Ontario Grade 10 Academic Math (MPM2D) curriculum and lessons

The course map includes Quadratic Relations, Analytic Geometry, Trigonometry. Follow the complete section list above for the full study path.

درس ریاضی نظری پایه دهم انتاریو (MPM2D) چه مباحثی دارد؟ از جمله مباحث این درس روابط درجه دوم، هندسه تحلیلی، مثلثات است. فهرست کامل بخش‌ها در بالای صفحه قرار دارد.

35 of 41 written lessons are currently published and free to read. Open a linked lesson in the section map above. Check the official Ontario curriculum for exact requirements.

درس‌ها و برنامهٔ درسی ریاضی نظری پایه دهم انتاریو را از کجا پیدا کنم؟ اکنون 35 درس از 41 درس نوشتاری منتشر شده و خواندن آن‌ها رایگان است. درس‌های دارای پیوند را در نقشهٔ بخش‌های بالا باز کنید. برای شرایط دقیق به برنامهٔ درسی رسمی انتاریو مراجعه کنید.

You already know how to spot a linear pattern: the y-values go up (or down) by the same amount every time x increases by 1. That…

A line on a graph shows a steady relationship between two values. For example, a graph of distance against time may be a straight…

A right triangle is a triangle with one angle. You may already know how to find the perimeter or area of a triangle. Sine, cosine…

When you drop a ball, stretch a spring, or track the height of a launched object, the numbers you collect do not follow a straight…

Imagine two straight roads on a map that keep the same direction and never meet. They are like parallel lines. Two other lines might…

Two triangles can have the same shape but different sizes. When triangles are similar, their corresponding angles are equal and their…

You already know from Grade 9 that a linear function grows by adding the same amount each time, and that its graph is a straight…

One line can be described by several equations. The equations may look different, but they can still match the same points on a…

Data, parabolas, transformations, quadratic equations, and applications.

• Q1 · Identify quadratic patterns using second differences (published written lesson)
• Q2 · Collect quadratic data and draw a curve of best fit (published written lesson)
• Q3 · Identify the vertex, axis, intercepts, and extrema of a parabola (written lesson not published)
• Q4 · Compare quadratic and exponential graphs and interpret zero and negative exponents (published written lesson)
• Q5 · Investigate translations, reflections, stretches, and compressions of y = x² (published written lesson)
• Q6 · Explain the parameters and vertex of y = a(x − h)² + k (published written lesson)
• Q7 · Sketch a quadratic graph from vertex form (published written lesson)
• Q8 · Determine a vertex-form equation from a parabola graph (published written lesson)
• Q9 · Expand and simplify second-degree polynomial expressions (published written lesson)
• Q10 · Factor quadratics using common factors, trinomials, and differences of squares (published written lesson)
• Q11 · Connect quadratic factors to graph zeros (published written lesson)
• Q12 · Interpret real and non-real quadratic roots using graphs (published written lesson)
• Q13 · Complete the square without fractional coefficients (published written lesson)
• Q14 · Sketch a quadratic from standard form using suitable methods (written lesson not published)
• Q15 · Explore how the quadratic formula is developed (written lesson not published)
• Q16 · Solve real-root quadratic equations by factoring, formula, or graphing (written lesson not published)
• Q17 · Find zeros and maximum or minimum values from a graph or equation (written lesson not published)
• Q18 · Solve realistic problems modelled by quadratic relations (written lesson not published)

Linear systems, line segments, circles, geometric verification, and the 2022 slope addendum.

• G1 · Find slope from two points and write a line equation (published written lesson) (2022 transition addendum)
• G2 · Use slopes of parallel and perpendicular lines (published written lesson) (2022 transition addendum)
• G3 · Translate among common forms of a line equation (published written lesson) (2022 transition addendum)
• G4 · Solve two-variable linear systems by substitution or elimination (published written lesson)
• G5 · Model and solve real situations with linear systems (published written lesson)
• G6 · Develop and use the midpoint formula (published written lesson)
• G7 · Develop and use the distance formula for line segments (published written lesson)
• G8 · Develop the equation of a circle centred at the origin (published written lesson)
• G9 · Find a circle radius, write its equation, and sketch its graph (published written lesson)
• G10 · Solve problems using slope, distance, and midpoint (published written lesson)
• G11 · Investigate properties of geometric figures (published written lesson)
• G12 · Verify geometric properties with algebra and coordinates (published written lesson)
• G13 · Plan a multi-step coordinate proof of a geometric property (published written lesson)

Similar triangles, right-triangle ratios, and sine and cosine laws for acute triangles.

• T1 · Use sine, cosine, and tangent in right triangles (published written lesson)
• T2 · Investigate equal angles and proportional sides in similar triangles (published written lesson)
• T3 · Compare similarity and congruence (published written lesson)
• T4 · Solve realistic problems with similar triangles (published written lesson)
• T5 · Find right-triangle sides and angles using ratios and Pythagoras (published written lesson)
• T6 · Apply right-triangle trigonometry to real situations (published written lesson)
• T7 · Explore the development of the sine law for acute triangles (published written lesson)
• T8 · Explore the development of the cosine law for acute triangles (published written lesson)
• T9 · Find acute-triangle sides and angles with sine or cosine law (published written lesson)
• T10 · Solve real problems involving acute triangles (published written lesson)

For y = x² − 4x + 3, find the outputs at x = 0, 1, 2, 3, 4.

Worked method: Substitute each x: the outputs are 3, 0, −1, 0, 3. The first differences are −3, −1, 1, 3; the second differences are 2, 2, 2. The constant second difference is a clue that this is quadratic.

Find the equation of the line through (1, 3) and (3, 7).

Worked method: The rise is 7 − 3 = 4 and the run is 3 − 1 = 2, so the slope is 4 ÷ 2 = 2. Use y = 2x + b and (1, 3): 3 = 2 + b, so b = 1. The line is y = 2x + 1.

A right triangle has legs 6 cm and 8 cm. Find the angle opposite the 6 cm leg.

Worked method: For that angle, opposite ÷ adjacent = 6 ÷ 8 = 0.75. Therefore tan θ = 0.75 and θ ≈ 36.9°. Check that the angle is below 45° because the opposite leg is shorter than the adjacent leg.

For y = x² + 2x, find the outputs when x = 0, 1, 2, 3 and their second differences.

Find the equation of the line through (0, −2) and (2, 4).