 # Memory Aid Help.  b 2 = c 2 - a 2  a 2 = c 2 - b 2  “c” must be the hypotenuse.  In a right triangle that has 30 o and 60 o angles, the longest.

## Presentation on theme: "Memory Aid Help.  b 2 = c 2 - a 2  a 2 = c 2 - b 2  “c” must be the hypotenuse.  In a right triangle that has 30 o and 60 o angles, the longest."— Presentation transcript:

Memory Aid Help

 b 2 = c 2 - a 2  a 2 = c 2 - b 2  “c” must be the hypotenuse.  In a right triangle that has 30 o and 60 o angles, the longest side ( the hypotenuse) is always twice the length of the shortest side.

 Natural number: positive integers and no zero.  Example: 1,2,3,4,....89,.....756,.....1000000  Whole number: natural + zero.  Example: 0,1,2,3.....76....3456.....282763....  Integer: whole numbers and their opposites (no decimal)  Example: -45, -39, -8, 0, 123, 29874, 30000000  Rational: number can be written as a ratio (fraction) of two integers. (in decimal form are terminating or repeating.  Example: ½, 5.2222..., 0.19, -11/3, 2, -4.5, √25  Terminating decimal numbers: 5/2 = 2.5, 5/8 = 0.625  Repeating decimal numbers: 1/9 = 0.1111111...... or 0.1  Irrational: number that cannot be written as a fraction of integers and whose decimal numbers are infinite and non- periodic (does not repeat).  Example: √2, √5, ∏

 Reverse x and y to get an inverse function  If x increases, y decreases and vice versa  When the product of each variables’ values is a constant you get an inverse variation function.

 a relation is a function when each value of the x-axis (abscissa) has one y-axis (ordinate) associated with it. x-axis (abscissa) = independent variable y-axis (ordinate) = dependent variable

 [included]  ]excluded[ Intervals with infinity: infinity is never included. [-4, +∞[ = from -4 to positive infinity. ]- ∞, -1[ = negative infinity up to but excluding -1.

 Domain (X): all x values from left to right.  Range (Y): all y values from down to up  Variation (X): it can increase, decrease or remain constant.  Extrema (Y): The minimum: smallest value of y. The maximum: largest value of y.  Sign (X): above x-axis is positive and below is negative.  X-intercept (zero) & y-intercept (initial value).

 Domain: ]-∞,+ ∞[  Range: ]- ∞,8]  Variation  Increasing: ]- ∞,-4] U [-1,3]  Decreasing: [-4,-1] U [3, + ∞[  Constant: none  Extrema  Min: - ∞  Max: 8  Sign  Positive: [-6,-2] U [1,5]  Negative: ]- ∞,-6] U [-2,1] U [5,+ ∞[  Zero: -6, -2, 1, 5  Initial value: -2

 Variables are qualitative (words) or quantitative (numbers).  Discrete quantitative (counting numbers) E.g. Dolls on a shelf  Continuous quantitative (all values included within an interval – can be decimal points) E.g. Height

 1. simple random: by chance (from a hat)  2. systematic: regular intervals from a list of the whole population ( every 10th member)  3. cluster: A random selection of clusters is chosen to represent the whole. Every individual within a selected cluster is selected.  4. stratified: taking representative samples from each group.

Percentage: 10% of 254 = 10/100 x 254 = 25.4

 Sources of bias are different reasons that could lead researchers or survey people to draw the wrong conclusion from a survey or census.  There are 6 different sources of bias:  A non-representative sample of the population  A poorly formulated question  The attitude of the person doing the survey  Inadequate representation of the results  Large part of the sample is rejected  A processing error that occurs when compiling the data.

 Median: is the number in the middle when values are placed in order.  Mode: the number that occurs most often in a distribution (list of numbers).  Mean: average of all numbers (sum of all values divided by the number of values).  Range: highest value – lowest value

 Table of condensed data: mostly used when data values are repeated.  Table with data grouped into classes: data is grouped into intervals [a,b[ (included, excluded) – very few repeated values. Need to determine the number of groups and how much data each one can carry (amplitude). Amplitude = range/number of classes. Amplitude of each interval must be the same!

 A) mode: class with highest frequency is called the modal class.  Middle of modal class ≈ mode  B) median: the class that includes the median is called the median class.  Middle of median class ≈ median  C) mean: sum of midpoints of each class multiplied by its frequency divided by the number of data values.  D) range is a measure of dispersion  In condensed data: Highest value – lowest value  In grouped data: upper bound of highest group or class – lower bound of smallest group or data.

Relative frequency Relative frequency is a percentage of a group within the total (how many red pens in a box full of colored pens)

 Independent = x values  Dependent = y values  ______y______ depends on ____x________.  Before starting a slope type word problem, figure out which variable is x and which is y.

 1. locate two ordered pairs (table or graph)  2. find the rate of change (y2-y1)/(x2-x1)  3. using the a you just found, substitute the variables of an ordered pair from your graph or table of values.  4. solve for b.  5. put a and b in the generic rule.  6. y=ax+b

 1. using the a you are given, substitute the variables of an ordered pair from your graph, table of values or description.  2. solve for b.  3. put a and b in the generic rule.

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