Math Hysteria Trivia Quiz

Answer: 30

The perimeter of a rectangle is the sum of twice the length and twice the width (2*9+2*6=18+12=30).

Answer: 35

Angelica's age is x, Lexie's age is x-9, Rachel's age is x-9-3, and Dana's age is x-6. Since the sum of all four of their ages equals 113, we combine like terms. Adding the 4 x variables gives us 4x and adding -9, -9, -3, and -6 gives us -27. Then we add 27 to 113 to give us 140, leaving 4x by itself. Finally, we divide 140 by 4, leaving x to equal Angelica's age, which is 35.

Answer: 2, 50, 98, 146, 194

An arithmetic sequence consists of a series of numbers that have one common difference between each of them. The arithmetic sequence 2, 50, 98, 146, and 194 all have a common difference of 48 (50-2=48, 98-50=48, 146-98=48, and 194-146=48). The other sequences listed are geometric (7, 56, 448, 3584, 28672), exponential (5, 25, 625, 390625, 152587890625), and factorial (1, 2, 6, 24, 120).

Answer: 1 and 6

The mode is the number that appears the most times. In this question, there are two modes because 1 and 6 both appear the most frequently in the series.

Answer: 136

The supplement of an angle can be found by subtracting the given angle from 180 degrees (180-44=136).

Answer: 125250

The sum of consecutive natural numbers is represented by the formula n(n+1)/2 where n is the last number added, which in this question, is 500. This formula is preferred over adding each and every number in the series, which tends to be tedious, especially if the last number added is a very large number.

Answer: 16

The determinant of a 2x2 matrix can be found by multiplying the number on the upper left hand side of the matrix by the number on the lower right hand side of the matrix. Then that number is subtracted by the product of the number on the upper right hand side of the matrix and the number on the lower left hand side of the matrix (5*11-3*13=55-39=16).

As matrices grow, the formula for a determinant grows very quickly.

Answer: 28

The slope of the secant line can be found with the formula f(x2)-f(x1)/x2-x1. Using the equation f(x)=4x^2-8x, and the points P(1,-4), x is substituted by 8 to get 4(8)^2-8(8)-(-4) to get 196 which is then divided by 7 (8-1) to get 28.

Answer: 0.7

Sometimes the limit can be found by substituting the number x approaches, but in this case, substituting by x yields division by 0. Instead, you see if any part of the expression can be factored out and if the common factors can be cancelled out. In this question, notice that in the numerator can be split into 5x^2-25x+3x-15 because 5 (the first coefficient) and -15 (the third coefficient) can be multiplied to equal to -75.

Then you find another factor of the two numbers to equal -75 that is also added to equal -22 (the second coefficient). Those happen to be -25 and 3 (-25*3=-75 and -25+3=22).

The numerator is then factored as 5x(x-5)+3(x-5). The common factor of the numerator is x-5, so the expression of the numerator is factored as (5x+3)(x-5). Even though the denominator can be factored as 4(X^2-25), x^2-25 can further be factored as (x-5)(x+5) as a difference of two squares.

The final factored form is (5x+3)(x-5)/4(x-5)(x+5). Notice that x-5 can be cancelled out, leaving (5x+3)/4(x+5). Now 5, the number x approaches can be substituted in the expression. Doing so yields 5*5+3/4(5+5)=25+3/4(10)=28/40 which can be simplified as 7/10 or 0.7.

Answer: 264x^3-132x^2+sin(x)

This problem can be solved by finding the derivative of (22x^3)*(3x-2) with the product rule and the derivative of cos(x). The derivative of a function using the product rule can be done by adding the product of f(x)*g'(x) to the product of g(x)*f'(x). Here, we have 22x^3 (f(x))multiplied by 3 (g'(x)) added to 3x-2 (g(x)) multiplied by 66x^2 (f'(x)). Adding these terms will equal to 264x^3-132x^2.

As for cos(x), its derivative is -sin(x). However since -sin(x) is being subtracted from 264x^3-132x^2, -sin(x) becomes +sin(x) since two negatives make a positive. So the final result is 264x^3-132x^2+sin(x).