Dear Parents and Students,

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1 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 8 th or 9 th 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 cstone@mths.us or Honors Geometry teacher, Mrs. Gualandri, at egualandri@mths.us 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

2 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 Multiplying Polynomials Find the product. 5. 5a 2 (a 3 5a 2 + 3a) 6. (y 5)(4y + 3) 7. (2t 1)(4t + 3) 8. (7x 1)(7x + 1) 9. (x + 8) 2 Factoring Polynomials Factor completely x 2 30x a a x 2 6x a a x x 3 + 2x 2 5x y 2 12y + 4 Radicals Simplify. 17. Slope and Equations of Lines Given an equation of a line, name its slope and y-intercept. 21. y = ¼ x x + 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 x + 3y = 7 x = 1 4y 26. 3x 5y = 8 4x 7y = 12 Quadratic Equations Solve for x. 27. x 2 + 4x 12 = x = x 2 3x Quadratic Formula Solve using the quadratic formula y 2 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!

3 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

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5 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

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7 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).

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9 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 80 0, find the measure of all angles in the third diagram.

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11 Goals: Identify and use special pairs of angles. Identify perpendicular lines. Vocabulary Definition Drawing Adjacent Angles 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.

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13 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 3 Polygon Name Find the perimeter of a polygon with vertices A(-1,1), B(3,4), C(6,0), and D(2,-3) n n-gon

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15 Algebra Review / a 5 25a a y 2 17y t 2 + 2t x x x (5x 1)(5x +1) 11. (a+5)(a+6) 12. (x-8)(x+2) 13. 3(a 2 + 4a 1) 14. (7x 1)(7x + 1) 15. (x 2 5)(x +2) 16. (3y-2)(3y-2) m = ¼, b = m=-2/3, b = y = 1/5 x y = -x (5,-1) 26. (-4, -4) 27. x = 2 or x = 0 or y = 5 or 3/2 1-1 Practice: Possible Answers plane S 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 /16in mm (4.2cm) m; /8in; 7 1/8 7 3/ mm; cm /8 in cm 9. r = 3, KL = s = 6; KL = no 12. yes 13. no Practice = = = (-2, 5) 14. (-10, -5.5) 15. D(3, -2) 16. D(-4, 3) 17. F(5, 4) units 1-4 Practice 1. M 2. P 3. O 4. M <3, <RPQ 10. <MPO, <OPM, <MPN, <NPM , right , acute , obtuse , acute m<1=90 0, right; m<2=130 0, obtuse 1-5 Practice 1. Possible Answer: <GFH, <CFE 2. <GBC, <CBA 3. <FED 4. <BCG or <DCH 5. 23, , No; m<nqp is not known to be 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 units units 9. 3in, 3in, 10in, 10in cm, 17cm, 5cm ft, 18ft, 36ft, 17ft in in