A scientist arrives at her lab to find that 24 out of 250 samples have been improperly stored. If she is able to salvage 12 of the improperly stored samples, what percent of the total number of samples was she not able to salvage?

Not Answered A)
4 . 8 % B)
5 . 3 % C)
9 . 6 % D)
10 . 6 % Which of the following equations is equivalent to y

x 2 + 6 x + 8 ?

Not Answered A)
y

( x − 3 ) 2 − 1 B)
y

( x + 3 ) 2 − 1 C)
y

( x − 3 ) 2 + 1 D)
y

( x + 3 ) 2 + 1 A meteorologist is measuring the snowfall in two locations. During a winter storm, Location A accumulates snow at a rate of 1 . 25 inches per hour, while Location B accumulates snow at a rate of 0 . 75 inches per hour. Assuming the snow continues to fall at a steady rate, how long will it take for the two locations to accumulate a combined total of one foot of snowfall during this storm? (Note: 1 foot = 12 inches.)

Not Answered A)
4 hours 48 minutes B)
6 hours 0 minutes C)
9 hours 0 minutes D)
9 hours 36 minutes A student studying triangles made the following rule:

For any triangle with side lengths a , b , and c , a 2 + b 2

c 2 .

Which of the following is a counterexample that disproves the above statement?

Not Answered A) A triangle with sides measuring 3 , 4 , and 5 units B) A triangle with sides measuring 5 , 12 , and 13 units C) A triangle with sides measuring 8 , 15 , and 16 units D) A triangle with sides measuring 9 , 40 , and 41 units An equilateral triangle has a side length of 8

units . What are the area and perimeter of the triangle, respectively?

Not Answered A)
16 units 2 , 24 units B)
16

units 2 ,

( 12

4 √ 3 )

units C)
16 √ 3 units 2 , 24 units D)
32 √ 3

units 2 ,

( 12

4 √ 3 )

units If p is an odd positive factor of the positive integer q , what must be true of ( q p ) 2 ?

Not Answered A) It is odd, but not necessarily positive. B) It is positive, but not necessarily odd. C) It is both odd and positive. D) It is neither odd nor positive. A store offers a 15 % discount on a jacket priced at $ 80 . What is the final price of the jacket after applying the discount?

Not Answered A)
$ 68 B)
$ 72 C)
$ 74 D)
$ 76 A jar contains red and blue marbles in a ratio of 5 : 3 . If there are 40 marbles in total, how many red marbles are there?

Not Answered A)
8 marbles B)
15 marbles C)
20 marbles D)
25 marbles Which of the following is perpendicular to the line that passes through ( 3 ,

7 ) and ( 2 ,

2 ) ?

Not Answered A)
y

=

− 5 x

3 B)
y

=

− 1 5 x

−

7 C)
y

=

1 5 x

8 D)
y

=

4 x What is sin ( 0 ) ?

Not Answered A)
− 1 B)
0 C)
1 D)
π Suppose m is a perfect square. Which of the following must be true?

Not Answered A) The square root of m is prime. B)
m + 4 is a perfect square. C)
m is even. D)
m is not prime. ( a 3 ) 2 a 2 is equivalent to which of the following?

Not Answered A)
a 2 B)
a 3 C)
a 4 D)
a 6 What is the solution for x in the equation x ²

−

6 x

9

=

0 ?

Not Answered A)
x

=

− 3 B)
x

=

0 C)
x

=

9 5 D)
x

=

3 In a right triangle, if sin θ

5 13 , what is cos θ ?

Not Answered A)
5 13 B)
5 12 C)
1 2 D)
12 13 In the right triangle below, what is the value of sin θ ? (Note: The figure is not necessarily drawn to scale.)

passage_107 Not Answered A)
0 . 60 B)
0 . 75 C)
0 . 80 D)
1 . 00 A circle has a circumference of 16 π inches Which of the following is true?

Not Answered A) The area of the circle is 64 π

inches 2 . B) The radius of the circle is 4

inches . C) The circle has the same diameter as a circle with an area of 64

inches 2 . D) The circle has the same circumference as a circle with a diameter of 4

inches . If y z

x and 8 z

x y , then what is x + y + z if y is half the value of z ?

Not Answered A)
13 B)
22 C)
71 D) There is not enough information to answer the question. A circle with center F is shown in the figure below. The radius of Circle F is 12 units, and the length of ¯¯¯¯¯¯ B D is also 12 units. The measure of arc A E , x degrees, is twice the measure of arc B D , y degrees. If the measure of angle C is given by 1 2 ( x °

−

y ° ) , what is m ∠ C ? (Note: The figure is not necessarily drawn to scale.)

passage_110 Not Answered A)
30 ° B)
45 ° C)
60 ° D)
90 ° A chemist tests 30 samples, all of which are known to contain copper or zinc (or both). The test shows 22 samples contain copper and 12 contain zinc. How many samples contain both copper and zinc?

Not Answered A)
2 B)
4 C)
6 D) It is impossible to determine from the given information. The circumference of Circle A is approximately 31 inches. Circle B has a radius of 8 inches. Circle C has a diameter twice the length of Circle B ’s circumference. Which of the following ranks the area of the circles from least to greatest?

Not Answered A) Circle A , Circle B , Circle C B) Circle B , Circle A , Circle C C) Circle A , Circle C , Circle B D) Circle C , Circle A , Circle B Triangle A is an isosceles right triangle that is similar to Triangle B . Which of the following would prove that Triangle A and Triangle B are congruent?

Not Answered A) Triangle A and Triangle B both have one right angle. B) Triangle A and Triangle B both have three acute angles. C) The corresponding side lengths of Triangle A and Triangle B are equal. D) The corresponding angles of Triangle A and Triangle B are congruent. What is the y -coordinate of the point ( x ,

y ,

z ) that would satisfy the three equations below?

x

− 10 y z

x z

− 18 − y

x 2

25

Not Answered A)
− 1 B)
0 C)
2 D)
5 A garden is in the shape of a right triangle with a base of 12 meters and a height of 9 meters. The garden is to be covered with a layer of topsoil 0 . 1 meters thick. What is the volume of topsoil required?

Not Answered A)
2 . 10 cubic meters B)
3 . 60 cubic meters C)
4 . 32 cubic meters D)
5 . 40 cubic meters Which of the following describes the graph of y

=

sin ( x

−

π 2 ) ?

Not Answered A) The graph of y

sin ( x ) shifted right by π 2 units​. B) The graph of y

sin ( x ) shifted left by π 2 units​. C) The graph of y

sin ( x ) shifted up by 1 unit. D) The graph of y

sin ( x ) stretched vertically. Line z is tangent to the circle ( x

−

4 ) 2

( y

−

3 ) 2

=

100 at point ( 4 ,

13 ) in the ( x , y ) -coordinate plane. Line w is tangent to this circle at point B , with line w parallel to (but distinct from) line z . What are the coordinates of point B ?

Not Answered A)
( 4 , 3 ) B)
( 4 , −7 ) C)
( −4 , 13 ) D)
( 4 , −13 ) A line in the ( x , y ) -coordinate plane of the form y

=

m x

b , where b

≠

0 , is reflected across the x -axis and then reflected across the y -axis. Which transformation of the original line would result in the same image?

Not Answered A) A 180 ° counterclockwise rotation about the origin B) A 360 ° clockwise rotation about the origin C) A 360 ° counterclockwise rotation about the origin D) None of the above What is the area of the circle represented by the equation ( x − 1 ) 2 + ( y − 3 ) 2

25 in the ( x , y ) -coordinate plane?

Not Answered A)
9 π

units 2 B)
10 π

units 2 C)
16 π

units 2 D)
25 π

units 2 Which of the following lists contains exactly one composite number? (A composite number is an integer greater than one that is not prime.)

Not Answered A)
− 1 , 0 , 1 , 2 B)
0 , 2 , 5 , 7 C)
1 , 2 , 3 , 4 D)
2 , 3 , 6 , 9

Let's go through each question one by one and provide the answers.

1. Percent of samples not salvaged:

   • Total samples = 250
   • Improperly stored samples = 24
   • Salvaged samples = 12
   • Not salvaged = 24 - 12 = 12
   • Percent not salvaged = (12 / 250) * 100 = 4.8%
   • Answer: A) 4.8%

2. Equivalent equation for (y = x^2 + 6x + 8):

   • Completing the square: (y = (x + 3)^2 - 1)
   • Answer: B) (y = (x + 3)^2 - 1)

3. Time for combined snowfall of one foot:

   • Location A: 1.25 inches/hour
   • Location B: 0.75 inches/hour
   • Combined rate = 1.25 + 0.75 = 2 inches/hour
   • 1 foot = 12 inches, so time = 12 / 2 = 6 hours
   • Answer: B) 6 hours 0 minutes

4. Counterexample for the triangle rule:

   • The rule (a^2 + b^2 = c^2) is true for right triangles. A counterexample would be a triangle that does not satisfy this.
   • Answer: C) A triangle with sides measuring 8, 15, and 16 units

5. Area and perimeter of an equilateral triangle with side length 8:

   • Area = (\frac{\sqrt{3}}{4} \times 8^2 = 16\sqrt{3})
   • Perimeter = (3 \times 8 = 24)
   • Answer: C) (16\sqrt{3}) units², 24 units

6. If (p) is an odd positive factor of (q):

   • ((qp)^2) is positive and since (p) is odd, (qp) is also odd, thus ((qp)^2) is odd.
   • Answer: C) It is both odd and positive.

7. Final price of the jacket after a 15% discount:

   • Discount = 15% of $80 = $12
   • Final price = $80 - $12 = $68
   • Answer: A) $68

8. Number of red marbles in a 5:3 ratio with 40 total marbles:

   • Total parts = 5 + 3 = 8
   • Red marbles = (5/8) * 40 = 25
   • Answer: D) 25 marbles

9. Line perpendicular to the line through (3, 7) and (2, 2):

   • Slope of the line = (7 - 2) / (3 - 2) = 5
   • Perpendicular slope = -1/5
   • Answer: B) (y = -\frac{1}{5}x - 7)

10. Value of (\sin(0)):

    • (\sin(0) = 0)
    • Answer: B) 0

11. If (m) is a perfect square:

    • (m) can be any perfect square, including 1, which is prime.
    • Answer: D) (m) is not prime.

12. ((a^3)^2 a^2) equivalent:

    • ((a^3)^2 = a^6), so (a^6 a^2 = a^{6+2} = a^8)
    • Answer: D) (a^6)

13. Solution for (x^2 - 6x + 9 = 0):

    • This factors to ((x - 3)^2 = 0), so (x = 3)
    • Answer: D) (x = 3)

14. If (\sin \theta = \frac{5}{13}), find (\cos \theta):

    • Using (\sin^2 \theta + \cos^2 \theta = 1):
    • (\cos^2 \theta = 1 - \left(\frac{5}{13}\right)^2 = 1 - \frac{25}{169} = \frac{144}{169})
    • (\cos \theta = \frac{12}{13})
    • Answer: D) (\frac{12}{13})

15. Value of (\sin \theta) in a right triangle:

    • Without the figure, we cannot determine the value.
    • Answer: D) There is not enough information to answer the question.

16. Circle with circumference (16\pi):

    • Circumference = (2\pi r), so (r = 8)
    • Area = (\pi r^2 = \pi (8^2) = 64\pi)
    • Answer: A) The area of the circle is (64\pi) inches².

17. If (yz = x) and (8z = xy), find (x + y + z) if (y) is half of (z):

    • Let (z = 2y), then (x = 2y^2) and (8(2y) = 2y^2y) leads to (16y = 2y^3) or (y^3 - 8 = 0) giving (y = 2).
    • Then (z = 4) and (x = 8), so (x + y + z = 8 + 2 + 4 = 14).
    • Answer: D) There is not enough information to answer the question.

18. Angle (C) in the circle:

    • (x = 2y), so (m∠C = \frac{1}{2}(2y - y) = \frac{1}{2}y).
    • If (y = 12), then (m∠C = 6).
    • Answer: D) 90°

19. Samples containing both copper and zinc:

    • Let (x) be the number of samples containing both.
    • Using the principle of inclusion-exclusion: (22 + 12 - x = 30) gives (x = 4).
    • Answer: B) 4

20. Ranking areas of circles:

    • Circle A: Area = (\frac{31}{2\pi}^2)
    • Circle B: Area = (\pi(8^2) = 64\pi)
    • Circle C: Diameter = (2 \times 8\pi), Area = (\pi(16^2) = 256\pi)
    • Answer: A) Circle A, Circle B, Circle C

21. Proving Triangle A and Triangle B are congruent:

    • Corresponding side lengths must be equal.
    • Answer: C) The corresponding side lengths of Triangle A and Triangle B are equal.

22. Finding the (y)-coordinate:

    • From (x^2 = 25), (x = 5) or (-5).
    • Substitute into the other equations to find (y).
    • Answer: C) 2

23. Volume of topsoil required:

    • Area of the triangle = (\frac{1}{2} \times 12 \times 9 = 54) m².
    • Volume = Area × thickness = (54 \times 0.1 = 5.4) m³.
    • Answer: D) 5.40 cubic meters

24. Graph of (y = \sin(x - \frac{\pi}{2})):

    • This is a horizontal shift to the right.
    • Answer: A) The graph of (y = \sin(x)) shifted right by (\frac{\pi}{2}) units.

25. Coordinates of point B:

    • The radius is 12, and the tangent point must be vertically aligned with the center.
    • Answer: B) (4, -7)

26. Transformation of the line after reflections:

    • Reflecting across the x-axis and then y-axis is equivalent to a 180° rotation.
    • Answer: A) A 180° counterclockwise rotation about the origin.

27. Area of the circle represented by the equation:

    • Radius = 5, Area = (\pi(5^2) = 25\pi)
    • Answer: D) (25\pi) units².

28. List with exactly one composite number:

    • Answer: C) 1, 2, 3, 4 (4 is composite).

If you have any further questions or need clarification on any of the answers, feel free to ask!