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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