Intro to Calculus Jeopardy 1

Complex fractions

100

(1/x)/6+(3/x)

Simplify

1/3(2x+1)

200

((x+1)/x)/((1/x)+(3/2))

Simplify

2(x+1)/3x+2

300

((x-2)/x+(1/x))/(3+x)/3

Simplify

3x(x-2)/(x²+1)(3+x)

400

((12/7)+(x²/9))/((3x/4)+(1/3))

Simplify

4(108x+7x²)/21(9x+4)

500

(x-2)/(x+(1/x))/(x+3)/(3+(2/x²))

Simplify

(x-2)(3x²+2)/x(x²+1)(x+3)

Solving fractional equations

100

2/3 - 5/6 = 1/x

Solve for x

x=-6

200

x-7/x+3 = 4/9

Solve for x

x=15

300

x+6/x = 7

Solve for x

x=6,1

400

2/x+5 + 1/x-5 = 16/x²+25

Solve for x

x=7

500

2x/x+11 - 3x/x-12 = 19x/x²-x-132

Solve for x

x= 0, -76

Inequalities involving variables and absolute value

100

5(x-6)>12(x-4)

Solve for x

x<18/7

200

5/6>x+4>1/8

Solve for x

-31/8<x<-19/6

300

|2x-6|>x-1

Solve for x

x<7/3 OR x>5

400

|3x² -7| < 4x

Solve for x

1<x<7/3

500

|x+1| < |x-6|

Solve for x

x <5/2

Natural logs/Exponential functions

100

Express 4ln5 as one logarithmic function.

ln625

200

e^x/3+4 = 22

Solve for x (in ln form)

x=3ln18 

300

Solve 8e^2x-5 = 56 for x (in ln form)

x= (ln7 +5)/2

400

lnx + ln(x-3) = ln10

Solve for x

x=5 and x=-2

500

How long will it take to double your money if you deposit $500 at an annual rate of 7.2% compounded continuously? (Use A= Pe^rt)

Leave answer in ln form or round to two decimal places.

t = ln2/0.072 or t=9.63

Solving trig equations and trig identities

100

What is sin²x +cos²x?

1

200

Prove: 1+cot²θ=csc²θ using trigonometric identities

1+cot²θ=(1+cos²θ/sin²θ)

(sin²θ/sin²θ)+(cos²θ/sin²θ)

(sin²θ+cos²θ)/sin²θ

1/sin²θ=csc²θ

300

Verify that cscθcosθtanθ=1.

csc = 1/sin

tan = sin/cos 

1/sin * cos/1 *sin/cos = 1

400

Verify that sec²θ−1/sec²θ=sin²θ

sec² = tan² +1

(tan² +1)-1 = tan²

tan² / sec² = tan² * 1/cos²

tan² = sin²/cos²

sin²cos² / cos² = sin²

500

Rewrite the trigonometric expression 4cos²θ−1 using difference of squares.

4cos²θ−1=(2cosθ)²−1

(2cosθ−1)(2cosθ+1)