Common Core Geometry Cumulative Exam Review

A prize bag contains four country music CDs, eight pop music CDs, and five classic rock CDs. What is the probability of pulling out a classic rock CD and then, without replacing it, pulling out a country music CD? Express your answer in decimal form, rounded to the nearest hundredth.

0.07

The manager of a grocery store reports that there is a 12 percent chance that a customer buys apples during a shopping trip, a 5 percent chance that a customer buy apples and carrots, and a 17 percent chance that a customer buys apples or carrots. What is the probability of a customer buying carrots?

10

Four interior angles of a pentagon measure 88°, 118°, 132°, and 100°. What is the measure of the fifth interior angle? 82° 92° 102° 112°

102°

The law of cosines is used to find the value of m. m2 = 272 + 182 - 2(27)(18)cos(28°) m2 = 729 + 324 - (972)cos(28°) m2 = 1053 - (972)cos(28°) To the nearest whole number, the value of m is

14

In circle O, MP is a diameter. If m is 6 more than 5 times the measure of , what is m? 139° 145° 151° 174°

151°

Line segment ON is perpendicular to line segment ML, and PN = 10. What is the area of triangle MOL? 200 square units 250 square units 300 square units 500 square units

300 square units

Heron's formula: Area = What is the area of triangle ABC? Round to the nearest square unit.

33 square units

In the diagram of circle O, what is the measure of ∠ABC?

34

A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines? 21.2 m 27.5 m 32.5 m 38.2 m

38.2 m

The chords intersect at point U. What is the value of y? 2 4 6 8

6

A right prism has a rhombus as a base. The height of the prism is 6 inches and the volume is 144 cubic inches. Which could be the lengths of the diagonals of the rhombus? 2 in. by 12 in. 4 in. by 11 in. 6 in. by 8 in. 8 in. by 9 in.

6 in. by 8 in.

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: a2 = b2 + c2 - 2bccos(A) Rounded to the nearest meter, the distance between the docks is

705

An oblique prism has a square base and height of 3 centimeters. What is the volume of the prism? 30 cm3 45 cm3 60 cm3 75 cm3

75 cm3

Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase. He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet. What is the volume of material he must purchase? 2 ft3 4 ft3 6 ft3 8 ft3

8 ft3

The owner of a minigolf course is replacing the artificial grass on a portion of the course. The area to be replaced is shown in the diagram. What square footage of artificial grass is needed to cover this portion of the course? 8π + 180 16π + 180 8π + 228 16π + 228

8π + 180

The measure of central angle XYZ is radians. What is the area of the shaded sector? 32 85 96 256

96

The hypotenuse of a 45°-45°-90° triangle measures in. What is the length of one leg of the triangle? A B C D

B

Which circle has a central angle that measures 40°?

B

Which equation can be used to find the measure of angle LKJ? A B C D

D

Triangle JKL is equilateral. One side of the triangle, JL, is a diameter of circle M. Which is true about line segments JK and KL? Both segments are tangent to circle M but are not chords. One segment is tangent to circle M and one segment is a chord in circle M. Both segments are chords in circle M but are not tangents. Neither segment is a chord nor tangent to circle M.

Neither segment is a chord nor tangent to circle M.

Ariana, Boris, Cecile, and Diego are students in the service club. Three of the four students will be chosen to attend a conference. Which choice represents the sample space, S, for this event? S = {ABC, ABD, ACD, BCD} S = {ABC, BCA, CDA, DAC} S = {ABC, ABD, BAC, BDA, ACD, ADC, BCD, BDC} S = {ABC, ABD, ACD, BCA, BCD, BDC, CAB, CBD, DAC, DBC}

S = {ABC, ABD, ACD, BCD}

The diagonals of a parallelogram are congruent. Which could be the parallelogram? trapezoid rectangle kite rhombus

rectangle

A cross section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base. The cross section can be which of these shapes? Check all that apply. square triangle trapezoid circle non-square rectangle

square triangle trapezoid

Which equation represents the parabola shown on the graph? y2 = -2x y2 = -8x x2 = -2y x2 = -8y

y2 = -8x

Given: RT ≅ TV and ST ≅ TU Prove: RSVU is a parallelogram. 1. RT ≅ TV; ST ≅ TU 1. given 2. ∠RTS and ∠VTU are vert. ∠s; ∠RTU and ∠VTS are vert. ∠s 2. definition of vertical angles 3. ∠RTS ≅ ∠VTU; ∠RTU ≅ ∠VTS 3. vertical angles are congruent 4. ? 4. SAS congruency theorem 5. ∠VRS ≅ ∠RVU; ∠USR ≅ ∠SUV; ∠VRU ≅ ∠RVS; ∠RUS ≅ ∠USV 5. CPCTC 6. ∠VRS and ∠RVU, ∠USR and ∠SUV, ∠VRU and ∠RVS, ∠RUS and ∠USV are each a pair of alternate interior angles 6. definition of alternate interior angles 7. RS ∥ UV and RU ∥ SV 7. converse of the parallelogram diagonal theorem 8. RSVU is a parallelogram 8. definition of parallelogram What is the missing statement in step 4? △RTS ≅ △VTU and △RTU ≅ △VTS △RTS ≅ △RVS and △RTU ≅ △STV △VRS ≅ △VRU and △USR ≅ △USV △VUR ≅ △VUS and △UVS ≅ △SRU

△RTS ≅ △VTU and △RTU ≅ △VTS