521B Jeopardy (A)

Trigonometry

100

This trigonometric ratio is defined as the adjacent side-length divided by the hypotenuse.

What is the cosine ratio?

200

sin(180^o) - cos(0^o) + 2tan(45^o) = 

1

300

cos(60^o) + sin(30^o) + sin(0^o) = 

1

400

State the Sine Law.

sin(A)/a = sin(B)/b = sin(C)/c

OR

a/sin(A) = b/sin(B) = c/sin(C)

500

Suppose that you are given side-lengths a, c, and ∠B of a triangle. What equation can be used to solve for side-length b?

b² = a² + c² - 2acCos(B)

Quadratic Functions and Equations

100

The graph of a quadratic function.

What is a parabola?

200

The vertical line that divides a parabola into two symmetrical halves.

What is the axis of symmetry?

300

For the quadratic function y = -2(x - 11)² + 5, how many roots are there?

2 distinct roots

400

Given y = (x + 5)² + 9, in which quadrant is the vertex located in?

QII

500

Given 0 = 2x² - x + 5, how many solutions are there?

No solutions; b² - 4ac < 0

Radical Expressions and Equations

100

√5 - 5√2 + 4√5 - 11√2

5√5 - 16√2

200

√225 + √25 = 

20

300

3√128 / √2 = 

24

400

Solve √x - 2 = 2√x - 18

x = 256

500

√8(2√3 - √8) = 

4√6 - 8

Rational Expressions and Equations

100

For x/[x²(x - 1)], what is/are the non-permissible value(s)?

x ≠ 0, x ≠ 1

200

For (1/x) + (x/x²(x - 5)), what is the lowest common denominator?

x²(x - 5)

300

[x²(x - 5)] / x²(x - 5)²

1/(x - 5)

400

Solve:

1/x = x/49

x = -7, x = 7

500

How do you know if an expression is rational?

If it can be expressed as a ratio of polynomials.

Absolute Value and Reciprocal Functions

100

|-3| - 3|2 - 3| + 3|9/-3| = 

9

200

Express |x - 7| as a piecewise function.

|x - 7| = 

x - 7 if x ≥ 7

7 - x if x < 7

300

Solve:

|x² - 5x + 17| = -2

There is no solution

400

Given y = |x² - 5x|, for what values of x will y = 5x - x²?

0 < x < 5

OR

0 ≤ x ≤ 5

500

Given y = 1/(x² - 100), what is/are the vertical asymptote(s)?

x = -10, x = 10