sr17 - geometry

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Summer Review for Students Taking Geometry in 2016 - 2017 Be sure to show all work to earn credit.

No calculators. Simplify each expression completely.

Order of Operations: http://www.purplemath.com/modules/orderops2.htm Perfect Squares 1 – 10: http://www.math.com/school/subject1/lessons/S1U1L9DP.html Operations on Polynomials: https://www.youtube.com/watch?v=TRPxMv29rX0

1. 36 + (32 + 1) ÷ 2 + 6 · 3 2. −2(−5)!

3. 3𝑥! ! 4. !"!

5. !

!𝑛 − 9− !

!𝑛 + !

!

Solve each equation.

Solving Equations with Variables on Both Sides: http://www.shmoop.com/basic-algebra/equations-variables-both-sides.html

Solving Proportions: http://www.regentsprep.org/regents/math/algebra/AO3/Lprop.htm Solving Quadratic Equations by Extracting the Root:

http://www.purplemath.com/modules/solvquad2.htm Solving Quadratic Equations using the Zero Product Property:

http://www.purplemath.com/modules/solvquad.htm 6. 9 3− 2𝑤 = −2(10− 8𝑤) 7. 𝑛! − 7 = 18

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8. (2𝑥 − 7)(𝑥 + 6) = 0 9. !!!!!

= !!!"

10. !!3𝑥 + 2 = 5 𝑥 − 1

Solve the system of equations below using elimination.

http://www.purplemath.com/modules/systlin5.htm 11. 3𝑥 + 4𝑦 = 11

𝑥 − 7𝑦 = 12

Solve the system of equations below using substitution. http://www.regentsprep.org/Regents/math/ALGEBRA/AE3/AlgSys.htm

12. 𝑦 = 3𝑥 − 4 6𝑥 + 𝑦 = 5

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Solving Quadratic Equations

Using the Quadratic Formula: http://www.regentsprep.org/Regents/math/algtrig/ATE3/quadformula.htm

By Completing the Square: http://www.purplemath.com/modules/sqrquad.htm 13. Solve the equation 𝑥! − 10𝑥 − 11 = 0 using the Quadratic Formula. 14. Solve the equation 𝑥! − 4𝑥 − 6 = 0 by completing the square. Factor each expression completely.

GCF: http://www.purplemath.com/modules/simpfact.htm or

http://www.regentsprep.org/regents/math/algebra/AV6/Lfaccom.htm Grouping: https://www.youtube.com/watch?v=HvBiJ9W00Z4,

https://www.youtube.com/watch?v=KU6rNWjIZB4, or http://www.regentsprep.org/regents/math/algebra/AV6/Lfaccom.htm

Perfect Square Trinomials: http://www.regentsprep.org/regents/math/algebra/AV6/Lfaccom.htm

Difference of Two Squares: http://www.regentsprep.org/regents/math/algebra/AV6/Lfaccom.htm

15. 14𝑥! − 21𝑥! 16. 𝑥! + 24𝑥 + 144

17. 4𝑥! + 12𝑥 + 5 18. 𝑥! − 64 19. 𝑥! − 2𝑥 − 3

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Writing Equations of Lines

Equations of Lines: http://www.regentsprep.org/regents/math/algebra/ac1/eqlines.htm Equations of Horizontal Lines: http://www.mathwords.com/assets/movies/horizline.mov Equations of Vertical Lines: http://www.virtualnerd.com/algebra-2/linear-equations-

functions/writing/writing-horizontal-vertical-lines/vertical-line-example Parallel and Perpendicular Lines:

http://www.mathsisfun.com/algebra/line-parallel-perpendicular.html 20. Write the equation 𝑦– 5 = −3(𝑥 + 4) in slope-intercept form. 21. Write the equation of the line in slope-intercept form that passes through the

points (5, 3) and (9, 1). 22. Write an equation in point-slope form for the line that passes through (-4, 5) and

is parallel to the graph of the line 5𝑥 + 4𝑦 = −10. 23. Write the equation of a horizontal line that passes through the point (9, -5). Proportional Reasoning

http://www.studyzone.org/mtestprep/math8/e/ratio6l.cfm 24. The scale on a map shows that 5 centimeters = 2 miles. What number of

centimeters on the map represents an actual distance of 5 miles?

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25. The official height to width ratio of the U.S. flag is 1:1.9. If the height of the U.S. flag is 6 feet, how wide is the flag?

26. The ratio of two supplementary angles is 2:3. Find the measure of each angle. Probability

http://www.regentsprep.org/regents/math/algebra/APR5/LProb.htm 27. The spinner shown is divided into 8 equal sections.

The arrow on this spinner is spun once. What is the probability that the arrow will land on a section labeled with a number greater than 3?

Pythagorean Theorem

https://www.youtube.com/watch?v=ku4rEwRxZOc 28. Find the length of the hypotenuse of the right triangle below.

29. A baseball diamond is a square with sides of 90 feet. To the nearest tenth, what is

the shortest distance between first base and third base?

30. Find the length of 𝐴𝐵. Round to the nearest tenth.

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Area and Perimeter

NECAP Formula Sheet: http://education.vermont.gov/documents/educ_necap_resource_math_reference_sheet_grade_11.pdf

Areas of Polygons: http://www.math.com/school/subject3/lessons/S3U2L4DP.html or http://www.math.com/school/subject3/lessons/S3U2L4EX.html

31. A garden is 15 feet long by 5 feet wide. The length and width of the garden will

each be increased by the same number of feet. This expression represents the perimeter of the larger garden:

𝑥 + 15 + 𝑥 + 5 + 𝑥 + 15 + (𝑥 + 5) Which expression is equivalent to the expression for the perimeter of the larger garden? Select all that apply.

A. 4𝑥 + 40 B. 2 2𝑥 + 20 C. 2 𝑥 + 15 (𝑥 + 5) D. 4 𝑥 + 15 (𝑥 + 5) E. 2 𝑥 + 15 + 2(𝑥 + 5)

32. Find the area of the given polygon.

33. Find the value of x in the parallelogram below given that its area is 104 square

meters.

34. Find the height of the triangle below given that its area is 68 square feet.

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35. Find the area of the shaded region. Assume that these figures are rectangles.

36. Write a simplified expression to represent the area of the shaded region given that

the figures are rectangles.

Transformations

Translations: http://www.regentsprep.org/Regents/math/geometry/GT2/Trans.htm Reflections: http://www.mathsisfun.com/geometry/reflection.html Dilations: http://www.regentsprep.org/Regents/math/geometry/GT3/Ldilate2.htm

37. The point (3, –4) is translated 2 units to the right and 3 units up. What are the

coordinates of the image of (3, –4)?

38. ∆𝐴𝐵𝐶 has vertices A(-2, 2), B(-4, -1), and C(0, 5). Give the coordinates of ∆𝐴′𝐵′𝐶′, the image ∆𝐴𝐵𝐶, after a dilation with scale factor !

!.

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Describe the transformation shown in each diagram. Be as specific as possible.

39. 40.

Surface Area and Volume


41. Find the surface area and volume of the rectangular prism below.

42. Find the volume of the composite solid shown below.

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Simplify each expression completely.

Order of Operations: http://www.purplemath.com/modules/orderops2.htm Working with Square Roots: http://www.virtualnerd.com/algebra-1/algebra-

foundations/powers-square-roots/square-roots/squaring-square-roots

43. 9 𝑥! + 1 − 6 𝑥! + 1 44. !"!!

!+ 3𝑥

45. !"!

!

Solve each equation.

Solving Equations with Variables on Both Sides: http://www.shmoop.com/basic-algebra/equations-variables-both-sides.html

Solving Proportions: http://www.regentsprep.org/regents/math/algebra/AO3/Lprop.htm Solving Quadratic Equations by Extracting the Root:

http://www.purplemath.com/modules/solvquad2.htm 46. !

!!!= !!!

! 47. 5𝑥 + 3 ! = 25

48. !

!2𝑥 − 10 + 4𝑥 = −3 !

!𝑥 + 4

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Solve each system of equations using the most appropriate method. State the method that you used.

Substitution: http://www.regentsprep.org/Regents/math/ALGEBRA/AE3/AlgSys.htm Elimination: http://www.purplemath.com/modules/systlin5.htm

49. 3𝑥 + 8𝑦 = 20 50. 𝑦 = 3𝑥 − 4

3𝑥 + 6𝑦 = 14 6𝑥 + 𝑦 = 5 Solving Quadratic Equations

Using the Quadratic Formula: http://www.regentsprep.org/Regents/math/algtrig/ATE3/quadformula.htm

By Completing the Square: http://www.purplemath.com/modules/sqrquad.htm 51. Solve the equation 𝑥! + 6𝑥 = 16 using the Quadratic Formula. 52. Solve the equation 4𝑥! + 4𝑥 = 3 by completing the square.

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Factor each expression completely. GCF: http://www.purplemath.com/modules/simpfact.htm or

http://www.regentsprep.org/regents/math/algebra/AV6/Lfaccom.htm Grouping: https://www.youtube.com/watch?v=HvBiJ9W00Z4,

https://www.youtube.com/watch?v=KU6rNWjIZB4, or http://www.regentsprep.org/regents/math/algebra/AV6/Lfaccom.htm

53. −48𝑥𝑦𝑧 − 24𝑥𝑦 + 40𝑦𝑧 54. 6𝑥! − 19𝑥 − 7 Writing Equations of Lines

Equation of a Line: http://www.regentsprep.org/regents/math/algebra/ac1/eqlines.htm Parallel and Perpendicular Lines:

http://www.mathsisfun.com/algebra/line-parallel-perpendicular.html 55. Write an equation in point-slope form for the line that passes through (-4, 5) and

is parallel to the graph of the line that passes through the points 8, 1 and (-2, -4). 56. Write an equation in point-slope form for the line that passes through (-4, 5) and

is perpendicular to the graph of 𝑦 = !!𝑥 + 6.

Proportional Reasoning

http://www.studyzone.org/mtestprep/math8/e/ratio6l.cfm 57. The scale on a map shows that 5 centimeters = 2 miles. What is the actual

number of miles that is represented by 2 centimeters on the map?

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58. Find the value of x given that ∆𝐶𝐴𝑇~∆𝐷𝑂𝐺.

Probability

http://www.regentsprep.org/regents/math/algebra/APR5/LProb.htm 59. Find the probability that a point chosen at random on 𝑅𝑆 is on 𝑇𝑈.

Pythagorean Theorem https://www.youtube.com/watch?v=ku4rEwRxZOc

60. Find the height of an equilateral triangle, to the nearest tenth, whose sides are 12

inches.

Angles in Polygons


61. Given the diagram at the right, what is the value of x?

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62. What is the value of x given that this is a regular octagon?

Area and Perimeter


Areas of Polygons: http://www.math.com/school/subject3/lessons/S3U2L4DP.html or http://www.math.com/school/subject3/lessons/S3U2L4EX.html

Area of Composite Figures: http://www.virtualnerd.com/geometry/length-area/regular-polygons-composite-figures-area/composite-figure-area 63. Judi built the fence shown below.

The fence costs $12 per foot. What was the total cost for the fence? Find the area of each polygon. 64. 65.

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66. A circular mirror has a diameter of 12 inches and has a 3-inch wide frame surrounding the mirror. Find the combined area, in square inches, of the circular mirror and the frame. Give your answer in terms of 𝜋.

Transformations

Translations: http://www.regentsprep.org/Regents/math/geometry/GT2/Trans.htm Reflections: http://www.mathsisfun.com/geometry/reflection.html

67. ∆𝐽𝐾𝐿 has vertices J(4, 5), K(6, 2), and L(3, 2). Give the coordinates of ∆𝐽′𝐾′𝐿′, the image ∆𝐽𝐾𝐿, after a reflection over the y-axis.

68. ∆𝐴𝐵𝐶 has vertices A(1, 2), B(-3, -1), and C(0, -2). Give the coordinates of ∆𝐴′𝐵′𝐶′, the image ∆𝐴𝐵𝐶, after a dilation with scale factor 2.

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Surface Area and Volume


69. Find the surface area and volume of the cylinder below. Leave your answer in

terms of 𝜋.

sr17 - geometry

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