Honors Calculus Quiz 1 Jeopardy!

Factoring

100

Factor completely: 8x + 12

What is 4(2x + 3)?

200

Factor completely: x² + 7x + 10

What is (x + 2)(x + 5) ?

300

Factor completely: 3x² + 9x + 6

3(x + 1)(x + 2)

400

Factor completely: 4x³ + 12x² + 8x

What is 4x(x + 1)(x + 2) ?

500

Factor completely: 6sin²x + 15sinx + 9

What is 3(2sinx + 3)(sinx + 1) ?

Logarithms

100

log₂(x) = 5

What is 32?

200

log_b(25) = 2

What is 5?

300

log₃(x + 6) = 2

What is 3?

400

Expand the logarithm as much as possible: log(12x²y)

What is log12 + 2logx + logy?

500

Condense the logarithm as much as possible, with no rational exponents: loga + logb - (1/2)logc

What is log(ab/√c) ?

Unit Circle

100

The exact value of sin(π/6)

What is 1/2 ?

200

The exact value of tan(π/4) 

What is 1?

300

Solve sinx = √3/2 on the interval [0,2π)

What is π/3 and 2π/3 ?

400

Solve cosx = -1/2 on the interval [0,2π)

What is 2π/3 and 4π/3 ?

500

Solve 2cos²x - 1 = 0 on the interval [0,2π)

What is π/4, 3π/4, 5π/4, 7π/4 ?

Right Triangle Trig

100

In a 30°-60°-90 triangle, the shorter leg is 5. Find the hypotenuse and the longer leg.

What is hypotenuse = 10 and longer leg = 5√3?

200

A right triangle has a 40° angle and an adjacent side of 8. Find the length of the side opposite the 40° angle. Round to the nearest hundreth. 

What is 6.72 ?

300

A right triangle has an angle of 25° and the side opposite this angle is 7. Find the hypotenuse. Round to the nearest hundreth. 

What is 16.55 ?

400

A right triangle has a leg of 9 and a leg of 12. Find the angle opposite the shorter leg. Round to the nearest hundreth.

What is 36.87^o ?

500

A person is standing 50 ft from the base of a building. The angle of elevation to the top of the building is 30°. How tall is the building? Round to the nearest hundreth.

What is 28.87 ft ?

Trig Identities

100

1/cscx

What is sinx?

200

secx/cscx

What is tanx?

300

sec²x - tan²x

What is 1?

400

csc³x−cot²xcscx

What is cscx?

500

(sec²x - 1)/(sec²x)

What is sin²x ?