MATH FOR LIBERAL ARTS REVIEW 3

Find the value of the annuity. Round to the nearest cent.

A =P 1 + r

nnt

- 1

rn

P =A r

n

1 + rn

nt- 1

1) Periodic Deposit: $100 at the end of each yearRate: 5% compounded annuallyTime: 9 years

Determine the periodic deposit. Round to the nearest cent.

A =P 1 + r

nnt

- 1

rn

P =A r

n

1 + rn

nt- 1

2) Periodic Deposit: $? at the end of every six monthsRate: 10% compounded semiannuallyTime: 8 yearsFinancial Goal: $310,000

Solve the problem.3) The price of a home is $260,000. The bank requires a 20% down payment and one point at the time of closing.

The cost of the home is financed with a 15-year fixed-rate mortgage at 7%.a. Find the required down payment.b. Find the amount of the mortgage.c. How much must be paid for the one point at closing?d. Find the total cost of interest over 15 years, to the nearest dollar.

4) A real estate company borrowed $415,000 to develop some condos. It amortized the loan to pay monthly for 4years at 7% interest. Find the amount of each monthly payment.

1

Provide the following information. a. Name the vertex of the angle. b. Name the sides of the angle. c. Name the angle in three different ways.

5)

Solve the problem.6) The hour hand of a clock moves from 12 to 10 o'clock. Through how many degrees does it move?

7) The hour hand of a clock moves from 12 to 1 o'clock. Through how many degrees does it move?

Find the measure of the angle in which ?° appears.8)

13°

9)

71°

Find the measure of the complement of the angle.10) Find the complement of 40°.

Find the measure of the supplement of the angle.11) Find the supplement of 127°.

2

Find the measures of angles 1, 2, and 3.12)

113°

Find the measure of angle A for the triangle shown.13)

31°

108°

Find the measure of the angle.14) Find the measure of angle 2 in the figure shown.

Use similar triangles and the fact that corresponding sides are proportional to find the length of the side marked with anx.

15)

15 m 3 m 5 m

12 m 4 m

3

Use similar triangles and the fact that corresponding sides are proportional to find the length of the segment marked withan x.

16)

10 in.8 in.

10 in.

Use the Pythagorean Theorem to find the missing length in the right triangle. Use a calculator to find square roots,rounding, if necessary, to the nearest tenth.

17)c

6 in.

9 in.

18)a

10 m20 m

Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding, if necessary, tothe nearest tenth.

19) If you drive 16 miles south, then make a left turn and drive 12 miles east, how far are you, in a straight line,from your starting point?

Use the quadrilaterals below to solve the problem.

20) Which of the quadrilaterals shown have sides of equal length? Name these quadrilaterals.

4

Find the perimeter of the figure shown. Express the perimeter in the same unit of measure that appears on the given sideor sides.

21)27 in.

5.5 in.

9 in. 12 in.3.5 in.

15 in.

Solve the problem.22) Find the sum of the measures of the angles of a 6-sided polygon.

Use formulas to find the area of the figure.23)

14 in.

15.7 in.

17 in.

24)

6 ft

10 ft 10 ft

9 ft

Solve the problem.25) What will it cost to tile a rectangular floor measuring 296 feet by by 36 feet if the tile costs $13 per square foot?

Solve the problem. Round all circumference and area calculations to the nearest whole number.26) How much fencing is required to enclose a circular garden whose radius is 70 m?

5

27) If asphalt pavement costs $0.90 per square foot, find the cost to pave the circular road (indicated by dots) in thefigure shown.

80 ft

60 ft

Use the given right triangle to find the trigonometric function.28) cos B

29) sin A

Find the measure of the side of the right triangle whose length is designated by the lowercase letter. Round your answerto the nearest whole number.

30)

129 in.

40°

6

Use the inverse trigonometric keys on a calculator to find the measure of angle A, rounded to the nearest whole degree.31)

12 m

27 m

Find the measures of the parts of the right triangle that are not given. Round your answers to the nearest whole number.32)

ca

31°b = 59 yd

Solve the problem.33) To find the distance across a large pond, a surveyor took the measurements in the figure shown. Use these

measurements to determine how far it is across the lake. Round to the nearest foot.

50°140 feet

Graph the equation. Select integers for x, -3 x 3.34) y = -4x - 2

7

Evaluate the function at the given values of the variable.35) f(x) = 5x2 + 5 a. f(-1) b. f(-7)

Evaluate f(x) for the given values for x. Then use the ordered pairs (x, f(x)) from your table to graph the function.36) f(x) = x2 + 1

x f(x)-2-1 0 1 2

Use the x- and y-intercepts to graph the linear equation.37) x - 3y = -9

Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whetherthe line rises, falls, is horizontal, or is vertical.

38) (7, 3), (-16, -7)

8

Graph the linear function using the slope and y-intercept.

39) y = 12

x - 3

In the following problem: a. Put the equation in slope-intercept form.b. Identify the slope and y-intercept. c. Graph the line.

40) 3x + 8y = 24

Graph the horizontal or vertical line.41) x = 2

9

42) y = 5

The graph shows that the cost of the average college mathematics textbook has been rising steadily since 1990.

43) a. What is the y-intercept?b. What is the slope?c. What is the equation of this line, in slope-intercept form?d. Predict the cost of an average college mathematics textbook in 2030.

10

Solve the system by graphing. Check the coordinates of the intersection point in both equations.

44) 3x + y = -113x + 5y = 5

Solve the system by the substitution method. Be sure to check all proposed solutions.45) x - 5y = 7

2x - 4y = 14

Solve the system by the addition method. Be sure to check all proposed solutions.46) x + 2y = 25

-7x + 2y = -31

Solve the problem.47) A couple have bought a new house and are comparing quotes from two moving companies for moving their

furniture. Company A charges $80 for the truck and $55 per hour for the movers. Company B charges $70 forthe truck and $65 per hour for the movers. Create a cost equation for each company where y is the total cost andx is the number of hours of labor. Write a system of equations.

Graph the linear inequality.48) 2x + 4y 8

11

Graph the system of inequalities.49) x - 2y 2

x + y 0

12

Answer KeyTestname: SPR2015 TEST 2

1) $1102.662) $13,103.673) a. down payment: $52,000

b. amount of mortgage: $208,000c. points paid at closing: $2080d. total cost of interest over 15 years: $336,521

4) $9937.595) a. point A

b. AB and ACc. A, BAC, CAB

6) 300°7) 30°8) 77°9) 109°

10) 50°11) 53°12) m 1 = 67°, m 2 = 113°, m 3 = 67°13) 41°14) 120°15) 9 m16) 2.5 in.17) 10.8 in.18) 17.3 m19) 20 mi20) a. rhombus, d. square21) 72 in.22) 720°23) 243.35 in.2

24) 240 ft225) $138,52826) 440 m27) $7916.81

28) 45

29) 1213

30) 99 in.31) 24°32) a = 35 yd; c = 69 yd; B = 59°33) 167 feet

13

Answer KeyTestname: SPR2015 TEST 2

34)

35) 10, 25036)

x f(x)-2 5-1 2 0 1 1 2 2 5

37)

38) 1023

, rises

14

Answer KeyTestname: SPR2015 TEST 2

39)

40) a. y = -38

x + 3

b. slope = -38

, y-intercept = 3

c.

41)

15

Answer KeyTestname: SPR2015 TEST 2

42)

43) a. 46b. 6c. y = 6x + 46d. 286

44) {(-5, 4)}45) {(7, 0)}46) {(7, 9)}47) y = 55x + 80

y = 65x + 7048)

49)

16