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# Math 112B Final Review Math 112b Sec 004

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This 12 page Study Guide was uploaded by amber weiss on Friday April 29, 2016. The Study Guide belongs to Math 112b Sec 004 at Southern Illinois University Edwardsville taught by cheryl eames in Spring 2016. Since its upload, it has received 33 views. For similar materials see elementary mathmatics in Mathmatics at Southern Illinois University Edwardsville.

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Date Created: 04/29/16

Math 112b Final Exam Chapter 9 Section 1 Terminology: Geometry- lines, angles, surfaces and solids Undefined terms- point, line, plane Defined terms- might use undefined terms to define other things Axioms- assume to be true without proving them Theorems- things we prove using undefined terms, definitions, axioms and other theorems that have been proved. Collinear- points are called if same if share same line Line segment- consists of 2 points (endpoints) and all points between are collinear Segment- endpoint and all collinear points between them Line- goes on forever in 2 directions Ray- point on line with all points that lie on 1 side of point Acute angle- less than 90 degrees Right angle- exactly 90 degrees Obtuse angle- more than 90 degrees Straight angle- 180 degrees exactly Reflex angle- greater than 180 degrees Vertical angles- opposite angles formed by 2 intersecting lines Adjacent angles- 2 angles vertex and common sides do NOT overlap Complementary- 2 angles sum of 90 degrees Supplementary- 2 angles sum is 180 degrees Perpendicular lines- intersect create right angles Parallel- do not intersect coplanar Corresponding angles- occupy SAME position relative to transversal and original lines (are congruent) Alternate exterior angles- occupy opposite sides of transversal on exterior of original lines (congruent) Alternate interior angles- occupy opposite sides of transversal on interior of original lines (congruent) Curve- set of points which can be connected by a single smooth, continuous motion (drawn without lifting pen) Simple curve- curve can be drawn without lifting pencil and WITHOUT intersecting itself (maybe start and end point) Closed curve- curve but has to touch bach to start (start stop at same point) but doesn’t have to be simple Simple closed curve- starts and stops same point and cannot intersect itself Plane origin- union of simple closed curve and its interior Convex- 2 points in a region Nonconvex (concave)- 2 points outside of region Circle- set of all points in a plane that are equidistant from a fixed point Tangent- touch circle at one point (line) Secant- cut through the circle (line) Chord- stretch across circle (segment) Diameter- line within circle Radius- half of the diameter For more of this, download the chapter 9 section 1 notes! This is just vocab and the main parts! NO EXAMPLES 1. Nonstandard units to measure area? - Right triangles; rectangular tile; legos 2. Connect the dots into triangles… (should be perfect) Area using triangles: 17 Connect the dots into squares… Should be 6 full squares and 5 half squares Area using squares: 8.5 3. Using squares… Area? a. 3*4= 12 b. 5*5= 25 – 2*2=4 = 21 c. ½(4)(4) = 8 d. ½(8)(3) = 12 Height: imagine parallel line to base and capture entire triangle, goes through peak of triangle 4. Why are the last 2 harder than the first 3? They are hard to count the partial squares 5. How many square inches are in a square feet? 1foot=12inches (12in)(12in)= 144inches squared or 1ft squared to inches…. 6. How many square centimeters are there in a square meter? 1meter= 100cm (100cm)(100cm)= 10,000 centimeters squared We need to memorize the formulas and where the come from: 7. Rectangle = base * height 8. Area of a parallelogram: A=base*height Think: cut the parallelogram into parts and rearrange parts to form a rectangle. Area= base * height same as area of parallelogram A= 5*2 = 10cm2 for the picture 9. Area of triangle: A=1/2 base * height Think: about copy the triangle and put them together to make a parallelogram. The area of this triangle, this half of area to parallelogram. The parallelogram is base * height A= ½ 5*2 = 5cm squared 10.Area of trapezoid: A= ½ (base1+base2) * height Think: copying the trapezoid an putting them together to form a parallelogram. The area of trapezoid is half of the area of a parallelogram, So, Area of a trapezoid is ½ (base1+base2) For circles… we did a twizzler exercise! 11.Find the area for the following: a. A= (8)(3) = 24 centimeters squared b. A= ½ (4+10in)(5in) = 35inches squared c. A=b*h = (10)(4) = 40 centimeters squared d. A= pie r squared = pie * (2*5)^2 = 6.25 pie meters squared e. A= ½ (3cm)(4cm) = 6centimeters squared f. A= (7)(5) = 35 + A= (3)(3) = 9 = 44inchese squared g. A= (6)(6) = 36inches squared radius= 3 because it is half of the diameter… A= ½ pie (3inches)^2 = 9/4 pie inches squared + 36inches squared h. A= (8)(6) = 48 cm squared – whole A= (6)(4) = 24 cm squared – non-shaded Shaded= 24cm squared Normal Distribution of Normal Curve - In a perfectly notmal distribution mean, median and mode all same value. This is the value of the peak - 68-95-99.7 is the EMPIRAICAL RULE - 68% = 1 Standard Deviation of the mean - 95% = 2 Standard Deviations of the mean - 99.7% = 3 Standard Deviations of the mean - If the curve is really fat and low, it is caused by a really high standard deviation - If the curve is really tall and skinny, it is caused by a very low standard deviation 5 9 101 4. Scores on an exam are normall7 dist6ibuted with0the mean of 68 and a standard deviation of 11. What perc8nt of the students scored… - How do get the standard deviation numbers in the boxes above? All we do is take the mean, and if we are moving to the right it is Mean plus the standard deviation… If we are moving to the left, it is mean minus the standard deviation - there are many ways that you can solve these… By adding up all the percentages from the score that you need By taking 100 and subtracting the data from the other point By subtracting the percentage that you know from the others… Ill show you how to solve using every one of these ideas.. a) below 68% _____50%__________ Way 1: (we get this because we see that half of the data is less than 68. We can also find this by adding up the percentages 34+13.5+2.35+.15) Way 2: (100-34-13.5-2.35-.15) b) below 57% ________16%______ Way 1: ( .15+2.35+13.5= 16) Way 2: (50-34) Way 3: (95-68) c) below 90% _______97.5%________ Way 1: (50+34+13.5) Way 2: (100-2.5) d) above 90% ________2.5%________ Way 1: (100-97.5) e) between 57 and 90 _____81.5%_________ Way 1: (34+34+13.5) Way 2: (97.5-16) f) between 46 and 90 ______95%________ Way 1: (68+13.5+13.5) Way 2: (68+27) Way 3: (34+34+13.5+13.5) For these, take advantage of the given percentages and the data! It will make this 100 x’s easier! 5. Length of adult feet is normal distribution with the mean of 12.2 inches and a standard deviation of .7in. it is a random sample of 1500. Approximately, how many do we expect to have a foot between 11.5 and 12.9 inches? 12. 11. 12. - Again, the same idea, we take the mean plus/minus the standard deviation - We know from the figure about that from 11.5 to 12.2 = 34% and from 12.2 to 12.9 it is also 34%... 34+34= 68% - What is 68% of 1500? (.68)(1500)= 1020 adults 12 140 160 180 200 6. The mean is 140 students and the SD is 20 students. 1000 kids, how many percentage is less than 200 students. What percent would be in 120 students or less? a) Less than 200: normal rounding rules!!! We take (100-.15) and we get 99.85 (.9985)(1000) = 998.5 = 999 999 kids are less than 200 b) 120 students or less: 50%- 34% = 16% or 13.5+ 2.35+.15= 16% (.16)(1000) = 160 160 kids are 120 or less 1. Describe how you would help students discover the sum of measures of the 3 angles in a triangle. - Measure the angles and add them up (need to know how to use a tool) - Cut, tear the corners of the triangle, stack and see which one is larger ; make another shape, in this case a line. - Rule: a straight line = 180 degrees 2. What must students know before completing number 1? - How to use the tool (protractor) - That a straight line is 180 degrees 3. How can we expand problem 1 to find the sum of measures of the 4 angles in a quadrilateral? - First, we draw a quadrilateral (4 sided figure) - Then, we cut a diagonal from one of the vertexes. - We should be able to see 2 triangles - The black dots represent vertex - the black line represents the diagonal to see the 2 triangles 6 5 2 4 1 3 - M<1+m<2+m<3 = 180 - M<4+ m<5+ m<6 = 180 - M<all = 180+180 = 360 degrees - CONNECT NONADJACENT VERTICES WITH A DIAGANOL - Sum of angles = vertex angle 4. Name # of sides # of triangles Sum of angles Triangle 3 1 180 Quadrilateral 4 2 360 Pentagon 5 3 540 Hexagon 6 4 720 Heptagon 7 5 900 Octagon 8 6 1080 Nonagon 9 7 1260 Decagon 10 8 1440 Dodecagon 12 10 1800 n-gon n (n-2) (n-2) * 180 5. WE SKIPPED NUMBER 5 2 plane figures are congruent if… They are same size and shape Place 1 on other so they coincide Segments are congruent if… Same length Angles are congruent if… Same measure Figures are congruent if… Corresponding sides are congruent Corresponding angles are congruent 6. In each of the following diagrams, explain why they are not regular polygons. a) not congruent sides or angles b) sides are not congruent c) not even a polygon, doesn’t have sides or angles Central angle Exterior angle 7. verte x Name Sum of Vertex angle Central Angle Exterior angle angles Equilateral 180 180/3 = 60 360/3 = 120 180-60=120 Triangle Square 360 360/4 = 90 360/4= 90 180-90=90 Regular Pentagon 540 540/5 = 108 360/5= 72 180-108=72 Regular Hexagon 720 720/6= 120 360/6= 60 180-120=60 Regular Heptagon 900 900/7= 128.6 360/7= 51 180-128.6=51.4 Regular Octagon 1080 1080/8= 135 360/8= 45 180-135=45 Regular Nonagon 1260 1260/9= 140 360/9= 40 180-140=40 Regular Decagon 1440 1440/ 10= 360/10= 36 180-144=36 144 Regular 1620 1620/12= 135 360/12= 30 180-135=45 Dodecagon Regular n-gon (n-2) * 180 Total degrees/ A circle= 360/ 180- vertex number of number of angle straight sides sides line=180 8. The graph above is #8 Pictograph: is typically the type of graph that students are first introduced to. It uses pictures to display data. - Here is an example… Like the example we did in class with the ice cream flavors… - Chocolate= 6 Vanilla= 9 Strawberry= 3 - 1 step… Draw 3 cones nd - 2 step… pile on 6,9,3 scoops or circles onto the cones Bar Graphs and Pie charts - Use when data can fit into categories - ROLL A DIE 10 TIMES Outcome Talley Frequency 1 2 2 2 2 2 3 1 1 4 1 1 5 3 3 6 1 1 TOTAL: 10 Features of a Well-Drawn Bar Graph: 1. Title 2. Axis labels 3. Vertical= frequency Horizontal= Outcome 4. Scale Rolls of Die 3.5 3 3 2.5 2 2 2 FREQUENCY 1.5 1 1 1 1 0.5 0 1 2 3 4 5 6 OUTCOMES USE DATA FROM BAR GRAPH TO CREATE A PIE GRAPH OUTCOME FREQUENCY ANGLE 1 2 72 DEGREES 2 2 72 DEGREES 3 1 36 D 4 1 36 D 5 3 108 D 6 1 36 D TO FIGURE OUT THE ANGLE… Example) if a die is rolled 25 times, and a specific roll appeared 5 out of the 25 rolls, that is 20% Method 1: 5/25 = .2 = 20% Method 2: 5/25 x/360, we cross multiple… the 360 represents the degrees of a circle. And the x is what we are trying to figure out. The 5 represents how many times that number was rolled out of 25 times… Transformations: 1. Translation 2. Rotation 3. Reflection - Original figure = pre-image - Resulting figure = image Scatter Plot: - On our notes packet there is a list of questions that go along with the scatter plot of fata points based on the weight of infants. - - The following questions are included… 1. Plot an age of 10 days and a weight of 8.75lbs… the dot would be on the 10 day mark and you would plot it on the point in between 9 and 8.5. the talleys on the vertical line are going up by .25 2. Does there appear to be a linear relationship between age in days and weight in pounds for the selected group of infants? YES 3. If so, is it a positive or negative correlation? Positive 4. What is the largest weight for any of the infants measured? 10.5 lbs 5. What is the age of the infant listed in number 4? 16 days 6. What is the smallest weight for any of the infants measured? 6.75lbs 7. What is the age of the infant In question 6? 1 day old 8. If an infant were 13 days old, approximately how much would that child weigh, based on the given data? Make a trend line the best of your ability… The best estimate based on my trend line would be around 9.25lbs. It will vary based on your line. - Also, this graph needs a break in between the 1 and the 0 on the horizontal line. Frequency and Histograms - Construct a frequency table for weights in the scatter plot. Use a 5 intervals of equal width… - The weight range would be 3.75 because you take the largest and subtract the smallest (10.5-6.75) - How to find the interval width: you take the range and divide it by the number of intervals… - 3.75/5 = .75 (you can use 1, here we are using .99) Interval 6.25-7.24 7.25-8.24 8.25-9.24 9.25-10.24 10.25-11.24 frequency 3 5 10 6 1 Histogram 12 10 8 6 4 2 6 7 8 . . 9 1 . . 0 2 2 2 2 . 5 5 5 5 2 - - - 7 8 - 5 9 1 - . . . 0 1 2 2 2 . 1 4 4 4 2 . 4 2 4

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