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SAT Math Formulas
Terms in this set (157)
Integers (^) -3, 0, 2 no fractions or decimals! Real #s integers, fractions, deciamls, and irrationals(π √2) Orders of Operations
PEMDAS
Arithmetic Sequence Each terms is equal to the previous term plus d Ex: d = 4 and t1 = 3 gives the sequence 3, 7, 11, 15 Geometric Sequence Each term is equal to the previous term times r r = 2 and t1 = 3 gives the sequence 3, 6, 12, 24 Prime Factorization Breaking up of a # in to its prime factors use factor tree to do this
factor
that divdes in to another
evenly without a
remainder Ex: the factors of 52 are 1, 2, 4, 13, 26, and 52 multiple multiples of a # are divisible by that # without a remainder the positive Ex: multiples of 20 are 20, 40, 60, 80, GCF (Greatest Common Factor) Ex GCF (200,60) use factor tree to find prime factors 200 = 2 × 2 × 2 × 5 × 5 60 = 2 × 2 × 3 × 5 multiply common prime factors 2 × 2 × 5 = 20 LCM(Least Common Multiple) Ex LCM (200, 60) use factor tree to find prime factors 200 = 2 × 2 × 2 × 5 × 5 60 = 2 × 2 × 3 × 5 Multiply common prime factors the greatest # of times they appear in either # (every prime factor is included) 2 × 2 × 2 × 3 × 5 × 5 Percent Equation (^) part= (Percent/100) * whole Percent Equation Example 75% of 300 is what? part= (Percent/100) * whole x = (75/100) * 300 Percent Equation Example 45 is what percent of 60? part= (Percent/100) * whole 45= (x/100) * 60 Percent Equation Example 30 is 20% of what? part= (Percent/100) * whole 30= (20/100) * x
Fundamental Counting Principle Example Mark has 5 pants and 7 shirts in his closet. He wants to wear a different pant/shirt combination each day without buying new clothes for as long as he can. How many weeks can he do this for? 5 *7 = 35 days or 5 weeks Exponent rule (multiplication) x³ * x² x³ * x² = x³⁺² = x⁵ Exponent Rule (power raised to a power) (x³)² (x³)²= 3 * 2 = x⁶ Exponent Zero Rule x⁰ = 1 2⁰ = 1 2x⁰ = 2 Exponent rule (division) x⁴/x² x⁴/x² = x⁴⁻² = x² Exponent Rule (xy)² (xy)² = x²y² Radical Rule √xy √xy = √x * √y Negative Exponent Rules 1/x² x⁻³ 1/x² = x⁻² x⁻³ = 1/x³
Exponet Rule (-1)ⁿ +1 if n is even -1 if n is odd FOIL (x+a)(x+b) x² +(b+a)x +ab Difference of Squares a² - b² a² - b² = (a+b) (a-b) Difference of Squares Example 4x² - 81y² 4x² - 81y² (2x)² - (9y)² (2x+ 9y) (2x - 9y) Difference of Squares a² + 2ab + b² a² - 2ab + b² a² + 2ab + b² =(a+b) (a+b) a² - 2ab + b²= (a-b) (a-b) How to solve a quadratic equal to 0 Ex: x²+ 4x+3=
- factor x²+ 4x+3 (x+3) (x+1)=
- set both parts = 0 and solve for x (x+3)= 0 (x+1)= 0 x=- 3 x=- 1 To solve 2 linear equations Substitution x + y = 3 and 4x − y = 2
- solve for a variable in one equation y=-x+
- substitute that variable in to the other equation and solve 4x - (-x+3)= x=
- substitute the solved variable back in to one of the original equations to solve for other variable 1+y= y= If f(x) = 0.5 · x (^) then y or f(x) is directly proportional to x If f(x) = 5/x (^) then y or f(x) is inversely proportional to x
Perpendicular lines have... slopes that are negative reciprocals y=4x+ y=-(1/4)+ Intersecting Lines opposite angels are equal Special Right Triangle 1 3-4-5 triangle and multiples of this triangle (ex: 6-8- 10, 9-12-15) Special Right Triangle 2
and multiples of this triangle 30-60-90 triangle x-x√3-2x side opposite 30° is x side oppiste 60° is x√ side opposite 90° is 2x Area of a Triangle (^) (b*h)/2 or 1/2 b h Quadratic Formula (can be used to solve for x in quadratic equation) SOHCAHTOA sine- opp/hyp cos- adj/hyp tan- opp/adj Special Right Triangle (Isoceles Triangle) x-x-x√ the x's are across the 45° angles the x√2 is across the 90° Sum of Interior Angles Equation (n-2) n= # of sides of a polygon
Complex Conjugate (a+bi)(a-bi) (a+bi)(a-bi)= a²+b² Simple Interest A= Prt p=principal amount = initial or starting amount amount (borrowed or invested) r = interest rate (expressed as decimal) t = time Compound Interest A= P(1+r/n)ⁿ⁺ P= initial or starting amount r= interest rate(decimal) t= time n= the # of times the interest compounded Exponential Growth y= a(1+r)× a= initial value r= rate of growth x=time Exponential Decay y=a(1-r)× a= initial value r= rate of decay x=time Equation of a Circle (x-h)² + (y-k)² = r² (h, k)Conveting = point for center of circle r= radius Convert radians to degrees (radians)(180/π) Convert degrees to radians (degrees)(π/180) Area of a Circle (^) πr² Circumferecne of Circle (^) 2πr or πd
Elimination 3x + 4y = 52 5x + y = 30 The canceling out of a variable by adding or subtracting equations 1) line up same variables and figure out which variable to cancel 3x+4y= −4(5x+y)=−4(30)
- Cancel out a variable by adding them together x+4y= −20x-4y=−
- Solve for left over variable −17x=- 68 x=
- Substitute answer in to one of the original equations and solve for the other variable if f(a)= if f(4)= x f(x) 0 3 2 1 4 0 then (x-a) or (x-4) is a factor of f(x) if a system of linear equations has no solution then... the slopes of the equations have to be the same(lines are parallel) *same slope means graphs of the lines are parallel How do you figure out many zeroes a function has? By looking at how many times the function touches the x-axis How to find x- coordinte of vertex x=-b/2a
How to find y coordinate of vertex plug in the # solved for the x coordinate in to the quadratic if 24x² + 25x − 47/ ax-2 = 8x-3 -53/ax- 2 then (8x-3)(ax-2)- 53 = 24x² + 25x − 47 the remainder goes over the outside term Simplifying Radicals
- get prime factors27
- write them under the radical√27
- simplify the radical (square of a # will always cancel out and come out of the radical as the number)7√ hamburger has 50 more calories than each order of fries means h=f+ In a right triangle the sine of one acute angle equals the cosine of the other acute angle When dealing with similar right triangles the sine of an angle of one triangle equals the cosine of an angle of the other triangle When making proportions the same units equal each other Each successive year 1% of the current value is added to the value of the account exponential growth
Rule of discriminant when determining type of solution b²-4ac= positive then ther will be 2 real solution b²-4ac=0 then 1 real solution b²-4ac= negative then no real solution (a+b/2)² (^) (a+b/2)(a+b/2) SAT problem If aⁿ÷⁴ = 16 for positive integers a and n, what is one possible value of n? When bases are the same you can make their exponents equal 1)Get same base on both sides 2ⁿ÷⁴ = 2⁴
- make exponents equal to each other n÷4= 4
- solve n SAT Problem How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution? liters of saline solution × percent of saline solution x=liters 3(0.10) + 0.25x = 0.15(x + 3) the final amount of liters has to be added to the 3 liters already there
