Transcript Grade 9 math midyear exam memory aid helpx

Memory Aid Help


 “c”
b2 = c2 - a2
a2 = c2 - b2
must be the hypotenuse.
 In a right triangle that has 30o and 60o
angles, the longest side ( the hypotenuse) is
always twice the length of the shortest side.

Natural number: positive integers and no zero.


Whole number: natural + zero.


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: 0,1,2,3.....76....3456.....282763....
Integer: whole numbers and their opposites (no decimal)


Example: 1,2,3,4,....89,.....756,.....1000000
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 nonperiodic (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.
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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

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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:
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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 is a percentage of a group within
the total (how many red pens in a box full of
colored pens)
Relative frequency
 Independent
= x values
 Dependent = y values
 ______y______
 Before
depends on ____x________.
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.