AnswersSS Integrated Math IIB 2026Performance Task: Applying Probability Concepts

Performance Task: Applying Probability Concepts — Cumulative exam Answers

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Parallelogram A B C D is shown. Line segment X Y goes from point X on side A B to point Y on side C D to form 2 trapezoids. The length of X Y is 11 and the length of Y C is 4. Sides X B and C Y are congruent.

Question illustration
A
99 square units
B
110 square units
C
126 square units
D
143 square units
2
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A polygon with 3 sides is stacked to form a prism.

Question illustration
A
square
B
trapezoid
C
triangle
D
non-square rectangle
3

The hypotenuse of a 45°-45°-90° triangle measures in.

Question illustration
A
5 StartRoot 5 EndRoot
Option A
B
5 StartRoot 10 EndRoot
Option B
C
10 StartRoot 5 EndRoot
Option C
D
10 StartRoot 10 EndRoot
Option D
4

An oblique square prism is shown.

Question illustration
A
x(x – 2) cubic units
B
x(x +1) cubic units
C
x2(x – 2) cubic units
D
x2(x +1) cubic units
5

Which statements about the cylinder are true? Select two options.

A
The radius of the cylinder is 2x units.
B
The area of the cylinder’s base is πx2 square units.
Option B
C
The area of the cylinder’s base is πx2 square units.
Option C
D
The height of the cylinder is 2x units.
E
The height of the cylinder is 4x units.
6

Juanita has a storage closet at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented. If she reaches into the closet and grabs a bottle without looking, she has a 42% chance of grabbing a bottle of shower gel.For the events "shower gel” and "scented” to be independent, what must be shown to be true?

A
P(lotion) = 42%
B
P(scented) = 42%
C
P(shower gel | scented) = 42%
D
P(scented | shower gel) = 42%
7

Line EF is tangent to circle G at point A.

Question illustration
A
90°
B
95°
C
190°
D
195°
8

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 10.5 centimeters. Angle A B C is x.

Question illustration
A
27.7°
B
31.7°
C
58.3°
D
62.3°
9

On a coordinate plane, triangle R S T has points (negative 3, 2), (3, 2), and (negative 1, 1). An altitude is drawn from point T to point U at (negative 1, 2).

Question illustration
A
6 square units
B
9 square units
C
12 square units
D
18 square units
10

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
72 = 82 + 112 – 2(8)(11)cos(N)
B
82 = 72 + 112 – 2(7)(11)cos(M)
C
72 = 82 + 112 – 2(8)(11)cos(P)
D
82 = 72 + 112 – 2(7)(11)cos(P)
11

Points D, E, and F are on circle C and EF ≅ DF.

Question illustration
A
14°
B
19°
C
26°
D
38°
12

The law of cosines is used to find the value of m.

Question illustration
A
13
B
14
C
43
D
45
13

Triangle A B C is shown. Angle A B C is a right angle. Angle B C A is 22 degrees and angle C A B is 68 degrees.

Question illustration
A
cos(B)
B
sin(B)
C
cos(C)
D
tan(C)
14

A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand.Law of cosines:

Question illustration
A
589 meters
B
705 meters
C
792 meters
D
861 meters
15

A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius. Each of the central angles has a measure of 40°. How many sides does the polygon have?

A
8
B
9
C
10
D
12
16

Line segment ON is perpendicular to line segment ML, and PN = 10.

Question illustration
A
200 square units
B
250 square units
C
300 square units
D
500 square units
17

Consider circle C with angle ACB measuring radians.

Question illustration
A
6 inches
B
12 inches
C
18 inches
D
24 inches
18

The equation can be used to find the length of .

Question illustration
A
14.3 in.
B
20.5 in.
C
21.3 in.
D
22.6 in.
19

On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2).

Question illustration
A
The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
B
The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2.
C
The area of parallelogram 1 is equal to the area of parallelogram 2.
D
The area of parallelogram 1 is 2 square units less than the area of parallelogram 2.
20

Parallelogram P Q S R is shown. The length of P Q is (2 x + 5) centimeters and the length of R S is (4 x + 1) centimeters.

Question illustration
A
2 cm
B
5 cm
C
6 cm
D
9 cm

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