Download Geometry - Cliffside Park School District

CLIFFSIDE PARK HIGH SCHOOL
HONORS SUMMER PACKET 2016
Geometry
Directions: attached is your summer packer
 It is to be completed and returned by Thursday, September
8, 2016.
 This will be graded and counted as a test grade.
 All questions require work to be shown. No credit is given if
the work is not included with your answer.
 Use extra paper if necessary
Summer Assignment: Geometry
Name:
Solve the following equations for ‘x’:
1.
–5x = 21 + 2x
2.
12 – 6(5 – x) = 2(7x – 1)
3.
x + 3 + x = 17
4
Solve and graph the following inequalities:
4.
5.
6.
15 + 2x ≥ 3(x + 2)
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5 – 4(6 – x) < 10 + 3x
Find the slope of the line that goes through the points (1, 5) and (2, 1).
1
7.
Graph the line 𝑦 = − 𝑥 + 5 on the graph below.
8.
Write the equation of the line, in slope-intercept form, that goes through the
points (4, 5) and (2, 1).
9.
What is the area of the circle pictured below?
Area of a Circle = π·r2. Use: π = 3.14, and make sure the answer uses the
CORRECT UNITS. Give answers in both π notation and rounded to the
nearest hundredth.
3
12 in
10. N is the midpoint of OE. Calculate ON, NE, and OE.
O
N
│
E
│
3(x – 1)
│
17 – (x – 4)
11. Calculate the perimeter of the triangle below, in terms of x. If the perimeter of
the triangle is equal to 40, calculate x. You MUST solve for ‘x’ algebraically.
9 – 3x
10 – 4x
25 + 9x
12. In the picture below, solve for ‘y’. Then calculate the measure of each angle:
3y
( 4 + 18)º
(y + 8)º
13. The length of a rectangle is twice as big as its width. If the area of the
rectangle is 87.12 m2, calculate the length and width of the rectangle.
Use the correct units in the answer.
The area of a rectangle is: (length)·(width)
14. A and B are supplementary angles (meaning their sum = 180 º). A is 8º
more than twice the measure of B. Calculate the measures of A and B.
15. The rectangle and triangle below have the same area. Find the value of 𝑥, then
calculate the area of each shape.
8
2x
12
2x + 3
16. In the picture below, the area of rectangle #1 is twice as much as the area of
rectangle #2. Calculate the length and width of each rectangle.
Rectangle #1
Rectangle #2
x–1
12
10
2x – 5
17. Below is triangle MNO. Calculate the measure of each angle.
(Remember: The angles of a triangle is equal to 180°.)
N
xº
M
(2x – 35)º
(x + 7)º
O
18. In the rectangle pictured below, the length is 35 inches and the width is 1 foot.
Calculate how big the diagonal is. You must use 𝑎2 + 𝑏 2 = 𝑐 2 ,answer in both
feet and inches.
Diagonal
19. Calculate the area of the right triangle below. Area = ½·(base)·(height).
10√2
2
20. Find the area of the triangle pictured below.
Area of a triangle = ½·(Base)·(Height).
To answer the problem, you must use: a2 + b2 = c2, in order to calculate the
height. Make sure the answer uses the CORRECT UNITS.
5 in.
3 in.
8 in.
21. Given one square inscribed in a larger square. Calculate the area of the
smaller square, ABCD. Make sure the answer uses the CORRECT UNITS.
8
B
6
8
6
C
A
8
6
6
D
8
22. Maria, a firefighter, is responding to a fire burning in Cliffside Park. Maria
places the base of the ladder 18 feet from the building. The ladder is 82 feet
long. Calculate how high up the building the ladder is able to reach.
(Picture below)
Maria
LADDER
BUILDING
23. Calculate the area and perimeter of the right triangle graphed below.
24. a). Find the surface area of the shape pictured below. Surface area of a
rectangular prism = sum of the areas of all the sides. Make sure the
answer uses the CORRECT UNITS.
6 in
3 in
12 in
b). Find volume of the above prism.
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑖𝑠𝑚 = (𝐿𝑒𝑛𝑔𝑡ℎ) ∙ (𝑊𝑖𝑑𝑡ℎ) ∙ (𝐻𝑒𝑔ℎ𝑡)
Use CORRECT UNITS.
25. Given the circle below, find the area of the shaded region and find the length
̂
of 𝐴𝐵
A
6"
120°
𝑥
B