## Geometry
Finding a missing internal angle: a + b + c = 180°50° + 30° + c = 180°180° - 50° - 30° = c100° = cStraight lines are equal to 180 degrees. Finding the exterior/internal angle with a straight line: x + y = 180°40° + y = 180°180° - 40° = y140° = y## Polygons
Find the sum of interior angles of a nine (9) sided polygon. 180°( n - 2)180°(9 - 2) 180°(7) 1260° Find the measure of interior angles of a 3 sided polygon: (180°( n - 2))/n(180°(3 - 2))/3 (180°(1))/3 180°/3 60° ## Quadrilaterals
Squares are also Rhombus, Rectangles, and Isosceles Trapezoids ## Diagonals
Diagonals - Cut parallelograms into two equal triangles. - Bisect each other. Adjacent angles in a parallelogram add up to 180° Opposite angles are equal to each other. ## Diagonal Diagram## Adjacent/Opposite Angles Diagram## Probability
Probability of picking card #5: 1/5 Odds of picking card #5: 1:4 Odds of not picking card #5: 4:1 Theoretical Probability: 1/5 chance of choosing card #5. Experimental Probability: He picked up card #5 two times. 2/5 of picking card #5. There is a 1 in 5 chance of winning $4.00. It costs $1.00 to play. EV=[%(gain) $(gain)] - [%(loss) $(loss)]EV=[1/5 4] - [4/5 1]EV=[0.2 4] - [0.8 1]EV=0.8 - 0.8 EV=$0 |
## Law of Sines
Find side a:a/sin(30°) = 15cm/sin(45°)a = sin(30°)(15cm/sin(45°))a = 10.61cmFind sin(C): sin(C)/9 = sin(47)/11 sin(C) = 9*[sin(47)/11] C = sin ^{-1}(0.59838)C = 36.75° ## Find Side Diagram: Law of Sines## Find sin(C) Diagram## Law of Cosines
a/sin(40°) = 15/sin(B) = 8/sin(C) cannot be calculated so Cosine Law is usedFind side ( a)a^{2} = b2 + c2 - 2bcCosAa^{2} = 15^{2} + 8^{2} - 2(15)(8)Cos(40°) a^{2} = 225 + 64 - 240 Cos(40°)a^{2} = 105.14933a = √105.14933a = 10.25Find cosine(A) Cos(A) = ( b^{2} + c^{2} - a^{2})/2bcCos(A) = (7 ^{2} + 5^{2} - 6^{2})/2(7)(5)Cos(A) = (49 + 25 - 36)/70 Cos(A) = 0.542857 A = cos ^{-1} (0.542857)A = 57.12° ## Diagram: What to use## Measurement
Tolerance: (Maximum Value - Minimum Value)/2 [Eg. (130-120)/2 = ∓5]. 125 ∓ 5 = (125 - 5 = 120) or (125 + 5 = 130) Tolerance can have different maximum and minimum values. Eg. 125 (+5) (-3) = [125 + 5 = 130] or [125 - 3 = 122] ## Measurement (continued)Nominal Value: Minimum Value + Tolerance Eg. 120 + 5 = 125. Precision: Lowest unit of measurement of the measuring device or the significant decimal place. 87.32kg = 0.0> 1<.Uncertainty: Because not all measuring devices are accurate, you include an error with the measurement. (Smallest Measure/2) Eg. 0.1/2 = ∓0.05 ## Central Tendency
5, 7, 8, 8, 8, 9, 10, 12, 13, 14, 15 Mean: (5+7+8+8+8+9+10+12+13+14+15)/11 = 9.9 = 10 Median (Odd): Middle value = 9 5, 7, 8, 8, 8, 9, 10, 12, 13, 14, 15, 35 Median (Even): ( X[12/2] + (X[(12/2)+1]/2 = ( X[6] + X[6+1])/2= (10 + 12)/2 = 22/2 = 11 Mode: 8 ## Other Statistical Measurements
5, 7, 8, 8, 8, 9, 10, 12, 13, 14, 15, 35 Trimmed Mean: Remove 5 and 35. (7+8+8+8+9+10+12+13+14+15)/10 = 10.4, rounded up = 10 Weighted Mean: Will be in a diagram because I cannot figure out how to use cells. ## Weighted Mean Diagram## Percentiles
Ron scores 82% on his biology exam. A total of 200 students who wrote the same exam. 135 scored lower than Ron. What is Ron's percentile rank? P=(B/n) * 100P=(135/200) * 100P=(0.675) * 100P=67.5P=68th Percentile Rank## Stem Leaf Plot Diagram |

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# Geometry, Probability, Stats, and Measurements Cheat Sheet by ArcelM4

A cheat sheet or test review for Grade 12 Geometry, Probability, Statistics, and Measurements. Colour-coded for organization Navy: Geometry Cyan: Measurements Red: Probability Magenta: Statistics

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