Merced College; Don Power

MATH 2 – STUDY GUIDE FOR CHAPTER 2

2.1 Solve:

2.1 Solve:

2.1. In 1989, a company had revenues of 2.3 million dollars, and in 1993, it had revenues of 3.0 million dollars.

· Write a linear equation giving the revenue as a function of time.

· Use your equation to predict the company’s revenue in 1996.

2.1 A chemist has on hand a 30% solution of acid and an 80% solution of acid. How much of each must he use to get exactly 10 liters of a solution that is 60% acid?

2.1 Joe could paint a house in 12 hours. Joe and Fred, working together, could paint the same house in only 8 hours. How many hours would it take Fred, working alone, to paint the house?

2.1 A boat travels 60 miles upstream. On the return trip downstream, the boat travels 2 mph faster, and completes the trip one hour faster. Find the speed of the boat in calm water.

2.1 Solve for x: 4 + b(3 − x) = ax

2.1A Write an equation that represents: " b varies jointly as t and r, and inversely as the square of s."

2.1A Find the constant of variation if P varies inversely as Q and P = 25 when Q = 30.

2.1A If G varies jointly as H and T, and G = 20 when H = 15 and T = 2,
find G when H = 10 and T = 5.

2.2 Find the discriminant for the equation y = 3x² − 5x + 2

2.2 Match the discriminant with the interpretation:

a. No real solution Discriminant = 3 ________

b. One rational solution Discriminant = 25 ________

c. Two rational solutions Discriminant = −16 ________

d. Two irrational solutions Discriminant = 0 ________

2.2 Solve using the quadratic formula and your calculator 2.3x² − 5.2x − 3.1 = 0

2.3 Solve an equation by using your calculator to graph the appropriate equation and find the roots/zeros/x-intercepts. Examples:

a. (x − 2)^0.3 + 4 = x

b. log (x+5) = x³

c. x⁵ / 10 + 3 = 2x

2.4 Solve:

a. Polynomial equations: 4x⁴ − 13x² + 3 = 0 (Text's example 1)

b. Radical equations: 5 + sqrt(3x−11) = x (Text's example 4)

c. Absolute value equations: abs(3x-4) = 8 (Text's example 7)

2.5 Solve linear inequalities:

a. Continued inequality: 2 ≤ 3x + 5 < 2x + 11 (Text's example 3)

b. Absolute value with "less than": abs(3x − 5) ≤ 4 (Text's example 6)

c. Absolute value with "greater than": abs(5x + 2) > 3 (Text's example 7)

2.6 Solve polynomial and rational inequalities:

a. Polynomials: (x + 15)(x − 2)⁶(x − 10) ≤ 10 (Text's example 4)

• Find the critical points (values that make the factors 0)
• Plot the critical points on a number line
• Write the intervals, going from left to right on the number line
• Apply the analysis illustrated for examples 4 and 5 in the textbook

b. Rational inequalities: x / (x − 1) > −6 (Text's example 5)

• Start by moving all terms to the left, leaving a zero on the right side
  (notice the "caution" after example 5)
• Add the fractions together and factor both the numerator and the denominator.
• Then apply the same analysis as for polynomial inequalities.

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