Download Goals - Metamora Township High School

Dear Parents and Students,
Mathematics is a discipline that constantly builds on previous knowledge. Students entering Honors Geometry
will be expected to recall and apply the material that they learned in Algebra during 8th or 9th grade. To help
ensure your success in Honors Geometry, the high school mathematics department has compiled a list of
problems that represent some of the most frequently used Algebra concepts as well as some basic Geometry
problems. Please take some time this summer to go over these problems. We have even included the solutions
for you!
When you return to school in the fall, be prepared to ask questions on any problems that have you stumped. We
will take approximately a day to review the algebra concepts and then take the prerequisite test to help
determine your placement and readiness for Honors Geometry. This will count as a test grade in Honors
Geometry since Algebra I concepts are a prerequisite! We will then spend only a few days to stress the
important concepts in chapter 1 before taking a Chapter 1 Test. This will allow us more time to devote during
the year to common core activities. You must complete this packet before you return to school because the
review is closely tied to the Algebra I material and the Chapter 1 concepts will be tested within a few days. This
packet may be collected for a completion grade. See instructions below for how to access my classroom
website. This has videos of me teaching each problem from the Algebra review as well as videos of some
problems from the Chapter 1 information. I have also added some more Algebra Review problems for those of
you who need extra help.
You are required to have a graphing calculator for Honors Geometry. Please see my web page or the
Mathematics Department web page for information regarding which calculators are acceptable.
If you lose this packet, the high school guidance department will have extra copies available. The packet is also
on Mrs. Gualandri’s website. Feel free to contact our department chair, Mrs. Stone, at [email protected] or
Honors Geometry teacher, Mrs. Gualandri, at [email protected] if you have any questions.
The following instructions will get you to Mrs. Gualandri’s teacher page for an extra summer packet, calculator
requirements, helpful videos or other information: classroom.google.com -> Type in the code: cgg3w5o
Have a wonderful summer!
The Mathematics Department
Metamora High School
Goals: Review order of operations, factoring polynomials, simplifying radicals, slope and equations of lines,
systems of equations, quadratic equations, and the quadratic formula.
Order of Operations
Simplify.
1.
2.
3.
4.
Multiplying Polynomials
Find the product.
5. 5a2(a3 – 5a2 + 3a)
6. (y – 5)(4y + 3)
7. (2t – 1)(4t + 3)
8. (7x – 1)(7x + 1)
9. (x + 8)2
Factoring Polynomials
Factor completely.
10. 75x2 – 30x + 3
11. a2 + 11a + 30
12. x2 – 6x – 16
13. 3a2 + 12a – 3
14. 49x2 – 1
15. x3 + 2x2 – 5x – 10
16. 9y2 – 12y + 4
Radicals
Simplify.
17.
18.
19.
20.
Slope and Equations of Lines
Given an equation of a line, name its slope and y-intercept.
21. y = ¼ x – 3
22. 2x + 3y = 6
Write the equation in slope-intercept form of the line:
23. slope 1/5, contains (5, -1)
24. contains (-4,2) and (1, -3)
Systems of Equations
Solve the system of equations.
25.
2x + 3y = 7
x = 1 – 4y
26.
3x – 5y = 8
4x – 7y = 12
Quadratic Equations
Solve for x.
27. x2 + 4x – 12 = 0
28. 5x = x2 – 3x
Quadratic Formula
Solve using the quadratic formula.
29. 2y2 – 7y – 15 = 0
REMEMBER:
IF YOU STRUGGLE WITH THIS, THERE ARE MORE
PRACTICE PROBLEMS AND VIDEOS ON MRS.
GUALANDRI’S GOOGLE CLASSROOM. PLEASE TRY
THESE PROBLEMS OUT AND BE SURE TO REVIEW THE
ALGEBRA CONCEPTS IN AUGUST SO THAT YOU ARE
READY FOR THE FIRST TEST!
Goals: Identify and model points, lines, and planes.
Identify collinear and coplanar points and intersecting lines and planes in space.
Vocabulary
Point
Line
Collinear
Plane
Coplanar
Space
In geometry, point, line, and plane are considered undefined terms because they are only explained using
examples and descriptions.
Study Tip: Three-Dimensional Drawings
Because it is impossible to show space or an
entire plane in a figure, edged shapes with
different shades of color are used to
represent planes. If the lines are hidden from
view, the lines or segments are shown as
dashed lines or segments.
1. Use the figure above to identify and name:
a) a line containing point C
b) a plane containing point A
c) a point on line j
d) three collinear points
e) three coplanar points
f) the intersection of line j and line m
g) Challenge: a line containing point D
(explain)
2. Draw a geometric figure with all of the following:
a. plane N intersects plane M at line AB
b. line j is in plane N and intersects line AB at point E
c. points C and D are on line j
d. point F is in plane M, but not collinear with points A and B
e. points A, F, and G are coplanar
Goals: Measure segments and determine accuracy of measurement.
Compute with measures.
Vocabulary
Line segment
Precision
Betweenness of points
Congruent
Construction
The precision of any measurement depends on the smallest unit available on the measuring tool. The
measurement should be precise to within 0.5 unit of measure. For example, in part a of Example 1 above, 3 cm
means that the actual length is no less than 2.5 cm, but no more than 3.5 cm.
Measurement of 28 cm and 28.0 cm indicate different precision in measurement. A measurement of 28 cm
means that the ruler is divided into cm. However, a measurement of 28.0 cm indicates that the ruler is divided
into mm.
3. Find the precision for each measurement.
Explain its meaning.
a. 6 mm
b. 7 ½ inches
c. 4.5 cm
4. Find the value/measure of:
a. MQ
b. y
c. ST
d. RT
Goals: Find the distance between two points.
Find the midpoint of a segment.
Vocabulary
Midpoint
Segment bisector
1. Find the distance between R(5,1) and S(-3,-4).
2. Find the coordinate of the midpoint of segment RS (from above).
3. Find the coordinates of X if Y(-2,2) is the midpoint of segment XZ with Z(2,8).
Goals: Measure and classify angles.
Identify and use congruent angles and the bisector of an angle.
Vocabulary
Degree
Ray
Opposite Rays
Angle
Sides (of an angle)
Vertex (of an angle)
Interior (of an angle)
Exterior (of an angle)
Straight Angle
Angle Bisector
1. Draw yourself a picture of an
angle and label all of the parts
defined above.
2. Use the angles to the left to answer the following:
a. Name two angles that have Q as a vertex.
b. Name the sides of <3.
c. Write another name for <BCD.
d. Classify <WXY.
e. Classify <PQR.
f. Name the vertex of <4.
g. Name a point in the interior of <SQR.
h. Name an angle with vertex Q that appears to be obtuse.
i. Name a pair of angles that share exactly one point.
j. If ray QT bisects <SQR and m<SQR is 800, find the measure of all
angles in the third diagram.
Goals: Identify and use special pairs of angles.
Identify perpendicular lines.
Vocabulary
Adjacent Angles
Definition
Drawing
Vertical Angles
Linear Pair
Complementary Angles
Supplementary Angles
Perpendicular
What can and cannot be assumed from a diagram:
Use the diagram to the left:
1. Name two acute vertical angles.
2. Name a pair of complementary adjacent angles.
3. Name a linear pair whose vertex is T.
4. Name an angle supplementary to <UVZ.
Goals: Identify and name polygons.
Find perimeters of polygons.
Vocabulary
Polygon
Concave
Convex
n-gon
Regular Polygon
Perimeter
1. Draw some examples of polygons.
2. Draw some examples that are not polygons.
Number
of sides
Polygon Name
3
4
5
3. Find the perimeter of a polygon with vertices
A(-1,1), B(3,4), C(6,0), and D(2,-3).
6
7
8
9
10
12
n
n-gon
Algebra Review
1. 5
2. 72
3. 25
4. –5/66
5. 5a5 – 25a4 + 15a3
6. 4y2 – 17y – 15
7. 8t2 + 2t – 3
8. 49x2 – 1
9. x2 + 16x + 64
10. 3(5x – 1)(5x +1)
11. (a+5)(a+6)
12. (x-8)(x+2)
13. 3(a2 + 4a – 1)
14. (7x – 1)(7x + 1)
15. (x2 – 5)(x +2)
16. (3y-2)(3y-2)
17. 4√2
18. 15√2
19. 13
20. 2√2
21. m = ¼, b = -3
22. m=-2/3, b = 2
23. y = 1/5 x –2
24. y = -x – 2
25. (5,-1)
26. (-4, -4)
27. x = 2 or –6
28. x = 0 or 8
29. y = 5 or –3/2
1-1 Practice: Possible Answers
1.
2.
3. plane S
4.
5.
6. 6
7. S, X, M
8. No; they do not all lie in the
same plane
9. plane and line
10. point
11. lines
12. line and point
13. plane
1-2 Practice
1. 1 11/16in
2. 42 mm (4.2cm)
3. 0.5 m; 119.5-120.5
4. 1/8in; 7 1/8 – 7 3/8
5. 0.05mm; 29.95-30.05
6. 23.1cm
7. 3 5/8 in
8. 10.4 cm
9. r = 3, KL = 9
10. s = 6; KL = 8
11. no
12. yes
13. no
14.
1-3 Practice
1. 4
2. 5
3. 3
4. 8
5. √65 = 8.1
6. √113 = 10.6
7. 15
8. √18 = 4.2
9. 1
10. –4
11. 2.5
12. –5.5
13. (-2, 5)
14. (-10, -5.5)
15. D(3, -2)
16. D(-4, 3)
17. F(5, 4)
18. 19.6 units
1-4 Practice
1. M
2. P
3. O
4. M
5.
6.
7.
8.
9. <3, <RPQ
10. <MPO, <OPM, <MPN,
<NPM
11. 900, right
12. 700, acute
13. 1100, obtuse
14. 200, acute
15. 55
16. 30
17. m<1=900, right; m<2=1300,
obtuse
1-5 Practice
1. Possible Answer: <GFH,
<CFE
2. <GBC, <CBA
3. <FED
4. <BCG or <DCH
5. 23, 67
6. 129, 51
7. 16
8. 4.5
9. No; m<NQP is not known to
be 90
10. Yes; they are adjacent
angles whose non-common
sides are opposite rays
11. No; the angles are adjacent
12. Possible Answer: Beacon is
perp. To Main; Olive divides
two of the angles formed by
Bacon and Main into pairs of
complementary angles.
1-6 Practice
1. hexagon, concave, irregular
2. nonagon, convex, regular
3. quadrilateral, convex, irreg
4. 53mm
5. 86mi
6. 56cm
7. 25.1 units
8. 17.5 units
9. 3in, 3in, 10in, 10in
10. 17cm, 17cm, 5cm
11. 18ft, 18ft, 36ft, 17ft
12. 40 in
13. 48 in