (intersection) Parabola Only __. ___. ________. ____ 2 π¦ = π₯ − 5π₯ + 2 How many roots does the function above have? Ans: 2 Line & Parabola _. ____. π¦ = 2π₯ − 5 _. ___________ π¦ = π₯ 2 − 5π₯ + 2 How many intersections do the functions above have? Ans: 2 AdmissionHackers.com - All rights reserved. Do not share, copy, reproduce or sell any part of this document unless you have written permission from AdmissionHackers.com. All infringements will be prosecuted. If you are the personal owner of the AdmissionHackers.com End User License then you may use it for your own use but not for any other purpose. Complete SAT Formula List Focus on UNDERSTANDING, not MEMORIZING β¦ SOH-CAH-TOA sin π = Example __. __. ______ _______. ________ πππππ ππ‘π π»π¦πππ‘πππ’π π πππ π = π΄πππππππ‘ π»π¦πππ‘πππ’π π π‘ππ π = πππππ ππ‘π π΄πππππππ‘ π If sin 40 = π , what is the value of H? Ans: 10 Rule: SCT could represent side lengths, but more commonly will represent a side length RATIO. β§ Complimentary Rule *In the question, 4/5 is the RATIO of the side lengths. Do NOT mistaken them for the ACTUAL side lengths and say x=5. Example __. __. ______ _______. ________ sin(30) = cos(π₯ − 20) In the equation shown above, what is the value of x that satisfies the equation? 1) Equation sin(π₯) = cos(90 − π₯) cos(π₯) = sin(90 − π₯) When sin and cos are the equal, their angles sum to 90. Ans: 80 β¨ Sector Area & Arc Length Example ____. _________________. Arc Length = Part of the circumference π΄ππ πΏππππ‘β = 2πr X πΆ π¨ππππ πππ π΄ 140° Sector area = Part of the area ππππ‘ππ π΄πππ = πr 2 X π΄ππππ ________ © π΅ π¨ππππ πππ Insight: The 360 represents the fraction/portion of the circle you’re finding. The circle above has a center at point B. What fraction of the circle is the area of the sector formed by the minor angle ABC? Ans: 7/18 AdmissionHackers.com - All rights reserved. Do not share, copy, reproduce or sell any part of this document unless you have written permission from AdmissionHackers.com. All infringements will be prosecuted. If you are the personal owner of the AdmissionHackers.com End User License then you may use it for your own use but not for any other purpose. Complete SAT Formula List β© Equations Of A Circle On The Coordinate Plane Equation: (π₯ − β)2 + (π¦ − π)2 = π 2 *If not in this form, you must complete the square to identify the center and the radius. Focus on UNDERSTANDING, not MEMORIZING Example ____. ___________________________ 2 π₯ + 6π₯ + π¦ 2 − 16π¦ = 71 What is the radius and center of the circle shown above? Ans: C = (-3,8) R = 12 βͺ Distance Formula Rule: Use the distance formula to find the distance between two points Example ____. ___________________________ What is the distance between the coordinates (2,3) and (-2,7)? Ans: 4√2 β« Area / Volume Formula Must be able to recall within 3 seconds AdmissionHackers.com - All rights reserved. Do not share, copy, reproduce or sell any part of this document unless you have written permission from AdmissionHackers.com. All infringements will be prosecuted. If you are the personal owner of the AdmissionHackers.com End User License then you may use it for your own use but not for any other purpose.
