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WORKS BEST IN WORD 2013 (ENABLE EDITING)!!!!! Just a basic outline of things that you learned in grade 10 math. Helpful for remembering all the topics you covered before your exam.
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Math Review
MPM2D5
Unit 1: Algebra
Expanding and simplifying [3a3b2 (2a4b5−4a3b2+5b4 )=6a7b7−12a6b4+15a3b6] Solving equations (4x+2=6 > x=2)
Greatest common factor 1. Factor tree2. Finding all factors3. Other way
Multiplying binomials When you multiply
conjugates together thete middle terms cancel out [(3x+4)(3x-4)]
When squaring a binomial it results in a trinomial. Square the first term > Square the last term > multiply the two terms together and double the coefficient.
Midpoint of a line segment
M=( x1+xz2 ) ,( y2+ y22 ) Given the midpoint find an endpoint
Common factoring [35=5 (7 )]
Simplifying radicals (2√18=2√9√2=6√2)
Length of a line segment |AB|=√(x1−x2 )+( y1− y2) Don’t forget to write units after the answer
Unit 2: Algebra II
Similar triangles (ΔABC ΔDEF) Prove 2 angles are similar (~AA, SAS, SSS) Area (The ratio of the areas of two similar triangles is equal to the square of
the ratio of the side lengths) Trigonometry (SOH CAH TOA)
1
Factoring simple trinomials [x2+13x+L10=( x+5 ) ( x+8 )]
Solving a linear system by substitution Proving it
Factoring special quadratics Difference of squares (conjugates) Perfect square trinomial (Binomial squared) Grouping (4 terms)
Solving right-angled triangles Determining a side length/angle with 2 right triangles
Slope (rise/run) Watch out for scale on diagrams Find a point given the slope and a point
Solving quadratic equations by factoring No constant term (common factor of X) (-4x2+7x=0) No middle term (conjugates) (4x2-100=0)
Unit 3: Algebra III
Solving a linear system with elimination
Factoring complex trinomials Always check for other factoring first (i.e. common factor) Factoring thought process
Sine law
sin Aa
= sinBb
= sin cc
For non-right angle triangles Prove it Need at least three pieces of information (an angle and its side plus one other
side or angle)
Triangle inequality The longest side is less than the sum of the two other sides
Cosine law a2=b2+C2−2bc (cos A ) −2bc (cos A ) > is one part
2
Use only if you don’t have an angle and its matching side
Quadratic formula
x=−b±√b2−4ac2a
b2−4 ac = The discriminant- used to determine the type of roots
Use only if not factorable (can determine by seeing if the discriminant is a perfect square)
No real roots for a √−¿¿ -No X-intercepts b2−4 ac is greater than 0 – 2 real roots (2 x-intercepts)
b2−4 ac is equal to 0 – 1 real root (1 x-intercept)
Simplify radicals
Equations of lines Horizontal Vertical
Unit 4: Functions
Function: A relationship in which one quantity depends on, determines, or corresponds to another
There is only 1 y output otherwise it is not a function (An odd exponent on the y means it is a function an even exponent means it is not.)
X-inputs (domain) Y-inputs (range) Maxima/Minima: Change from increasing to decreasing or vice versa Concavity: Hill or a valley Point of inflection: Where it changes from a hill to a valley or vice versa. About
halfway. Positive: Above the x-axis Negative: Below the x-axis Zero: on the x-axis
Unit 5: Functions II
3
OutputFunctionInput
Sketching parabolas in vertex form The right order to apply transformations Function form [y=a ( x−h )2+k ¿ Graphing of y=x2
Converting to vertex form Characteristics of vertex form
X-Vertex (−b2a
)
Insert x-vertex to get y-vertex
Distance from a point to a line The shortest path from a point to a line The line is perpendicular POI of the line and its perpendicular line
Calculate distance from the point to the POI [|AB|=√(x1−x2 )+( y1− y2)]
Geometric properties-Quadrilaterals
Shape Characteristics
Trapezoid
Exactly one pair of opposite sides parallel
Parallelogram
Two pairs of opposite sides parallel
Rhombus
All four sides equal in length
Kite
Two pairs of adjacent sides, that are equal in length
The diagonals are perpendicular
Rectangle
Two pairs of adjacent sides, perpendicular
Square
Two pairs of adjacent sides that are perpendicular
All four sides are equal in length
4
Property Characteristics
Right bisector
A line that is perpendicular to a line segment and divides the line into two equal parts.
Altitude
The perpendicular distance from a vertex to the opposite side (height of a triangle)
Median
A line joining a vertex of a triangle to the midpoint of the opposite side
Circumcentre
The intersection of the three right bisectors of a triangle
Centriod
Where the medians intersect
( x1+x2+x33 ) ,( y1+ y2+ y33 ) Geometric properties-Triangles
Triangle Characteristics
Isosceles
Exactly two sides are equal in length
Equilateral
All three sides are equal length
Scalene
All three sides have different lengths
Right-Angled
Has a right angle
Properties of a quadratic function Direction of opening Vertex Axis of symmetry Shape Domain, range X-Intercept(s) Y-intercept
5
Unit 6: Word Problems
Terms Sum of squares (a2+j2 = sum of squares) Is a minimum/maximum: Looking for the vertex (X,Y) (How/when max/min occurs, max/min value)
Canned word problems Given the equation Don’t need a let statement
Investment problems (Amount invested x first Interest rate ) + [(Total amount invested- amount
invested at first percent) x second interest rate] = Total interest received
Revenue problems (# of units sold)(Price) Is a parabola
Trigonometric application Don’t need a let statement Angle of elevation: is measured from a horizontal up Angle of depression: Is measured from a horizontal down Use SOH CAH TOA for right-angle triangles Can use Pythagorean theorem
Distance/Speed/Time D = S ∙ t
Fill in the table with known information. At the end you should have 1 piece of information you have not used
For distance your let statement should represent time
6
1 2
Factoring Thought Process
1. Is there a common factor?YES- Factor it out NO- continue
2. Count the number of termsBinomial (2) Trinomial (3) 4 Terms (4+ terms= poly)
Difference of squares
9 x2−49=¿(3 x−7 ) (3 x+7 )
Conjugates
Simple trinomial x2−2 x−8=¿
( x−4 ) ( x+2 ) Perfect square
trinomial4 x2−36 x+81=(2 x−9 )2
Grouping
Anything missed:
7