Math Exam

Keeshawn is building a fence around his backyard as shown in the figure. The cost of installing the fence is $500 for labor plus the cost of the fence. If the fence is bought in sections of 5 foot lengths and costs $7.50 per section, including the gate, what is the total cost to enclose his yard?

$785

On the chart of Bay Harbor, 1/4 of an inch represents 20 miles. How many inches on this map represent 100 miles?

1.25 inches

In the figure below, the circle has radius r. What is the area of the shaded region in terms of r?

1/2πr²+2r²

A right cylindrical tank with a total volume of 5,000 cubic units has an interior diameter of 20 units. The volume gauge indicates that the tank is 60% full. To the nearest 5 units, what is the interior height of the fluid in the tank?

10

^ In the figure below, AB with a sector angle of 45 is shown shaded in a circle with a radius of 6 inches. What is the length of ACB?

10.5π

Each day for 4 days, Malala read 1/12 of the Federalist Papers for her history class. Due to her busy schedule, she was only able to read at half that pace for the remainder of the assignment. How many days will it take Malala to finish the Federalist Papers at the new pace?

16

The perimeter of a parallelogram is 66 units, and one side has the length of 16 units. If it can be determined, what are the lengths in units of the other 3 sides?

16, 17, 17

What is the least common denominator of the fractions 1/3, 5/6, 5/9

18

The cost in dollars to carpet a room that has a floor area of A square feet is 50A + 12h, where h is the number of hours it takes to lay the carpet. What is the cost of carpeting a room that has an area of 40 square feet and takes 6 hours to lay the carpet?

2072

A straight 30-feet-tall ladder is leaning against a building as shown in the figure below. The wall of the building forms a right angle with level ground, on which the ladder rests. Which of the following expressions give the measure of , the angle between the ladder and the ground?

24 arcsign(----) 30

Qadaria is planting a flower garden in the shape of a right triangle in the back corner of her yard. The two sides shown are 7 feet and 8 feet. She would like to put a small fence around the garden, what is the approximate length, in feet, of the fence?

26

Which equation shows the correct use of the quadratic formula to solve x2 - 5x + 3?

5±√25 - 4(1)(3) --------------------- 2

A bag contains 15 blue marbles, 5 red marbles, and 11 green marbles. How many blue marbles must be removed from the 31 marbles in the bag so that the probability of randomly drawing a blue marble is 1/3 ?

7

This graph represents the projected and actual sales of cars for ABC Auto Emporium during a six-month period from January to June. What is the median of the actual sales for the six-month period shown in the graph?

70

Which graph represents the cost of the fence?

graph D

If 0 < xk < 1, and k is a positive integer, what must be true 1/k about the value of x?

h 1/k x<x

The Maximus Electric Company will increase employee's yearly wages by 2.5% next year. An employee whose yearly wages this year total $45,000 will earn what total yearly wages next year?

$46,125.00

The sum of (2x3 - 3x2 + 4) and which polynomial results in the polynomial (5x3 + 4x2 -1)?

(3x3 + 7x2 - 5)

The two right cylinders have diagonals EF and GH, respectively. The length of each radius is given in feet. What is the ratio of the length of EF to GH? (PICTURE HERE OF 2 CYLINDERS)

1:3

The first three terms of a geometric sequence are 8, 12, and 18. What is the fifth term?

40.5

ABC Auto Emporium gives bonuses to their employees when actual sales reach 150% of projected sales. For which month did employees receive a bonus?

February

If the parallelogram is rotated counterclockwise 90 about the y-axis, what are the coordinates of point D?

(0, f)

Line l, shown below, is perpendicular to and intersects line m, not shown, at point P. Line m runs through the origin. What are the coordinates of point P?

(1.6, 0.8)

What are the coordinates of C?

(d + f, e)

In the standard (x, y) coordinate plane, the graph of which of the following equation is a circle with center (5, -3) and a radius of 2 coordinate units?

(x - 5)² + (y + 3)² = 4

Which graph shows the solution set for the inequality 3x - 5 ≥ 10?

-----------------0-----------5----------> (B)

If a = −2, b = −3, and c = 1, what is the value of −a + b + c?

0

Which of the following sets of numbers could NOT represent the lengths of the sides of a triangle?

1, 1, 2

In /\ABC , the sum of the measures of /A and /B is 72. What is the measure of /C ?

108

For the polygon below, which of the following represents ___ the length, in meters, of DC ?

12 ------------- tan53

Jay is constructing card decks for a board game. There are 60 cards in a full deck. Jay has 4 partially constructed decks. Deck 1 is 1/2 complete, Deck 2 is 1/3 complete, and the last two are 3/5 complete. How many total cards does Jay have in his four partially completed decks?

122

The manager of ABC Auto Emporium wants to sell an average of 85 cars per month for the first seven months of this year. How many cars does his store need to sell in July to reach an average of 85 cars per month?

125

East Northern College is mailing out holiday greeting cards with a prepaid envelope asking 3,000 alumni for an annual donation. The college's goal is to have $2,500 after paying $750 for the mailing. According to past holiday mailings, the average donation was $25 per alumnus. Assuming this average, how many alumni need to donate to reach the goal?

130

The volume of a cube is 125 cubic centimeters. What is the total surface area of the cube?

150

What is the positive solution to the equation 25x2 = 40?

2√10 -------- 5

If 2n = m, what is 23n+1 in terms of m?

2m³

What is the solution to the equation 2(x − 3) - 2(−x + 6) = −6(x + 2) + 9?

3/2

A man purchased 100 shares of a company's stock at $3 per share. If each share rose $0.09 in value during the first month, decreased $0.02 during the second month, and gained $0.03 during the third month, what is the value, in dollars, of the man's total investment at the end of the third month?

310

The distance from Earth to the Sun is about 1.49 × 108 kilometers, and the distance from Earth to Neptune is about 4.337 × 109 kilometers. When the planets and Sun are aligned along a straight line, what is the distance, in kilometers, from the Sun to Neptune?

4.486 × 10⁹

The vertices of a trapezoid have the (x, y) coordinates indicated in the figure below. What is the area, in square coordinate units, of the trapezoid?

42

__ A gate will be put at point G. Path GB is 24 feet. If Keeshawn wants to make a path from the gate to the corner of the yard at point C, what is the length, in feet, of ___ the path,GC ?

51

All of the following monomials are factors of the polynomial 12x3 y2 − 18x2 y + 6x2 y2 EXCEPT:

6xy²

James is framing a rectangular print for art class and needs to know the perimeter. The length of the print is 24 inches and the width is 18 inches. What is the perimeter in inches of the print?

84

In the figure below, a square with a side of 3 units is inscribed in a circle. What is the area of the shaded region?

9/2π-9

In the right triangle shown below, the length of is 8 mm and the length of is 15 mm. For , which trigonometric expressions has the value of ?

sin C

If x ≤ 3, then |x - 3| = ?

−x + 3

In the standard (x, y) coordinate plane, the point (2, −1) is the midpoint of the line segment with endpoints (10, −6) and (c, d). What is (c, d)?

(−6, 4)

In the standard (x, y) coordinate plane, what is the slope of a line with the equation 5x + 3y = 12?

-5/3

A regular pyramid with a square base is shown in the figure below. The sides of the pyramid are equal to the sides of the base. What is the total surface area of the four triangular sides of pyramid?

36√3

For all x > 4, log(x - 4) + log(x) = ?

log(x² - 4x)

For ABC , the length of CB is 40 mm. Which of the following equations, when solved, will give the length, in millimeters, ofAC ?

sin62 sin54 ------- = ---------- 40 AC

Which equation is NOT graphed in Quadrant I (positive, positive) of the standard (x, y) coordinate grid?

y = -3x - 2

The solution of the system of equations below is the set of (x, y) coordinates for 3x - 4y = 12. What is the value of k? 18x - 24y = 72 9x + ky = −3k

−12

For what integer k are both solutions of the equation x2 + kx + 13 = 0 positive integers?

−14

-4|-6 + 8|=?

−8

What is the value of h(−3) when h(x)= 6x2 − 2x + 12?

72

If 12 + 3x = 36, then 2x = ?

16

The measure of ∠C is 47. What is the angle between and the y-axis?

43

In the plane shown in the figure below, lines l and m are cut by the transversal line n. The eight angles at the intersections of these lines are labeled. Which of the following statements, when it is true, CANNOT always be used to prove that lines l and m are parallel?

∠b≅∠z