5 Written Questions

1. Let l_1 and l_2 be two nonvertical lines that are not perpendicular, with slopes m_1 and m_2 respectively. The tangent of the angle θ from l_1 to l_2 is given by tan θ = (m_2 - m_1) / (1 + (m_1)(m_2))
2. tan θ = slope of l
3. tan x = sin x / cos x for x /= nπ + π/2, n any integer
4. If a < b and c > 0, then ac < bc.
5. Let l_1 and l_2 be nonvertical lines with sloped m_1 and m_2. Then l_1 and l_2 are parallel if and only if m_1 = m_2.

5 Matching Questions

1. Theorem of perpendicular lines
2. How to solve an inequality
3. Additivity of inequalities
4. Symmetry with respect to the origin
5. Sine function and cosine function

1. a Let l_1 and l_2 be nonvertical lines with slopes m_1 and m_2. Then l_1 and l_2 are perpendicular if and only if (m_1)(m_2) = -1.
2. b sin θ = y/r and cos θ = x/r
3. c 1) Algebraically make one side equal to zero.
   2) Express the other side as a product.
   3) Find the zeroes of factors of the product.
   4) Draw a diagram that shows the signs of the factors of the product from -∞ to ∞.
   5) Deduce the values of x for which the product satisfies the inequality.
4. d If a < b and c < d, then a + c < b + d.
5. e (-x, -y) is on the graph whenever (x, y) is

5 Multiple Choice Questions

1. |PQ| = sqrt((x_2 - x_1)² + (y_2 - y_1)²)
   1. Cosecant function
   2. Cotangent function
   3. Distance formula
   4. Tangent function
2. m = (y_2 - y_1) / (x_2 - x_1)
   1. Symmetry with respect to the x axis
   2. Slope of line l with points (x_1, y_1) and (x_2, y_2)
   3. Symmetry with respect to the y axis
   4. Composition of g and f
3. One of these three:
   (a, b) <-> all x such that a < x < b
   (a, ∞) <-> all x such that a < x
   (-∞, a) <-> all x such that x < a
   1. Closed interval
   2. Half-open interval
   3. Graph
   4. Open interval
4. Replace f (x) by f (x + c)
   1. Shift the graph of f right c units
   2. Shift the graph of f down c units
   3. Shift the graph of f up c units
   4. Shift the graph of f left c units
5. A function consists of a domain and a rule. The domain is a set of real numbers. The rule assigns to each number in the domain one and only one number.
   1. Distance formula
   2. Closed interval
   3. Function, domain, rule
   4. Open interval

5 True/False Questions

1. Symmetry with respect to the x axis → (x, -y) is on the graph whenever (x, y) is

   True        False

2. Trichotomy of inequalities → If a < b and b < c, then a < c.

   True        False

3. Relation between square root and absolute value → |x| = sqrt(x²)

   True        False

4. Secant function → csc x = 1/ sin x for x /= nπ, n any integer

   True        False

5. Approximate height of a falling object in meters → h (t) = -4.9t² + (v_0)(t) + h_0

   True        False