1. Memory Aid Help

5.  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.

6.  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, ∏

7.  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.

8.  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

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

10.  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).

11.  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

12.  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

13.  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.

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

15.  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.

16.  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

17.  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!

18.  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.

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

21.  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.

22.  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

23.  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.

28.  In 2 similar solids: corresponding angles are congruent and the measures of corresponding edges (sides) are proportional.  Ratio of similarity = measure of one edge of the mirror-image solid ÷ measure of corresponding edge of the initial solid

29.  Ratio of areas = area of mirror image solid/area of initial solid  Ratio of volumes = volume of mirror image solid/volume of initial solid  In 2 similar solids:  Ratio of areas is equal to the square of the ratio of similarity If ratio of area is 16, ratio of similarity is √16 = 4  Ratio of volumes is equal to the cube of the ratio of similarity If ratio of similarity is 4, ratio of volumes is 4 3 = 64

30. a m = a x a x a x... x a (m times) a 1 = a a 0 = 1 a -m = a ½ = √a a 1/3 = ∛ a a m x a n = a m + n a m ÷ a n = a m - n (ab) m = a m b m (a m ) n = a mn a m = a m b b m

31.  With negative exponents we invert the number to the denominator.  If the denominator has a negative exponent, we send it to the numerator position.  = x 3

37. Inequality Sign MeaningExample <less thanx < 5 >greater than, more than200 > 6 ≤ no more than, at most less than or equal to h ≤ 1.8 ≥ no less than, at least greater than or equal to n ≥ 180

38.  If dividing or multiplying both sides by a negative number you must switch the direction of the inequality sign. = -14a > 3 – 4 =-14a > -1 -14 -14 = a < 1/14 4 - 14a > 3

39.  By comparison (Exam type)  Both equations are equal to each other  Solve for x  Then solve for y

40.  Isolate y in equation so y =........  Give x random values and solve for y  Find two points for each equation  Plot points on graph and draw straight lines  Intersection = solution

42.  Order values in increasing fashion  Find the median (n+1)/2 = position of median  Q2  Find median of left and right  Q1 and Q3  Draw number line with every number  Put lines at Q1, Q2 & Q3 and draw box  Whiskers go to min and max values  Interquartile range = Q3 – Q1

44.  Theoretical probability =

45. and = multiply probabilities or = add probabilities.

47.  Permutation = all values of set used, order important, formula = n!  Arrangement = subset of values of the set used, order important, formula is:  Combination = subset of values of the set used, order is not important, formula is: n = total number of values in the set r = number of ways to arrange them

48.  One dimension = length  Two dimensions = area  Three dimensions = volume  Probability = favorable outcome/total outcomes  Example: probability that a point falls in circle is  Area of circle Area of square