13
MATH 205 This form is a review sheet for MATH 090 students based primarily around the teaching & instructions of Professor V. Smith of ESU. Created by: Jasmine E. Aue [email protected] HELPFUL TIPS FOR COURSE CONTENT (ie. not formulas but important) Lines, Arrows, Points & Planes This section is a review of lines, arrows, points & planes. How they are defined, look and interact with each other. Collinear: same line Coplanar: same plane Closed: a line with an endpoint on each end, kind of like this Half: a line with only one endpoint, kind of like this Open: a line with no endpoints, like this = → = → = → → = Intersecting Lines: lines that have only one point in common Intersecting Planes: planes that have only one line in common Skew: cannot be coplanar Concurrent: 3 or more intersections at the same point Parallel: same slope, non-intersecting There is exactly one line containing any two distinct points If two points are in a plane then the line of points are in a plane If two planes intersect, there is a line at that intersection There is exactly one plane that contains any 3 distinct noncollinear points Collinear points/lines can have infinitely many planes One line + one point = a unique line Parallel lines are on one plane Two intersecting lines are on one plane FORMULA LIST | (/5)(9)) 32 =( + Fahrenheit to Celsius formula | Celsius to (2)/9)(5) =( −3 Fahrenheit formula | Pythagorean a 2 + b 2 = c 2 Theorem | d = (x ) y ) 2 x 1 +( 2 y 1 Diameter of a Circle | Radius x ) y ) r 2 =( h 2 +( k 2 Formula | Pythagorean a 2 + b 2 = c 2 Theorem | y is from (x,y), m x y = m + b is the slope, x is from (x,y) & b is the y-intercept | this is y ) / (x ) m =( 2 y 1 2 x 1 the point-slope formula, use this to find the slope of a line given two coordinate pairs x , ) & (x , ) ( 1 y 1 2 y 2 | Perimeter of a Square s P =4 | Area of a Square A = s 2 | Perimeter of a w l P =2 +2 Rectangle | Area of a rectangle w A = l | Circumference d πr C =2 of a Circle | Area of a Circle r A 2 | Perimeter of a P = a + b + c Triangle | Area of a Triangle bh A = 2 1 FE ABAY

MATH 205 ABAY - esu.edu

  • Upload
    others

  • View
    10

  • Download
    0

Embed Size (px)

Citation preview

Page 1: MATH 205 ABAY - esu.edu

 

MATH 205 This form is a review sheet for MATH 090 students based primarily around the teaching & instructions of Professor V. Smith of ESU.  

Created by: Jasmine E. Aue [email protected] 

HELPFUL TIPS FOR COURSE CONTENT (ie. not formulas but important) 

Lines, Arrows, Points & Planes This section is a review of lines, arrows, points & planes. How they are defined, look and interact with each other.  

❏ Collinear: same line ❏ Coplanar: same plane ❏ Closed: a line with an endpoint on each end, kind of like this ● ● ❏ Half: a line with only one endpoint, kind of like this ●  ❏ Open: a line with no endpoints, like this  ❏ → ⋃ → ↔=  

❏ → ⋂ → =  ❏ ● ● ⋃ ●→ = → ❏ ○→ ⋂ ○→ = ○ ○ ❏ Intersecting Lines: lines that have only one point in common  ❏ Intersecting Planes: planes that have only one line in common ❏ Skew: cannot be coplanar ❏ Concurrent: 3 or more intersections at the same point ❏ Parallel: same slope, non-intersecting 

 

❏ There is exactly one line containing any two distinct points ❏ If two points are in a plane then the line of points are in a plane ❏ If two planes intersect, there is a line at that intersection ❏ There is exactly one plane that contains any 3 distinct 

noncollinear points  ❏ Collinear points/lines can have infinitely many planes ❏ One line + one point = a unique line ❏ Parallel lines are on one plane ❏ Two intersecting lines are on one plane 

 

  

 

 

FORMULA LIST 

|(℃/5)(9)) 32℉ = ( +  

Fahrenheit to Celsius formula 

| Celsius to(℉ 2)/9)(5)℃ = ( − 3  

Fahrenheit formula 

| Pythagoreana2 + b2 = c2  

Theorem 

| d = √(x ) y )2 − x1 + ( 2 − y1  

Diameter of a Circle  

| Radiusx ) y )r2 = ( − h 2 + ( − k 2  

Formula 

| Pythagoreana2 + b2 = c2  

Theorem 

| y is from (x,y), mxy = m + b  

is the slope, x is from (x,y) & b is the y-intercept 

| this isy ) / (x )m = ( 2 − y1 2 − x1  

the point-slope formula, use this to find the slope of a line given two coordinate pairs x , ) & (x , )( 1 y1 2 y2  

| Perimeter of a SquaresP = 4  

| Area of a SquareA = s2  

| Perimeter of aw lP = 2 + 2  

Rectangle 

| Area of a rectanglewA = l  

| Circumferenced πrC = π = 2  

of a Circle 

| Area of a CirclerA = π 2  

| Perimeter of aP = a + b + c  

Triangle 

| Area of a TrianglebhA = 21  

FE ABAY

Page 2: MATH 205 ABAY - esu.edu

Angles & Circles This section is a review of angles and circles, not including their formulas (see formula list for formulas). 

❏ Complementary Angles: add to 90° ❏ Supplementary Angles: add to 180°  ❏ Acute Angles: less than 90° ❏ Right Angles: equal to 90° ❏ Obtuse Angles: greater than 90° but less than 180°  ❏ Reflex Angles: greater than 180° but less than 360° ❏ Straight Angles: equal to 180°  ❏ Circle: 360° 

❏ (when going from degrees to minutes to1360 ° 0 600"= 1 = 6 ′ = 3  

seconds, multiply & when going from seconds to minutes to degrees, divide) 

Diagrams Related to Angles and Circles: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

| Area of ahA = b  

Parallelogram 

| Area of a(b )hA = 21

1 + b2  

Trapezoid 

| Area of a Diamondd dA = 21

1 2  

| Surface Area ofA B hS = 2 + P  

a Right Prism, where B = area of the base and P =perimeter of the base 

| Volume of a RighthV = B  

Prism 

| SurfaceA lh wh lwS = 2 + 2 + 2  

Area of a Rectangular Prism 

| Volume of awhV = l  

Rectangular Prism 

| Surface Area of aA sS = 6 2  

Cube 

| Volume of a CubeV = s3  

| Surface AreaA πrh πrS = 2 + 2 2  

of a Right Cylinder (regular cylinder like a pringles can) 

| Volume of a Rightr hV = π 2  

Cylinder 

|Surface Area of aA πrS = 4 2  

Sphere 

| Volume of a SphereπrV = 34 2  

| Surface Area ofA P lS = B + 21  

a Pyramid (using slant height) 

|Volume of a PyramidV = 3lwh  

| SurfaceA r rS = π √r2 + h2 + π 2  

Area of a Cone where √r2 + h2

is the slant height  

| Volume of a Coneπr hV = 31 2  

 

 

Interior Angles: 3, 4, 5, 6Exterior Angles: 1, 2, 7, 8Alternate Interior Angles: 3 & 6, 4 & 5Alternate Exterior Angles: 1 & 8, 2 & 7Corresponding Angles: 1 & 5, 2 & 6, 3 & 7, 4 & 8

d = a + b

K(O,r)Radius

Center

Circle “name”

Arc Minor

Chord

r

Arc Major

l

me

N

WHN

l is the transversal I\

Page 3: MATH 205 ABAY - esu.edu

Normal Distribution This is a diagram of Normal Distribution: 

 

 

 

 

 

 

 

 

 

 

Shapes This section is a review of shapes, triangles will have their own more detailed section following this one. (see formula list for formulas on area, perimeter, volume, etc.) 

❏ Simple: does NOT intersect itself ❏ Closed: the start of the shape is also its end & vice versa. ❏ Regular Polygon: equilateral (sides) & equiangular (angles) ❏ Trapezoid: at least one pair of parallel lines ❏ Kite: 2 pairs of adjacent & congruent angles ❏ Parallelogram: Both pairs of opposite sides are parallel ❏ Rhombus: two adjacent sides are congruent 

Diagrams Related to Shapes: 

 

 

 

 

 

 

 

 

 

 

 

 

STUDY TIPS 

Scheduling | keep up to date with all assignments, quizzes, tests, exams, etc. by documenting them onto a calendar you regularly check, using a reminders app, a planner or other scheduling tool(s) 

Review | attend regular tutoring sessions, create your own mock tests using practice problems, review past HW, quizzes, tests & exams 

Eat Well |maintain a healthy, balanced diet to increase brain function (memory, engagement, attention, etc.) & to decrease fatigue, fogginess, etc.  

Sleep Well | maintain a health sleep schedule of 6-8 hours of sleep per night 

TUTORING INFORMATION 

ESU Tutoring Website |  https://www.esu.edu/tutoring/index.cfm  

ESU’s WCOnline Tutoring Link |   https://esu.mywconline.com 

 

g.... ..

/"

i- I wearE " T

Ex. every quay is a rectangle .

every trapezoid is a quadrilateral .

EX.

NOT every rectangle is a quay.

Not every rhomboid is a rectangle .

Page 4: MATH 205 ABAY - esu.edu

Triangles This section is a review of Triangles. (see formula list for formulas for area, perimeter, etc.) 

Diagrams Related to Triangles: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Special Triangles

Page 5: MATH 205 ABAY - esu.edu

 

Miscellaneous Information This section is a review of miscellaneous information that does not fit a big enough category to be a separate section. These concepts are just as important though! 

❏ Area is always squared x )( 2  

❏ Volume is always cubed x )( 3  

❏ When going from to radians; °x °x • π180°  

❏ When going from radians to ; °x x • π180°  

❏ Kilo (1000), Hecto (100), Deka (10), GRAM (Base Measurement, 1),Deci (0.1), Centi (0.01), Milli (0.001) 

❏ 1 Ton = 1000000g = 1000kg ❏ 1kg = 1000g ❏ 1hg = 100g ❏ 1dkg = 10g ❏ 10dg = 1g ❏ 100cg = 1g ❏ 1000mg = 1g ❏ cm mL g1 3 = 1 = 1  

❏ dm L kg1 3 = 1 = 1  

❏ yd 6in1 2 = 3 2  

❏ 1ft = 12in ❏ 1yd = 3ft = 36in ❏ 1mi = 1760yd = 5280ft = 63360in 

Vectors: 

 

 

 

 

 

 

 

 

 

 

 

iBBq

Page 6: MATH 205 ABAY - esu.edu

GEOMETRY FINAL EXAM REVIEW

I. MATCHING _____reflexive A. a(b + c) = ab + ac _____transitive B. If a = b & b = c, then a = c. _____symmetric C. If D lies between A and B, then AD + DB = AB. _____substitution D. If a = b, then b = a. _____distributive E. a = a _____definition of midpoint F. If D is the midpoint of ̅̅ ̅̅ , then AD =

AB.

_____midpoint theorem G. If a + b = c and a = d, then d + b = c. _____segment addition postulate H. If D is the midpoint of ̅̅ ̅̅ , then AD = DB. II. Fill in the blank. 1. An equilateral triangle is also a(n) ___________triangle. 2. The ____________ is the longest side of a right triangle. 3. Similar triangles have congruent corresponding ____________ and the corresponding

__________ are in proportion. 4. In an isosceles triangle, the __________ angle is the angle that is different. 5. The __________ of a triangle is a segment from a vertex to the midpoint of the

opposite side. 6. A(n) ____________ of a triangle is a segment from a vertex A to the opposite side. 7. A(n) ____________ ____________ of a segment is a line, segment, or ray A to a

segment at its midpoint. 8. The measure of a central angle is _________ to its intercepted arc. 9. Two __________________ angles have a sum of 90q. 10. Two __________________ angles have a sum of 180q. 11. A __________ has only 1 endpoint. 12. If two lines are ____________, they form right angles. 13. Two lines intersect in a ____________. 14. Two planes intersect in a ____________. 15. Through any three collinear points there are ____________ ___________.

Through any three non-collinear points there is __________ ________ ________. 16. __________ angles measure between 0q and 90q. 17. __________ angles measure between 90q and 180q. 18. Find the side of square with area 16 units2. ____________. 19. If the ratio of the measures of the angles of a triangle is 2:2:5, then the triangle is a(n)

____________ triangle. 20. If 4 points all lie on the same line, then the points are ____________.

Name___________________

Page 7: MATH 205 ABAY - esu.edu

21. The interior angle sum of a hexagon is ____________. 22. The exterior angle sum of a decagon is ____________. 23. If each interior angle of a regular polygon is 144, then the polygon is a __________. 24. If each exterior angle of a regular polygon is 30, then the polygon has ____________

sides. 25. In a 30q - 60q - 90q triangle, the long leg is ______ times the short leg. 26. In a 45q - 45q - 90q triangle, the hypotenuse is ______ times the leg. 27. An angle inscribed in a semicircle is a __________ angle. 28. Write 32 in simplest radical form. ______ 29. If �A is a right angle and m�A = (4x + 10)°, then x = __________. 30. �3 & �5 are ____________ angles & therefore are ____________. 31. �4 & �5 are ____________ angles & therefore are ____________. 32. �2 & �6 are ____________ angles & therefore are ____________. 33. If m�6 = (x + 5)° and m�4 = (2x + 10)°, then m�4 =______. 34. True or False. A triangle may have sides of 7, 12, and 18. 35. To find the area of a right triangle, the ____________ can be used as the base and

height. 36. ̅̅ ̅̅ is a ____________. 37. ̅̅ ̅̅ is a ____________. 38. ̅̅ ̅̅ is a ____________. 39. ⃡ is a ____________. 40. ⃡ is a ____________. 41. Point O is the _______________. 42. Point A is the _______________. 43. x = _____ 44. m�ABD = _____

1 2 a 3 4

5 6 b 7 8

a __ b

A B x O

C

D

(3x + 10)° (4x)° (4x – 50)°

A B C

D

E

Page 8: MATH 205 ABAY - esu.edu

A O E B

C D

45. x = _____ 46. B and E are the midpoints of AD and AG. If DG = 40, then CF _____. 47. Find the perimeter of a right triangle with legs 6 and 8. _____ 48. If the diagonals of a rhombus are 20 and 36, then the area is _____. 49. Find the area of a right triangle whose hypotenuse is 25 and whose leg is 7. _____ Name the theorem or postulate used to prove the triangles congruent. 50. __________ 51. __________ 52. __________ 53. __________

54. m = _____

55. m =_____ 56. m�COB = _____ 57. m�AOB = _____ 58. Draw �ACB. m�ACB = ______

4

A B E C F D G

8 9 x

4

Given: O is the center.

m = 130q

Page 9: MATH 205 ABAY - esu.edu

35 37q

y

4 x°

XYZ is an equilateral triangle. 59. ZY = _____ 60. m�Z = _____ 61. altitude = _____ 62. Area of Circle = _____ 63. Area of Square = _____ 64. Area of shaded region = _____ 65. Circumference of Circle = _____ 66. Perimeter of Square = _____ 67. Area of parallelogram = _____ Round your answer to the nearest whole number or degree. 68. Find x | ___________. 69. Find y | _____________ 70. A ladder is positioned against a house at a 65q angle. The ladder is 10 feet tall. How far away from the house is the base of the ladder? Round your answer to the nearest tenth. 71. x = _____ 72. y = _____ 73. z = _____

X 8ft Y

Z

5

12

20 60q

x

105q

120q

z

y

6.1

Page 10: MATH 205 ABAY - esu.edu

O

W

X ZY

74. x = _____

75. 2 tangent lines drawn to a circle from the same point are __________. 76. If the diagonals of a quadrilateral are A, then the quad. is a ______ or a ________. 77. If the diagonals of a quad. are A and #, then the quad. is a ____________. 78. If the diagonals of a quad. are #, then the quad. is a ____________ or a ___________. 79. The legs of an isosceles trapezoid are 10 ft. and the bases are 10 ft. and 22 ft. The length of the median is _____. The area of the trapezoid is ___________. 80. In a parallelogram, ______ angles are supplementary and _______ angles are congruent.

81. Given ∆XYZ # ∆RSN, then �Y # _____ and _____

XZ # _____. 82. x = _____

O is the center & _____

WX is tangent to Circle O.

83. m = 100q, m = 90q, m�X = _____

84. is a __________ arc.

85. is a __________ arc. 86. Find the volume of a rectangular prism with length 6 in, width 3 in, and height 4 in. 87. Find the total (surface) area of a cylinder with radius 4 m and height of 3 m. 88. The total (surface) area of a cylinder is 66π cm2 and the radius is 3 cm. Find the volume. 89. What is the volume of a cone whose radius is 9 and slant height is 13? 90. The total (surface) area of a sphere is 64S . Find the radius of the sphere.

6 4

x

8

150q 80 q

x

Page 11: MATH 205 ABAY - esu.edu

A

B D

EC

8070

O A

B

O Y

X

Z

M

X

W

V

Z

Y

70°

80°

B

A C

91. Find m�BCD.

92. Given: Y is the midpoint of _____

XZ and _____

WV . Prove: �W # �V 93. List the sides from largest to smallest. 94. Points A, B, and C are collinear. If AC = 8, BC = 6, and AB = 14, which point is in between the other two? ________________ 95. OA = 8 and m�AOB = 90. Find AB. 96. In O, the radius is 41, and XZ = 18, find OM. 97. Find the scale factor of two rectangles if the perimeters are 36 cm and 48 cm respectively.

Page 12: MATH 205 ABAY - esu.edu

A

D

B C

E

X

Y

Z

98. Name the transformation. 99. Name the transformation that maps ABC to ADE. 100. Two similar polygons are shown. Find the scale factor and the value of x. 101. YZ = √ and XZ = √ . Find XY. Answer in simplified radical form. 102. Describe the triangle with sides of 8, 2√ , 9. 103. If the hypotenuse in an isosceles right triangle measures 6√ ft., then the length of each leg is ________. 104. Find the volume of a square pyramid with base edge 5 in. and height 3 in.

Page 13: MATH 205 ABAY - esu.edu

Answers Matching E, B, D, G, A, H, F, C Fill in the Blank

1) Equiangular 2) Hypotenuse 3) Angles; sides 4) Vertex 5) Median 6) Altitude 7) Bisector 8) Equal 9) Complementary 10) Supplementary 11) Ray 12) Perpendicular 13) Point 14) Line 15) Infinite Planes;

Exactly One Plane 16) Acute 17) Obtuse 18) 4 units 19) Isosceles 20) Collinear 21) 720° 22) 360° 23) Decagon 24) 12 25) √ 26) √ 27) Right 28) √ 29) 20 30) Same Side Int.;

Supplementary 31) Alt Int;

Congruent 32) Corresponding;

Congruent 33) 120° 34) True 35) Legs

36) Radius 37) Diameter 38) Chord 39) Secant 40) Tangent 41) Center 42) Point of Tangency 43) 20 44) 70° 45) 6 46) 30 47) 24 units 48) 360 units2 49) 84 units2 50) SAS 51) ASA 52) HL or AAS 53) SSS 54) 50° 55) 50° 56) 50° 57) 180° 58) 90° 59) 8 60) 60° 61) √ 62) 25π units2 63) 100 units2 64) (100 – 25π) units2 65) 10π units 66) 40 units 67) √ units2 68) 57° 69) 28 70) 4.2 ft. 71) 75° 72) 75° 73) 30° 74) 3 75) Congruent 76) Rhombus; square 77) Square 78) Rectangle; Square

79) 15 ft. and 128 ft2 80) Consecutive;

Opposite 81) S; ̅̅ ̅̅ 82) 70° 83) 35° 84) Minor 85) Major 86) 72 units3 87) 56π units2 88) 72π cm3 89) 54π√ units3 90) 4 91) 75° 92) Y is the midpoint

of ̅̅ ̅̅ and ̅̅ ̅̅ ̅ (Given), ̅̅ ̅̅ ̅̅̅̅ ̅̅ ̅̅ ̅ ̅̅ ̅̅ (Def of Midpoint),

(Vertical Angles are Congruent), (SAS), (CPCTC)

93) ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ 94) C 95) 8√ 96) 40 97)

98) Reflection 99) Dilation 100)

and x =

101) √ 102) Obtuse 103) 6 ft. 104) 25 in3

If you would like detailed answers please visit an MQC tutor (Tutoring Department contact information on

pg. 3)