Download Grade 9 Academic Exam Review

Grade 9 Academic Exam Review
Algebra:
 Algebraic terms have a constant and a variable term: 3x  2
 Adding and subtracting polynomials
o you have to have like terms (both variable and exponent are the same)
o Cannot add/subtract unlike terms i.e. 3 y  2 y 2
 Multiplying polynomials
o


3(4 x  3)
 12 x  9
Dividing polynomials
o

Can always multiply/divide polynomials using the distributive property
Cancel out common terms
24 x 4  16 x 3
 3x 2  2 x
2
8x
Exponent laws ALWAYS NEED THE SAME BASE
o Multiplying – add the exponents x 4  x 2  x 6
o Dividing – subtract the exponents y 8  y 3  y 5
o Power of a Power – multiply the exponents ( x 3 ) 3  x 9
Solving polynomial equations
o Isolate term – sings change when being moved over the equal sign!!!
o Do BEDMAS backwards
2(x+2) – 6 = 4
2(x+2) = 4 + 6
x+2 =10/2
x=5–2
x=3
Investigating Relationships:
 Scatterplots – a graph that shows the relationship between 2 sets of data
 Dependent variable: variable that depends on the other
 Independent variable: variable that doesn’t change based on the other
 Lines of best fit: a line the passes through as many of the points possibly with the remaining points
grouped equally above and below the line.
 Mean fit line: A more accurate line of best. This line has to pass through the mean point (the average
point)
 Correlations:
o Positive – slopes up to the right
o Negative – slopes down to the right
o No correlation – points all over the scatter plot
o Strong correlation – points nearly create a straight line
o Weak correlation – points are widely dispersed but still show a general trend
 Bias: The data is not an accurate representation of the truth. Can be caused by sample size, sampling
procedure
 Models of Movement – shows the distance travelled over a period of time. You can analyze direction,
distance, time, and speed.
x
y
 1st differences: determines if the data is linear.
1st diff’s
o To calculate the first differences from a table of values:
6
8
10-8 = 2
7
10
12-10
=2
8
12
14-10
=
2
9
14
Linear Relationships:
2nd
1st
(x,y)
x-axis (independent)
3rd
4th
y-axis (dependent)
rise y y 2  y1


run x x2  x1

Slope: m 

Tables of values, graphing from table of values
1. If necessary complete the table to values for unknown values.
2. Each set of x and y values are coordinates, plot these points
3. Connect the points
Creating an equation in slope, y-int form (y = mx + b)
1. Find the slope
2. Sub the slope and a coordinate (x,y) into y=mx+b to solve for b
3. Sub slope(m) and y-int(b) into equation
Graphing a line with slope and y-int,
1. Plot the y intercept
2. Move from the y-intercept the rise/run (slope) and make more points
3. Drawing a line connecting all points
Parallel lines have equal slopes
Perpendicular lines have negative reciprocal slopes. To find negative reciprocal flip and change sign.
Horizontal lines are parallel to the x-axis, have the form y = # and a slope of 0.
Vertical lines are parallel to the y-axis, have the form x = # and an undefined slope
Writing equations with two variables
o Combine two qualities represented by the equation







ax  by  c
o
To rearrange this equation to slope, y intercept form you need to isolate y
2 x  5 y  500
i.e. 5 y  2 x  500
y



2
 100
5
Standard form of a line Ax + By + C = 0 *no fractions and x must be positive*
Finding x and y intercepts (and graphing using that method)
To find x- int (set y=0)
To find y-int (set x=0)
2 x  5 y  500
2 x  5 y  500
2 x  500
5 y  500
x  250
y  100
(250,0)
(0,100)
Finding the POI of two lines
o Graph two set of lines (using table of values, slope y-int, or x and y intercepts)
o Find the POI by looking at the graph
o Sub the POI into BOTH equations to ensure that LS=RS
o A line can intersect:
 once – different slopes
 never – same slope, different y-intercept
 infinite # of times – same slope and y-intercept (same line)
Geometry:
 Angle theorems
o OAT – opposite angles are equal
o SAT – angles form 180°
o CAT – angles form 90°
o Patterns (need parallel lines and a transversal) Z, F, C

Pythagorean theorem
c
a
a2  b2  c2
*** c must always be the hypotenuse (the longest side) make sure you sub in
and solve the equation correctly

b
Sum of interior angles of a polygon
o 180n  360 or 180(n  2) where n= # of sides
Exterior angles always add to 360, no matter the number of sides of the polygon
Polygon properties
o Bisectors – splits in half
o Diagonals – cut diagonally through a shape
o Midsegments – line joining the mid-points of adjacent sides
o Midpoints – the middle point of a line
How to calculate areas and perimeters of 2 dimensional shapes (You have the EQAO formula sheet)

Area of regular polygons =

How to calculate the volume and surface area of 3 dimensional shapes - prisms, cylinders, pyramids,
cones, spheres (You have the EQAO formula sheet)



Slant height = a 2  h 2 REMEMBER HOW TO USE PYTHAGOREAN THEOREM PROPERLY
If dealing with 4 sides, the max area and min perimeter occurs with a square
Optimizing a Cylinder
Optimizing a Rectangular Prism
Occurs when h=2r
occurs when all sides are equal (a cube)
Max. Volume
Max. Volume



r
SA
then SA  6l 2
6
Min SA
r
V
then SA  6r 2
2
Pa
, where P=perimeter, a = apothem
2
l  3 V then SA  6l 2
Min SA
l
SA
then V  l 3
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