Download Grade 9 math midyear exam memory aid help

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.






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 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.
 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
 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 43 = 64
am = a x a x a x ... x a (m times)
a1
a0
=a
am x an = am + n
=1
am ÷ an = am - n
a-m
a½
=
= √a
a1/3
= ∛a
(ab)m = ambm
(am)n = amn
a
b
m
= am
bm
 With
negative exponents we invert the
number to the denominator.
 If the denominator has a negative exponent,
we send it to the numerator position.

= x3
Inequality
Sign
Meaning
Example
<
less than
x<5
>
greater than, more than
200 > 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
 If
dividing or multiplying both sides by a
negative number you must switch the
direction of the inequality sign.
4 - 14a > 3
= -14a > 3 – 4
=-14a > -1
=-14a > -1
-14
-14
= a < 1/14
 By



comparison (Exam type)
Both equations are equal to each other
Solve for x
Then solve for y
 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
 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
 Theoretical
probability =
and = multiply probabilities
or = add probabilities.
 Permutation
= all values of set used, order
important, formula = n!
 Arrangement = subset of values of the set
used, order important, formula is:
n = total number of values in the set
r = number of ways to arrange them
 Combination
= subset of values of the set
used, order is not important, formula is:
 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