MPM1D Main Ideas and Review
Chapter 1: Rational Numbers
 Adding and subtracting fractions
 Multiplying and dividing fractions
 BEDMAS
 Exponent rules (p.62)
 Convert a mixed number to a fraction
 +,-,×,÷ with negatives
Mid-chapter Review: p.40 #1-13
Chapter Review: p.66 #1-25
Self-Test: p.68 #1-11
Chapter 2: Powers and Polynomials
 Term
 Coefficient
 Variable
 Represent s,s2,s3
 Like terms
 Exponent rules (p.89, 95)
 Adding and Subtracting like terms
 Multiplying polynomials (distributive property)
Mid-chapter Review: p.101 #1-14
Chapter Review: p.131 #1-20
Self-Test: p.133 #1-14
Chapter 3: Linear Relations
 Relation
 Independent variable
 Dependent variable
 Discrete data
 Continuous data
 Graphing from a table of values
 Y-intercept
 X-intercept
 Partial variation
 Direct variation
𝑟𝑖𝑠𝑒
 Slope/rate of change/ 𝑟𝑢𝑛
 First differences
 𝑦 = 𝑚𝑥 + 𝑏
 Rearrange equations
 Graph from intercepts (𝐴𝑥 + 𝐵𝑦 = 𝐶)
 Recognize linear and non-linear relations from equations, tables of values, or graphs
Mid-chapter Review: p.163 #1-5
Chapter Review: p.183 #1-11
Self-Test: p.185 #1-7
Chapters 1-3 Cumulative Review: p.187 #1-22
Chapter 4: Linear Equations
 Finding the solution of a linear equation using a graph or table of values or equation
 Inverse operations to solve for a variable
 Multiply by the lowest common denominator to eliminate fractions
 Rearrange an equation to solve for a variable in terms of the other
 Point of intersection (on graph) is the solution to a system of linear equations
Mid-chapter Review: p.228 #1-7
Chapter Review: p.250 #1-17
Self-test: p.252 #1-6
Chapter 5: Analytic Geometry
 𝑦 = 𝑚𝑥 + 𝑏
 Horizontal, vertical, rising to the right, falling to the right: connection to slope
 Slope: positive, negative
 Y-intercept
 Rearrange equations (𝐴𝑥 + 𝐵𝑦 + 𝐶 = 0 𝑡𝑜 𝑦 = 𝑚𝑥 + 𝑏)
𝑦2−𝑦1
 Slope formula 𝑥2−𝑥1
 Point: (𝑥, 𝑦)
 Collinear
 Use two points to determine the equation of a line
 Use the slope and y-intercept to determine the equation of a line
 Use the slope and one point to determine the equation of a line
 Parallel lines: have the same slope
 Perpendicular lines: slopes are negative reciprocals
Mid-Chapter Review: p.283 #1-13
Chapter Review: p.309 #1-15
Self-Test: p.311 #1-13
Chapter 6: Investigating Relationships
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Plotting data on a Cartesian graph
Discrete (dotted line) vs. Continuous (solid line) data
Correlation (positive vs. negative)
Independent vs Dependent variable
Line of best fit
Curve of best fit
Determine equation of line of best fit using two points
Extrapolating vs. Interpolating
Evaluating a Conjecture about a relationship between two variables by examining trends in data
Using a graph to describe a situation or tell a story
On a distance-time graph, the slope (rise/run) = speed or velocity, because you are dividing
displacement (y) by time (x)
Mid-Chapter Review: p.343 #1-5
Chapter Review: p.374 #1-10
Self-Test: p.376 #1-7
Chapters 4-6 Cumulative Review: p.379 #1-17
Chapter 7: Properties of 2-D Figures
 Perpendicular lines form a 90 angle
 Sum of angles that form a straight line (supplementary) is 180
 Sum of angles that form a T (complementary) is 90
 Transversal Rules: X-pattern, C-pattern, F-pattern, and Z-pattern
 Polygons
 Interior vs Exterior Angles
 Sum of interior angles of a triangle = 180
 Sum of interior angles of a polygon with “n” sides = (𝑛 − 2) × 180° - you can visualize this by
dividing a polygon into non-overlapping triangles
 Sum of exterior angles of a convex polygon is always 360
 Testing conjectures about polygon properties
 Counterexample
 Kite, parallelogram, rectangle, square, rhombus, irregular quadrilateral, trapezoid, isosceles
trapezoid
 Diagonals
 Midpoints and Mid-segments
 Medians
 Bimedian
 Centroid/centre of gravity
Mid-Chapter Review: p.398 #1-6
Chapter Review: p.418 #1-15
Self-Test: p.420 #1-8
Chapter 8: Measurement
 Area, volume, surface area
 Net
 Pythagorean Theorem = 𝑎2 + 𝑏 2 = 𝑐 2 OR 𝑎2 = 𝑐 2 − 𝑏 2 OR 𝑏 2 = 𝑐 2 − 𝑎2
 Hypotenuse
 Composite Shape
 Prism (triangular, rectangular, etc.), cylinder, cone, pyramid (incl. regular (square-based) pyramid),
sphere
 Optimum
 A square is the optimum rectangle when looking for max. area or min. perimeter
 When looking for optimum values for a rectangle with border on 3 sides, see special rule below
 Be able to determine area or perimeter of composite shapes – you are expected to know the area
and perimeter formulas
 To determine area of a regular polygon – divide it up into triangles, as shown below
 Determine surface areas and volumes of cones, pyramids, cylinders, prisms, and spheres – formulas
will be given on exam
Mid-Chapter Review: p.460 #1-9
Chapter Review: p.484 #1-25
Self-Test: p.486 #1-8
Chapters 7-8 Cumulative Review: p.488 #1-21