Download Geometry Summer Work

Name
Date
Period
Geometry
Summer Packet
Review prerequisite skills: combining like terms, solving linear equations, finding slope,
midpoint, distance, plotting points on a coordinate plane, perimeter, circumference,
area, volume, systems of equations, and simplifying radicals
This Geometry summer packet contains math problems that were taught to students in Pre-Algebra and/or Algebra 1 and are important
prerequisite skills for Geometry beginning the 2016-17 school year. WSHS is requiring all students who are enrolled in Geometry for
the 2016-17 school year to turn in a completed packet on Monday, August 8 th (the first day of school) to his/her Geometry teacher.
We want to ensure all students feel prepared and confident in their background knowledge and ready for a successful experience in
Geometry.
ALL problems are to be worked out by hand on the pages provided. If you do your work on another sheet of paper, please keep the
problems in order of the packet, writing down the page numbers and problem numbers. When working the problems, students should
NOT use a calculator, and must show math work in detail in order to receive credit. During the school year, the students will
learn to use the TI-Nspire CX calculator when applicable and appropriate. Students who are planning to purchase a calculator for the
2016-17 school year need to consider (although it is not required) that the TI Nspire CX is the calculator that will be used in all
Geometry classrooms (throughout the entire school as well).
Students should expect their Geometry teacher to take this packet up for a grade on Monday, August 8 th and test them on these
concepts during the first week of school. The grade for summer work will be comprised as follows: 50% packet completion and
50% Test over summer work.
If you experience difficulty working through this packet, we recommend you utilize the following free websites:
1.
2.
www.khanacademy.org
www.coolmath-games.com/
3.
4.
www.teachertube.com/videos/
www.purplemath.com/modules/index.htm
If students need an additional copy due to “misplacement,” students may download and print a new copy of the packet which will be
posted in the “resources section of the WSHS website. www.whitestation.net , listed under “Mathematics Assignments.”
Students will benefit the most from this packet by starting it early. They should try a few problems each day, as if it were a daily
journal. Do not do all of it now, and do not wait and do it a week before we start school in August. Students are more likely to retain
the information if they spread it out and review throughout the summer. Please take these problems seriously. Students who are weak
in these skills will have a difficult time learning the new Geometry concepts. There will be a test during the first week of school over
the concepts in this packet!
We are excited about working with all of the students coming into Geometry in 2016-17. We want all students to feel prepared,
confident, and successful for all of the important new concepts they will learn next year.
Sincerely,
David Mansfield, Principal, and the White Station High School Math Department
Geometry Prerequisite Skills
Directions: Solve each problem in each section. Show all work .
Part I. Combining Like Terms.
Simplify.
1.
5x + 2y – 3x + 8y + 6
2.
3.
6ab – 4ab + ab
Directions: Solve for the variable. Show all work!
4.
5x + 3x = 80
5. 3x + 16 + 5x = 180
6.
180(n – 2) = 1080
7.
1 – x = 4x + 21
8.
9.
−5𝑦 − 1 4 = 9
10.
2
𝑥
3
11. 2(12b + 7) + 9b + 1 = 180
7x + 8x2 − 5x + x2 + 8x
Part II. Solving equations.
1
= 53
2|Page
7n + 9 + 3n – 3 = 6n
1
12. ½(4x – 8 ) - 3x - 6 = 90
Part III. Graphing in coordinate Plane
y
13.
Plot the following points on the coordinate plane. Then
connect the points and name the shape that is formed.
A (5, 2), B (3, -5), and C (-6, 4)
6
4
2
–6
–4
–2
2
–2
–4
Part IV. Slope
3|Page
–6
4
6
x
Directions: Plot the points on the coordinate plane and connect them with a line. Then find the slope of the
line connecting the two points by doing rise over run and then confirm your answer by using the slope
formula. Show ALL work.
14.
(1, 2) and (6, 6)
15.
(5, 6) and (5, -4)
y
7
y
7
6
6
5
5
4
4
3
3
2
2
1
1
–7 –6 –5 –4 –3 –2 –1–1
16.
1
2
3
4
5
6
7
x
–7 –6 –5 –4 –3 –2 –1
–1
–2
–2
–3
–3
–4
–4
–5
–5
–6
–6
–7
–7
(-3, 6) and (5, -4)
17.
1
4
5
6
7
x
y
7
7
6
6
5
5
4
4
3
3
2
2
1
1
1
2
3
4
5
6
7
x
–7 –6 –5 –4 –3 –2 –1
–1
–2
–2
–3
–3
–4
–4
–5
–5
–6
–6
–7
–7
Part V. Perimeter, Area and Circumference
4|Page
3
(6, -3) and (-2, -3)
y
–7 –6 –5 –4 –3 –2 –1
–1
2
1
2
3
4
5
6
7
x
Directions: For each problem, draw the figure and calculate the perimeter or circumference and area of each
figure. Remember to include the UNITS for each answer.
18.
A rectangle has a length of 10 inches and
a width of 4 inches
19.
A square has a side length of 6.25 centimeters
20.
A right triangle has a base of 16 meters and a
height of 12 meters (hint: you will need to use the
pythagorean theorem to find the third side.)
21.
A circle with a radius of 4.5 feet.
22.
A circle with a diameter of 15 inches.
23.
The area of a 10 cm wide rectangle is 176 cm.
Find the length.
24.
Find the area of the triangle below.
25.
If the area of a circle is 100π cm2, find the
diameter.
Part VI. Volume.
Volume is the measure of space occupied by a solid. Volume is measured in cubic units.
Find the volume of each figure. If necessary, round to the nearest tenth. Use the π key on the calculator.
26.
5|Page
27.
28.
29.
30.
31.
Part VII. Midpoint and Distance Formula in Coordinate Plane
Directions: Find the midpoint of line segment AB.
32.
a)
A(-4, 5) and B(0, 8).
b)
A(2, 7) and B(-4, -6).
Directions: Find the perimeter of pentagon ABCDE with A(0, 4), B(4, 0),
C(3, -4), D(-3, -4) and E(-3, 1).
33. Plot the points on the coordinate plane below and connect the points in alphabetical order.
34. a. Use the distance formula to find the length of segment AB.
y
7
6
5
4
b. Use the distance formula to find the length of segment BC.
3
2
1
–7 –6 –5 –4 –3 –2 –1–1
c. Use the distance formula to find the length of segment CD.
–2
–3
–4
–5
–6
d. Use the distance formula to find the length of segment DE
e. Use the distance formula to find the length of segment AE
35. Find the Perimeter of ABCDE.
6|Page
–7
1
2
3
4
5
6
7
x
Part VIII. Names of Polygons
36. Write the name of
each polygon based
on its number of
sides.
Name of Polygon
Number of Sides
Name of Polygon
Triangle
3
8
4
9
5
10
6
12
7
Part IX. Systems of Equations
Solve each equation by substitution. Answers should be written as an ordered pair.
37. 2x + 2y = 38
38.
y – 2x = 3
y=x+3
3x – 2y = 5
Solve by elimination. Answers should be written as an ordered pair.
39. 2x + 3y = 9
40.
6x – 3y = 15
x + 5y = 8
7x + 4y = 10
7|Page
Number of Sides
Part X. Simplifying Radicals.
Write answers in simplest radical form.
41.
a)
√80
b)
2√75
42.
a)
√36 ∙ √81
b)
√12 ∙ √20
43.
a)
√
44.
a)
√3
b)
4√5
√2
45.
a)
2√3 + 5√3
b)
3√2 + 4√3 + 5√2 − 6√3
46.
a)
(2 + 4√2)(2 − 4√2)
81
64
7
Part XI. Quadratic Equations
Solve each equation by factoring.
47.
x2 + 4x – 32 = 0
48.
p2 – 4 p = 21
Solve each equation by using the quadratic formula.
Round answers to the nearest tenth if necessary.
49.
2x2 – 3x – 5 = 0
50.
- 3x2 – 11x + 4 = 0
8|Page