MAT115/117 Final Exam Review - Practice Flashcards

A set of practice questions and answers drawn from the final exam review notes, covering inequalities, lines, systems, quadratics, exponentials, logs, trigonometry, and applications.

Solve the inequality: -6x + 7(4x - 24) < (x - 6) - 36. What is the solution set in interval notation?

(-∞, 6)

Solve the inequality: 5.7x - 1.7(x - 7) ≥ 39.9. What is the solution set?

[7, ∞)

Solve the absolute-value inequality: |8x − 48| ≥ 120. What is the solution set?

(-∞, -9] ∪ [21, ∞)

Find the equation of the line with slope 8 passing through (1, -9).

y = 8x - 17

Find the line through (-8, -9) with undefined slope.

x = -8

If f(x) = -8x − x^2, what is f(2)?

-20

If f(x) = -8x − x^2, what is f(0)?

0

Solve f(x) = 16 for f(x) = -8x − x^2.

x = -4

Compute the difference quotient [f(x+h) − f(x)]/h for f(x) = 10 + 3x (h ≠ 0).

3

Compute the difference quotient [f(x+h) − f(x)]/h for f(x) = 2x^2 + 6x + 5 (h ≠ 0).

4x + 2h + 6

Solve the system: -x − 2y = 13 and 2x − y = -11.

(-7, -3)

Solve the system: -6x + 6y = 3 and y = -x + 6.

(11/4, 13/4)

Let P = ax + b be a linear model where price drops from 566 to 200 in 6 years. Find a and b (P = ax + b).

P = -61x + 566

Using the price model P = -61x + 566, what is the predicted price after 8 years?

78

A jar has 23 coins (quarters and nickels) worth $3.55. How many quarters and nickels are there?

12 quarters and 11 nickels

Cesar invested a total of $41,000 in two accounts with 7% gain and 5% loss respectively, total gain $1,670. How much in each account?

First: $31,000; Second: $10,000

Value after 5 years for $35,000 at 6% (annual compounding). What are the values for annual, semiannual, and quarterly compounding?

Annual: $46,837.90; Semiannual: $47,037.07; Quarterly: $47,139.93

A 500-foot weather tower has a guy wire attached 175 feet up; the angle between the wire and the vertical is 17°. Approximate the wire length.

183 feet

A kite is held with a 29 m string at a 60° angle of elevation. Determine the kite’s height.

25 meters

Compute exact values: cos(-5π/6), sin(π/3), tan(π/4).

cos(-5π/6) = -√3/2; sin(π/3) = √3/2; tan(π/4) = 1

For f(x) = sin(4x), what are the amplitude and period?

Amplitude: 1; Period: π/2

For y = 2 sin(12x), what is the amplitude and the period?

Amplitude: 2; Period: π/6

Evaluate log base 4 of 2 plus log base 4 of 128.

4

Evaluate log base 4 of 32 minus log base 4 of 2.

2

Solve 8x = 16.

x = 2

Solve 2√x = 4.

x = 4

Solve 3(x^2) = 9.

x = ±√3

Solve 7√x − 6 = 49.

x = 3025/49 (since √x = 55/7)

Solve 7^(7x−9) = 5^(9x−4).

x = (9 − 4 log7 5) / (7 − 9 log7 5)

Solve log base 5 (x − 9) = 3.

x = 134

Solve log_x(−2x + 35) = 2.

x = 5

Solve log2 x + log2(x + 2) = 3.

x = 2

Solve log5 x − log5(x + 9) = 3.

No solution

Value of annual, semiannual, and quarterly compounding for $35,000 at 6% over 5 years (answers).

Annual: $46,837.90; Semiannual: $47,037.07; Quarterly: $47,139.93

What is the length of the guy wire if the angle with the vertical is 17° and the tower height to wire attachment is 175 ft?

183 feet

What is the height of a kite given a 29 m string at 60°?

25 meters

What is cos(-5π/6)?

-√3/2

What is sin(π/3)?

√3/2

What is tan(π/4)?

1

What are the amplitude and period of f(x) = sin(4x)?

Amplitude: 1; Period: π/2

What are the amplitude and the period of y = 2 sin(12x)?

Amplitude: 2; Period: π/6

What is the value of log base 7 of 5, used to express x = (9 − 4 log7 5)/(7 − 9 log7 5) for the equation 7^(7x−9) = 5^(9x−4)?

log_7 5 (a component in the expression for x)