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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Triangles
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Are three sides, three angles, and all angles add up to 180 degrees.
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Acute Triangles
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All interior angles must be 0-90 degrees. All equilateral triangles are acute.
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Scalene Triangles
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All sides and angles differ in measure.
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Right Triangles
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Only one angle is equal to 90 degrees
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Isosceles Triangles
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Two opposite sides and angles are equal to each other.
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Equilateral Traingles
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All sides equal. All angles equal to 60 degrees.
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Polygons
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Any enclosed geometrical shape that is composed of straight lines.
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Regular Polygons
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All sides and interior angles are equal.
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Diagonals
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A segment connecting two non-adjacent corners in a polygons.
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Formula to find the sum of interior angles:
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180°(n - 2). n = number of sides.
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Formula to find the measure of interior angles:
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(180°(n - 2))/n
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Quadrilaterals
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Any four sided polygon.
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Parallelograms
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Opposite sides are parallel to each other. Opposite sides and angles are equal in measure.
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Rhombus
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Parallelograms with all sides that are equal.
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Rectagles
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Parallelograms with opposite sides equal in measure. All angles equal to 90°.
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Squares
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Parallelograms with all sides that are equal. All sides are 90°
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Isosceles Trapezoids
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One set of sides are parallel. Other sides equal in measure.
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Kite
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Two sets of equal sides. No lines are parallel.
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Formula for finding the number of diagonals in a polygon:
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D = (n(n-3))/2
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Probability
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The mathematically likelihood that an event will occur. A ratio that compares the possible successful outcomes, to the total number of outcomes.
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Probability Formula
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Number of successful outcomes, divided by total number of outcomes. (1/10)
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Odds
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A ratio that compares the number of possible successful outcomes to the number of possible unsuccessful outcomes.
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Odds Formula
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Successful Outcomes : Unsuccessful Outcomes
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Theoretical Probability
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A ratio that compares the number of possible successful outcomes to the total number of possible outcomes Determined by reason or calculation.
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Experimental Probability
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A ratio that compares the number of times an event occurs to the total number of trials or tests Determined by experiment.
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Expected Value
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Expected value is an application of probability that involves the likelihood of a gain or loss.
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Expected Value Formula
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EV=[%(gain) x $gain]-[%(lose) x $loss]
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Sine Law
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Used to find lengths of sides, or angles of non-right triangles.
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Formula:
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a/sin(A) = b/sin(B) = c/sin(C)
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Cosine Law
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Used to find angles or sides when Sine Law isn't possible.
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Formula to find with a given angle:
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a2 = b2 + c2 - 2bcCosA
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Formula when there are no angles:
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Cos(A) = (b2 + c2 - a2)/2bc
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Accuracy
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Accuracy of a measurement is how close the measurement is to the true value.
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Precision
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Precision of measurements is how close they are to each other. The precision is determined by the number of decimal places.
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Uncertainty
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Uncertainty is the natural variation in measurements associated with instruments
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Tolerance (∓)
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The total amount that a measurement is allowed to vary. Add or subtract Tolerance to Nominal Value.
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Nominal Value
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The middle number that can be added or subtracted from to show the minimum or maximum value.
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Statistics
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Is based upon data collected. From that, inferences and speculations are made. It is reliant upon the data and the interpretation of the data.
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Mean
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The average of all data. The sum of all data, divided by the number of data.
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Median
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The set of values that is the middle of values arranged in ascending or descending order.
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Even Median Formula
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X[n/2] + X[(n/2)+1])/2. (n = number of values) (X = position of values)
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Mode
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The value that appears the most frequently.
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Outlier
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A piece of data that is significantly different from the rest.
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Range
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The difference from the highest value to the lowest value in the data set.
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Trimmed Mean
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Removing the highest and lowest values and calculating the mean so that data is accurately presented.
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Weighted Mean
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The average or mean of a data set in which each data point does not contribute an equal amount to the final average.
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Weighted Mean Formula
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Sum of the product of each item and its weight, divided by sum of the weightings
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Percentiles
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A value below which a certain percent of the data falls.
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Percentile Rank
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A percentile rank of 50 (usually written P50) is the median because 50% (or half) of the values in the set are below the median value.
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Percentile Rank Formula
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P=(B/n) * 100. B: The number of scores below a given score, n: The number of scores. Always rounded to the nearest whole number
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Stem Leaf Plot
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A way to organize data in order of place value. The "tens digit and greater" is the stem and the "ones digit" is the leaf.
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^
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Will show on a diagram because I cannot figure out cells.
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