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)

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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

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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

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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

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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

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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

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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:

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