# Name: Honors Geometry Summer Assignment 2016

## Transcription

Name: Honors Geometry Summer Assignment 2016
```Name:_________________________________
Honors Geometry Summer Assignment 2016
Find the volume of the solid. Round to the nearest
tenth if necessary.
____
4.
6 in.
Multiple Choice
____
1. Write  using an exponent.
a.
b.
c.
d.
4 in.
Use a net to find the surface area of the figure.
2 in.
Drawing not to scale
____
2.
a. 24 in.3
10 m
b. 96 in.3
c. 48 in.3
d. 16 in.3
____
5. A large aquarium is 8 m by 6 m by 5 m. What is the
difference in the volume of the aquarium if its
dimensions are doubled?
a. 240 m3 b. 1680 m3 c. 360 m3 d. 480 m3
____
6. Marcus has 68 feet of fencing. He wants to build a
rectangular pen with the largest possible area. What
should the dimensions of the rectangle be?
a. 19 ft by 21 ft
c. 17 ft by 17 ft
b. 21 ft by 13 ft
d. 19 ft by 15 ft
____
7. There are 60 pages in your journal. If you number all
of the pages, starting with 1, how many digits will you
have to write?
a. 62
b. 120
c. 111
d. 60
8 m
14 m
drawing not to scale
a. 332 m2 b. 504 m2 c. 440 m2 d. 664 m2
not drawn to scale
Find the missing length(s) of the triangle. Round to
the nearest tenth.
Find the area of the figure.
____
____
8.
13 in.
3.
45°
7 in.
11 in.
13 in.
h
45°
9 in.
Drawing not to scale
Drawing not to scale
a. 31.5 in.2 b. 173.3 in.2 c. 27 in.2
d. 63 in.2
a. h = 6.5 in.
b. h = 22.5 in. c. h = 26.0 in. d. h = 18.4 in.
Solve the equation.
____
____
13.
A 16-oz bottle of water costs \$1.44. What
is the cost per ounce?
a. \$0.09/oz b. \$0.18/oz c. \$0.90/oz d. \$1.78/oz
____
14.
A car is driving at a speed of 60 mi/h.
What is the speed of the car in feet per minute?
9.
a. –31
b.
85
2
5
c. –50
d. –35
a. 5,280 ft/min
b. 3,600 ft/min
c. 316,800 ft/min
d. 2,580 ft/min
____ 10.
a. –8
b. 2
c. –10
d. –4
____
____ 11. Which properties of equality justify steps c and f?
____
15.
The length of a rectangle is 5 centimeters
less than twice its width. The perimeter of the
rectangle is 26 cm. What are the dimensions of the
rectangle?
a. length = 5 cm; width c. length = 6 cm; width
= 5 cm
= 7 cm
b. length = 7 cm; width d. length = 4 cm; width
= 6 cm
= 9 cm
16.
Peter is reading a 193-page book. He has
read three pages more than one fourth of the
number of pages he hasn’t yet read.
a. How many pages has he not yet read?
b. Estimate how many days it will take Peter to
day.
a. Subtraction Property of Equality; Multiplication
Property of Equality
b. Addition Property of Equality; Division Property of
Equality
c. Addition Property of Equality; Subtraction Property
of Equality
d. Multiplication Property of Equality; Division
____
Property of Equality
____ 12. The perimeter of the rectangle is 24 cm. Find the
____
value of x.
3 cm
17.
Evaluate
a. –11
b. 1
18.
Evaluate
a. –9
b. –4
c. –6
c. –8
for x = 3.
d. 11
for x = –3.
d. 4
Use inductive reasoning to describe the pattern.
Then find the next two numbers in the pattern.
3x cm
____
a. 3
b. 12
c. 8
3
d. 18
19.
–9, –4, 1, 6, . . .
a. add 5 to the previous term; 11, 16
b. multiply the previous term by 5; 30, 150
c. subtract 5 from the previous term; 1, –4
d. multiply the previous term by 5; 11, 150
____ 20. –5, –10, –20, –40, . . .
a. multiply the previous term by 2; –80, –160 ____
b. add –5 to the previous term; –35, –30
c. subtract 5 from the previous term; –80, –160
d. multiply the previous term by –2; 80, –160
State whether the slope is 0 or undefined.
24.
y
5
4
3
2
Find the slope of the line.
1
–5
–4
–3
–2
y
____ 21.
–1
–1
1
2
3
4
x
5
–2
5
–3
4
–4
–5
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
____
–2
a. undefined
25.
b. 0
y
5
–3
4
–4
3
–5
a.
1

4
b. 1
4
2
c. 4
1
d. 4
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
Find the slope of the line that passes through
the pair of points.
____ 22. (1, 7), (10, 1)
a. 3
b. 2

2
3
c.

3
2
d. 2
3
–4
–5
a. 0
b. undefined
Write an equation of a line with the given slope
and y-intercept.
____
____ 23. A student finds the slope of the line between
(14, 1) and (18, 17). She writes
. What ____
mistake did she make?
a. She should have added the values, not
subtracted them.
b. She used y-values where she should have used
x-values.
c. She mixed up the x- and y-values.
d. She did not keep the order of the points the ____
same in numerator and the denominator.
26.
m = 1, b = 4
a. y = 4x + 1
b. y = x – 4
1
3
27.
m= ,b=
4
4
a.
3
y = 4x –
4
b.
1
3
y= x–
4
4
c. y = –1x + 4
d. y = x + 4
c.
3
1
y= x+
4
4
d.
1
3
y= x+
4
4
Find the x- and y-intercept of the line.
28.
(Short Answer) 2x + 3y = –18
29. (Short Answer) A line passes through (1, –5)
and (–3, 7).
a. Write an equation for the line in pointslope form.
____
Are the graphs of the lines in the pair parallel?
Explain.
33.
a.
b.
b. Rewrite the equation in slope-intercept
form.
c.
d.
y = 5x + 6
–18x + 3y = –54
No, since the slopes are different.
Yes, since the slopes are the same and the yintercepts are different.
No, since the y-intercepts are different.
Yes, since the slope are the same and the yintercepts are the same.
Tell whether the lines for each pair of equations
are parallel, perpendicular, or neither.
____ 30. 7x – 4y = 4
x – 4y = 3
a. perpendicular
1
____ 31. y =  x – 11
2
16x – 8y = –8
b. parallel
c. neither
____
34.
a. 12
b. 12 2
c. 6
d.
Simplify the expression.
____
35.
a.
a. neither
b. perpendicular
c. parallel
____
____ 32. Find a solution to the following system of
equations.
b.
c.
d.
36.
Find the GCF of the terms of the
polynomial.
8x6 + 32x3
a. x3
a. (–8, –15) b. (–2, –15) c. (0, 1)
b. 8x3
c. 8x3
d. 8x6
d. (2, 5)
y
6
37. The vertices of a triangle are A(–0.5, 2), B(1, –2),
and C(–2, –2). Graph the triangle and its image
after a translation of 1 units right, 1 units up.
4
2
38. Graph the point M(2, 3) and its image after a
reflection over y = 4.
y
2
–2
2
–2
–4
–2
2
–2
–6
4
–4
–4
–4
6
–6
–6
4
6
x
4
6
x
41.
Justify each step. Write a reason why you
get from one step to the next one.
39.
Graph the point R(–4, –5). Then rotate it
180° degrees counterclockwise about the origin
and graph the new point.
y
6
4
2
–6
–4
–2
2
4
6
x
–2
4
42.
–4
writes the odd
equation:
The42.
sumAofclass
3 consecutive
integers is 87. Find
n
+
n
+
1
+
n
+
2 = 87
the three integers.
to solve the following problem.
–6
The sum of 3 consecutive odd integers is 87. Find
the three integers.
40. The vertices of a triangle are E(1, 0), F(5, –1),
and G(4, –4). Graph the triangle and its image
after a rotation of 90° about the origin.
y
43. L(4, –2), M(3, –5), N(0, –3); Reflect over the line
What
y =error
1 did they make?
8
6
y
Name the property that the statement(s)
illustrates.
6
4
4
43. If –b = 14, then 14 = –b.
2
–6
–4
–2
Name the property that
2 the statement(s)
illustrates.
2
–2
–4
–6
4
6
x
–8
44.
45.
–6
–4
If
–2
2
and–2
–4
–6
–8
4
then d = 4.
6
8 x
44. The sum of four consecutive odd integers is
.
Write an equation to model this situation, and find
the values of the four integers.
y = 2x – 3
y = –x + 3
47.
y
5
4
3
2
1
–5
–4
–3
–2
Graph each system. Tell whether the system
has no solution, one solution, or infinitely many
solutions.
–1
–1
1
2
3
4
x
5
–2
–3
–4
y = 5x – 4
y = 5x – 5
45.
–5
y
5
Are the graphs of the lines in the pair parallel?
Explain.
4
3
1
x+8
6
–2x + 12y = –11
2
48. y =
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
49. Solve the following system of equations by
graphing.
–4x + 3y = –12
–2x + 3y = –18
–4
–5
46.
y=x+4
y–4=x
y
5
y
4
5
3
4
2
3
1
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
–6
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
6
x
57.
Niki has 8 coins worth \$1.40. Some of the
coins are nickels and some are quarters.
a. Let q = the number of quarters and n = the
number of nickels. Write an equation relating
the number of quarters and nickels to the total
number of coins.
Graph the function.
50.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
b.
Write an equation relating the value of the
quarters and the value of the nickels to the
total value of the coins.
c.
How many of each coin does Niki have?
x
–2
–3
–4
–5
Factor the expression.
51.
6x2 + 5x + 1
52.
12d2 + 4d – 1
53.
d2 + 10d + 9
54.
w2 + 18w + 77
58.
The standard method for solving an
equation like
is to use the Subtraction
Property of Equality and then the Division
Property of Equality. It is possible to solve the
equation using the properties in the reverse order.
Explain why the standard method is better.
Simplify the product using FOIL.
55.
(3x – 7)(3x – 5)
56.
Ronald is setting up an aquarium in his
new office. At one pet store, fish cost \$2 each and
an aquarium cost \$40. At another pet store, fish
cost \$3 each and an aquarium cost \$36. Write and
solve a system of equations to represent the cost of
x fish and an aquarium at each store. Solve this the
system. What does this solution represent? If
Ronald wants 5 fish, from which pet store should