Honors Math II
nd
2 Semester (Part I)
Review Packet
• All work must be shown on a separate sheet of paper.
• Make sure each unit is labeled as well as the problem
number.
Unit 8 – Right Triangles
Find the geometric mean between the numbers.
1. 8 and 18
2. 9 and 80
3. Simplify the radical expressions.
a.
2
3
b.
75
In the diagram, ∠ACB is a right angle and CD ⊥ AB.
C
4.  ABC ______, and  ADC ________ .
5. CD is the geometric mean between ________ and ________.
6. CB is the geometric mean between ________ and ________.
7. If AD = 9 and CD = 6, then DB = ________.
A
D
B
Tell whether a triangle formed with sides having the lengths named is acute, obtuse or right. If a
triangle can’t be formed, write not possible.
8.
2, 7, 10
9.
6, 6, 2
10.
5, 12, 13
11.
5, 8, 15
Find the value of x.
12.
13.
14.
10
10
15.
10
x
x
x
30°
45°
x
3
12
2x
For exercises 16 – 23, find angle measures and lengths correct to the nearest hundredth.
16.
17.
18.
19.
x
7
x
x
x
12
31°
40°
50°
55°
20.
5
24
4
21.
10
13
x°
12
22.
18
x°
35°
5
30°
x
23. A building casts a shadow 40 ft long when the sun’s angle of elevation is 58°. Find the height of the
building.
Unit 9 - Area
Find the area of each figure described.
1. A square with perimeter of 28 cm.
2. A rectangle with width of 7 and diagonal 25.
3. A parallelogram with sides 16 and 20 that form a 30° angle.
4. A trapezoid with bases 6 and 10 and height of 4.
5. A rhombus with diagonals 8 and 5.
6. A right triangle with legs 25 cm and 6 cm.
7. A triangle with sides 5, 5, and 8.
8. A regular hexagon with radius 12.
9. An equilateral triangle with radius 6 3.
10. Find the area of the region below.
4
3
3 2
45°
11. Two corresponding sides of two similar polygons have lengths 3 and 7. The perimeter of the larger
polygon is 91 cm. What is the perimeter of the smaller polygon?
12. A circle with diameter 18.
13. A circle with circumference 22π cm.
14. Sector AOB of O with radius 8 and m 
AB = 40.
Find the area of the shaded region.
15.
5
5
AB .
AB = 72 , and the area of sector AOB is 20π . Find the length of 
16. In O , m 
A
O
B
17. Two circles have radii 8 and 11. What is the ratio of the areas?
18. The dimensions of the small rectangle are one-third those of the large rectangle. A point is picked at
random within the large rectangle. What is the probability that it is within the small rectangle?
Unit 10 – Surface Area and Volume
1. Find the volume of a rectangular solid with length 6 cm, width 5 cm, and height 12 cm.
2. Find the volume and the total area of a cube with edge 5a.
3. A right triangular prism has height 15 and base edges 5, 12, and 13. Find the volume and total area.
4. Find the volume of a cone with radius 4 and height 7.
5. Find the lateral area and the total area of the cone in exercise 4.
6. Find the lateral area of a cylinder with radius 4 cm and height 6 cm.
7. A regular square pyramid has base edge of 8 and a lateral edge of 6. Find the lateral area and the total
area.
8. Find the area and the volume of a sphere with radius 6 cm.
9. Two similar regular triangular pyramids have total areas of 20 cm 2 and 80 cm 2 . Find the volume of the
smaller pyramid if the volume of the larger one is 10 cm3 .
10. The volumes of two spheres have a ratio of 27 : 64 . Find the area of the larger sphere if the area of the
smaller is 18.
11. The radii of two similar cylinders are 2 and 5. Find the ratio of their volumes and of their lateral areas.
12. Find the area of a sphere with volume 36π .
13. A cone with radius 5 cm has total area 90π cm 2 . Find its height.
14. The volumes of two similar rectangular solids are 125 cm3 and 64 cm3 . Find the ratio of their base
perimeters.