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Quantitative Reasoning
Simple Interest formula - I = Prt Compound Interest formula - I = P(1+ r/n)^nt N= # of times interest is compounded in a year. Quarterly would be n= (a + b)^2 = - a^2 + 2ab + b^ (a+b)(c+d) = - ac + ad +bc + bd a^2 - b^2 (difference of squares) = - (a+b)(a-b) a^3 + b^3 (sum of cubes) = - (a+b)(a^2-ab+b^2) Ex: Factor 27x^3 + 1 (3x+1)(9x^2-3x+1) a^3 - b^3 = (difference of cubes) - (a-b) (a^2 + ab + b^2) Ex:Factor x3y6 - 64 (xy^2-4)(x^2y^4+4xy^2+16) If ax2 + bx + c = 0, what is the quadratic formula? - -b+/-√((b^2 ) - 4ac)/2a
x^ax^b= - x^(a+b) Ex: x^2x^4=x^ x^a*y^a= - (xy)^a (x^a)^b= - x^(ab) X^(a-b)= - x^a / x^b To determine if a number is divisible by 3 - You add up all the digits and see if it is divisible by 3 To determine if a number is divisible by 4 - The LAST TWO digits have to be divisible by 4. Ex: 10224, 32, 164 When is a number divisible by 6? - When it is an even number and the sum of digits is divisible by 3 To be divisible by 8, a number has to satisfy? - Last three digits divisible by 8. Ex: 112, 1168 To be divisible by 9 - Sum of digits divisible by 9 If a right triangle has one side equal to 12, one side equal to 16, the last side is? -
- It is a 3-4-5 triangle
Distance equation when solving a rate problem? - D=RT (DiRT) logb(xy)= - logb(x) + logb(y) logb(x/y)= - logb(x) - logb(y) logb(x^n)= - nlogb(x) What is log1, log2, log3, log4, log5, and log6? - log1=0, log2=0.3, log3=0.5, log4=0.6, log5=0.7, log6=0. Equation of slope in terms of x and y? - Rise/Run = y2-y1/x2-x What is the shape of the graph y=x^3? - flip the left side of a parabola downwards and you get a squiggly line what is the graph of y=x^-1? - curve cupping the lower left corner, curve cupping the upper right corner What is the slope of a perpendicular line if the slope is 3/4 for the existing line? - m2 = -1/m1 = -4/ If you know the slope and the location of a point, what is the formula to turn it into y=mx+b form? - y - y1 = m(x - x1)
Solve: bx < 3b - Two things: x<3 if b is positive, or x>3 if b is negative. So the answer choice with both options or the one that says cannot be determined Distance formula when calculating the distance between two points? - d = √( (x2-x1)^2 * (y2-y1)^2 ) For a circle with radius r and center (h,k), what is the equation of the circle? - (x-h)^2 + (y-k)^2 = r^ What is the center of the circle (x - 5)2 + (y + 3)2 = 49? - (5,-3) flip the signs because you subtract both (h,k) from (x,y) Circumference of a circle? - 2(pi)r Volume of a sphere? - 4/3 (pi)r^ Volume of a cone? - 1/3 (pi)r^2h Volume of a cylinder? - (pi)r^2h Volume of a pyramid? - 1/3bh John drove for 3 hours at a rate of 50mph and for 2 hours at 60mph. What was his average speed for the whole journey? - ((50 x 3)+ (60 x 2))/5 = 270/5 = 54
