Download MPM2D Big Ideas

Grade 10 Academic Math – MPM2D
BIG IDEAS and PRIOR KNOWLEDGE
UNIT 1: Linear Systems

Prior Knowledge
o Integers (numbers and variables)
o Distributive property
o Subbing into expressions
o Solving equations
o Graphing:
 Table of values
 Slope-intercept
 x, y-intercepts

Model and solve problems involving the intersection of 2 straight lines
o 2 linear equations with 2 variables using substitution or elimination
o Solving problems described in words or represented by equations algebraically
or graphically
UNIT 2: Analytic Geometry

Prior Knowledge
o Pythagorean Theorem
o Equation of a line
o Slope of a line
o Parallel and perpendicular lines
o Similar and congruent triangles
o Intersection of lines

Solve problems involving properties of line segments
o Develop the formula for midpoint of a line segment and use it to solve problems
o Develop the formula for length of a line segment and use it to solve problems
o Develop the equation of a circle with centre (0, 0)
o Determine the radius/equation of circles

Verify properties of triangles and quadrilaterals
o Determine (by investigation) and verify characteristics and properties of
geometric figures
UNIT 3: Quadratics Relations

Prior Knowledge
o Scatter plots
o Translations and reflections
o Operations with powers
o Classifying polynomials
o Add/subtract polynomials
o Product of a monomial and a polynomial
o Factors
o Square roots

Determine the basic properties of quadratic relations
o Collect data (investigation or secondary sources) that can be represented as a
quadratic relation, graph it and draw a curve of best fit
o Recognize y = ax2 + bx + c is a parabola and table of values yields a constant
second difference
o Key features of a parabola
 Axis of symmetry
 Coordinates of the vertex
 y-intercept
 Zeros
 Max/min value
o Compare the graphs of y = x2 and y = 2x and determine the meaning of a
negative and zero exponent

Relate transformations of the graph of y = x2 to the algebraic representation
y = a(x-h)2 + k
o Identify by investigation the effect of transformations to the graph of y = x2
o Explain the roles of a, h, and k and identify key features
o Sketch the graph of y = a(x-h)2 + k by applying transformations to the graph of
y = x2
o Write the equation, in the form of y = a(x-h)2 + k of a given graph

Solve quadratic equations and interpret the solutions with respect to the
corresponding relations
o Expand and simplify second-degree polynomial expressions
o Factor polynomial expressions (common factoring, trinomials, and difference of
squares)
o Investigate connections between factors of a quadratic expression and the xintercepts of the graph expressed in the form y = a(x-r)(x-s)
o Express y = ax2 + bx + c in the form y = a(x-h)2 + k by completing the square
o Graph y = ax2 + bx + c using a variety of methods
o Solve quadratic equations using a variety of methods (factoring, quadratic
formula)

Solve problems involving quadratic relations
o Determine zeros and max/min of a quadratic relation from its graph or equation
o Solve problems arising from realistic situations
UNIT 4: Trigonometry

Prior Knowledge
o Angle properties (interior angles, supplementary, complementary, parallel
lines)
o Pythagorean Theorem
o Equivalent ratios
o Rearranging formulas

Use their knowledge of ratio and proportion to investigate similar triangles and solve
problems related to similarity
o Properties of similar triangles
o Concepts of similarity and congruence
o Solve problems involving similar triangles

Solve problems involving right triangles, using the primary trigonometric ratios and
the Pythagorean Theorem

Solve problems involving acute triangles, using the sine law and cosine law
o Explore development of the sine and cosine law within acute triangles
MPM2D
Unit 1: Linear Systems Checklist
Check
Learning Goal
Solving by Graphing
Graph a line using a table of values
Graph a line using slope-intercept form
Graph a line using x, y-intercepts
Find the point of intersection of two lines by graphing
Solving by Substitution
Find the point of intersection of 2 linear equations using
substitution
Solving by Elimination
Find the point of intersection of 2 linear equations using
elimination
Solving Problems
Know when to use substitution and when to use
elimination
Solve word problems using substitution or elimination
Plans
MPM2D
Unit 2: Analytic Geometry Checklist
Check
Learning Goal
Plans
Properties of Line Segments
Find the slope of a line
m
y 2  y1
x 2  x1
Understand parallel and perpendicular lines
Find the length of a line
l  ( x 2  x1 ) 2  ( y 2  y1 ) 2
Find the midpoint of a line
 x  x2 y1  y 2 
M  1
,

2 
 2
Find the equation and radius of a circle
x2  y2  r 2
Verify Properties of Triangles and Quadrilaterals
Understand types of triangles (equilateral, isosceles,
scalene, right)
Understand medians and altitudes of a triangle
Be able to verify different properties of triangles and
quadrilaterals
MPM2D
Unit 3: Quadratic Relations Checklist
Check
Learning Goal
Basic Properties of Quadratic Relations
Recognize y = ax2 + bx + c is a parabola and its table of
values produces constant second differences
Identify key features of a parabola (axis of symmetry,
vertex, y-intercept, zeros, max/min)
Graphing and Transformations
Understand how to graph y = x2 and apply transformations
y = a(x-h)2 + k
Understand what a, h, and k do to a graph
Write the equation in the form y = a(x-h)2 + k of a graph
Quadratic Equations
Expand and simplify binomials
Factor (common factoring, trinomials, and difference of
squares)
Solve quadratic equations using factoring and the
quadratic formula
Change y = ax2 + bx + c into the form y = a(x-h)2 + k by
completing the square
Be able to graph given any form:
y = ax2 + bx + c, y = a(x-h)2 + k, or y = a(x-r)(x-s)
Solve Problems
Find zeros of a quadratic relation
Find the maximum or minimum of a quadratic relation
Plans
MPM2D
Unit 4: Trigonometry Checklist
Check
Learning Goal
Similar Triangles
Solve proportions
Understand similarity and congruence
Solve similar triangles
Trigonometric Ratios and Pythagorean Theorem
Use sine, cosine and tangent ratios to find missing sides
Use sine, cosine and tangent ratios to find missing angles
Use the Pythagorean Theorem to find missing sides
Solve problems using trig ratios and the Pythagorean
Theorem
Sine and Cosine Law
Use sine and cosine law to find missing sides
Use sine and cosine law to find missing angles
Solve problems using sine and cosine law
Plans