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Honors Integrated Math / Summer Assignment
The rigor of the Honors Integrated Math curriculum includes ,luency of procedures, mathematical understanding of concepts, and the ability to apply concepts to real-‐life situations. Retaining mathematical concepts and practicing mathematical 4luency both are essential for students to succeed in Putnam County. The attached assignment is due on the 0irst day of your Honors Integrated Math $ class. This material is mostly a review of basic skills you are expected and required to have mastered for this course. The assignment is to be completed on separate notebook paper with each question clearly labeled. Only the solutions to graphs (grids/number lines) go directly on the packet. All other work and solutions must be on your paper stapled to the packet. While arriving at the correct answer is important, students are expected to understand how to arrive at the correct answer. We do NOT accept just answers. All work must be shown. You are to bring the completed work with you to the 6irst day of class and your teacher will answer any questions you may have at that time. A test will be administered on the material during the 3irst week of school to determine your eligibility to remain in the course. Anything you need to review should be researched. We suggest the websites below. www.purplemath.com www.khanacademy.com www.helpingwithmath.com The mathematics department is very excited to see our students ready for the curriculum in July! Sincerely, Putnam County Schools, Tennessee Cookeville High School Algood Middle School Monterey High School Avery Trace Middle School Upperman High School Prescott South Middle School Upperman Middle School
HONORS CRITERIA Honors courses will substantially exceed the content standards, learning expectations, and performance indicators approved by the State Board of Education. Teachers of honors courses will model instructional approaches that facilitate maximum interchange of ideas among students: independent study, self-‐directed research and learning, and appropriate use of technology. All honors courses must include multiple assessments exemplifying coursework (such as short answer, constructed-‐response prompts, performance-‐based tasks, open-‐ended questions, essays, original or creative interpretations, authentic products, portfolios, and analytical writing). Additionally, an honors course shall include a minimum of 0ive (3) of the following components:
!. Extended reading assignments that connect with the speci3ied curriculum.
!. Research-‐based writing assignments that address and extend the course curriculum.
!. Projects that apply course curriculum to relevant or real-‐ world situations. These may include oral presentations, power point presentations, or other modes of sharing 3indings. Connection of the project to the community is encouraged.
!. Open-‐ended investigations in which the student selects the questions and designs the research.
!. Writing assignments that demonstrate a variety of modes, purposes, and styles.
a. Examples of mode include narrative, descriptive, persuasive, expository, and expressive.
b. Examples of purpose include to inform, entertain, and persuade.
c. Examples of style include formal, informal, literary, analytical, and technical.
!. Integration of appropriate technology into the course of study.
!. Deeper exploration of the culture, values, and history of the discipline.
!. Extensive opportunities for problem solving experiences through imagination, critical analysis, and application.
!. Job shadowing experiences with presentations which connect class study to the world of work. Additional components of study may also be included in the honors curriculum. These are simply the MINIMUM requirements of the course.
Honors Integrated Math . Summer Assignment SHOW ALL WORK on a separate sheet of paper and staple it to the packet.
Part 1: Algebra Skills Review
1. Simplify the following expressions
a. b.
c. d.
2. The distance formula for finding distance between two points is . Solve the equation for x1.
3. Simplify the following expressions using the rules of exponents.
a. −22x5y6
14x13y−3 b. –a3b2( )
2–b2c2( )
3–a3c4( )
4
4. Simplify the following rational expressions. Rationalize any denominators.
a. 675 b. 56a2b4c5 c. 638
d. 3 75 + 4 125 − 5 50 e. 3 − 2( ) 3 + 2 2( )
f. 2 -7
3+6 7 g. -1- 5i
8 -8i
Part 2: Linear Review
5. Find the rate of change for the following graph to the right: a. Points (–3, 8) and (5, 4)
b. The graph to the right over the interval [–2, 0] c.
6. What is the equation of the vertical line that goes through the point ?
7. Write the equation of the line in slope-‐intercept form for the following lines.
a. Goes through the points (3, 4) and (–1, –5)
b. Parallel to the line 4x −3y = 9 and through the point (3, –1).
c. Given a line through (–2, 4) and (8, –1), write the equation of the line perpendicular to the line through the midpoint of those points.
d.
23x + 45y− 12x + 7y 2x 3w+ 4x( )+ 5w w− 2x( )+ 5w2 − 2x2
3x −1( )2 − x +3( ) x − 2( ) 5x −3x2 +15+11x2 − 21x +8
d = x2 − x1( )2 + y2 − y1( )2
3, – 34
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Part 3: Systems Review
8. Lucille has a total of 23 dimes and pennies. The value of her coin collection is $1.85. How many dimes does she have? How many pennies does she have?
9. Suppose you buy 3 shirts and 2 pairs of slacks on sale at a clothing store for $72. The next day, a friend buys 2 shirts and 4 pairs of slacks for $96. If the shirts you each bought were all the same price and the slacks were also all the same price, then what was the cost of each shirt and each pair of slacks? Set up and solve a system of equations.
10. Solve the following system of equations.
a. –x – 2y = –32x + 4y = 6
b. y = 2x2 + 4x −12x − y = 5
11. Graph the union of the inequalities 1x + y > -42
and y ≤ 2 to the right.
12. Given the system of inequalities , determine which of the following points is a solution.
a. (5, 1) b. (3, –2) c. (4, 1)
Part 4: Exponential Review
13. Solve 9x = 27x−2 for x.
14. Solve ( )− +
⎛ ⎞=⎜ ⎟
⎝ ⎠
25 61 2
2
xx for x.
Part 5: Polynomials Review
15. Classify the polynomial 4x3 − 5x5 +10x2 by degree and terms.
16. Subtract: ( ) ( )+ − − −27 9 3 5 2 .x x x Express as a polynomial written in standard form.
17. Expand ( )−32 3x . Express as a polynomial written in standard form.
3x − 4y > 82x2 + y > 5x ≤ 7y ≥ –1
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Part 6: Quadratic Review
18. Factor the following expressions: a. 25x2 −100 b. 2x2 + 9x − 5 c. x2 + 5x −36
d. 6x2 + 5x − 4 e. 6x2 +8 f. 8x6 + 4x4 − 2x2
g. 3y y−3( )− 4 y−3( ) h. a3 − a2b+ ab2 i. 3x2 −10x +3
19. Use the discriminant to determine the type(s) of solutions for the quadratic equations below.
a. 24 5 7 0− − =x x b. 2 11 3− + =m m c. 2 4 12 8+ + =p p
20. Graph the following quadratic functions. a. = −2( ) 2 3f x x b. = − − +2( ) ( 2) 4g x x c. = − +2( ) 3 6 5h x x x
21. Explain how to find the zeros of the quadratic function f x( ) =15x2 + x – 28 .
22. Solve each quadratic by factoring.
a. 3x 2x − 5( ) = 0 b. 2x −1( ) x − 5( ) = 0 c. 9+ x2 = 6x
d. 1− x = 2x2 e. 2x2 = x f. 15x2 +1= 8x
23. Fill in the blank to create a perfect square trinomial. (Complete the square)
a. x2 + 20x + _____ b. 2x2 +8x + _____ c. 3x2 + 9x + ______
Honors Integrated Math . Summer Assignment SHOW ALL WORK on a separate sheet of paper and staple it to the packet.
24. Gnash, the Predators mascot, launches T-‐shirts into the crowd during the intermission of all home
games. The height of the T-‐shirt can be modeled by the function h x( ) = −16x2 + 48x + 6 , where h(x) represents the height in feet of the T-‐shirt after x seconds.
a. At what height was the T-‐shirt launched?
b. What is the maximum height of the t-‐shirt?
c. When was the maximum height reached?
Part 7: Functions Review
25. If , find x if
26. Let the following graph to the right represent a function f(x)
a. Find f(0) =
b. Find f(–2)=
c. If you found f(–4) – f(5), would the answer be positive or negative?
27. Given the equation = −253
y x , fill in the table of values.
28. Write a function that is described by each of the following tables.
29. Determine whether each relation is a function. a. (5, 4), (–2, 6), (0, –8), (–2, 1) b. c.
f x( ) = 5x −12 f x( ) = 22
x y –3 17
3
5 1 9
25
Part 8: Basic Geometric Shapes Review
30. The table below lists some different shapes and properties. In each box place an “X” indicating the shape has the property. Square Rectangle Kite Trapezoid Isosceles
Trapezoid Rhombus Parallelogram
All angles are right angles
All sides are congruent
Diagonals bisect each other
Diagonals are perpendicular
31. Complete each of the following statements with sometimes, always, or never true.
a. A square is a rectangle b. A rectangle is a square c. A quadrilateral has four sides d. A pentagon has a greater perimeter than a triangle e. The angles in an octagon have a greater sum than the angles in a hexagon.
32. The three angles of a triangle are 3x, x + 10, and 2x – 40. Find the measure of the smallest angle in the
triangle.
33. Suppose one base angle of an isosceles triangle has a measurement of 440. What is the measure of the vertex angle?
Part 9: Trigonometry Review
34. Roger is looking up at a guard tower that is 45 feet tall in the forest. The angle of depression from the top of the guard tower is 400. How far is Roger from the guard tower?
35. Find the length of both AC and BC. 36. Using the diagram below, find the distance between CB.
Part 10: Angle Relationships
37. In the following diagram, line m and n are parallel.
a. If m∠4 = 2x −17 and m∠1= 85 , solve for x. b. If m∠1= 4y+30 and 7 8 6∠ = +m y , solve for y.
38. Find the measure of all angles below. Part 11: Surface Area and Volume Name the (igure. Find the surface area and volume of each (igure. Round your answers to the nearest hundredth, if necessary.
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