DoAssignment.ca
Ontario Grade 10 Applied math (MFM2P)
Browse the full MFM2P topic map, with starter examples and practice. Written lessons are added only after review and publication; the topic map itself is not a completed lesson library.
Publication status
0 of 34 written lessons published
The topic map covers the course expectations. A topic marked “written lesson not published” remains available for practice and tutoring, but does not have a reviewed written lecture yet.
MFM2P
Topics by strand
Similarity, right-triangle trigonometry, measurement systems, surface area, and volume.
- M1 · Solve practical problems with similar triangles (written lesson not published)
- M2 · Investigate properties of similar triangles (written lesson not published)
- M3 · Find corresponding side lengths in similar triangles (written lesson not published)
- M4 · Define sine, cosine, and tangent from similar right triangles (written lesson not published)
- M5 · Find right-triangle sides and angles using ratios and Pythagoras (written lesson not published)
- M6 · Solve real measurement problems with right-triangle trigonometry (written lesson not published)
- M7 · Describe how trigonometry is used in an occupation (written lesson not published)
- M8 · Solve measurement problems using imperial units (written lesson not published)
- M9 · Convert within and between metric and imperial systems (written lesson not published)
- M10 · Develop the surface-area relationship for a pyramid (written lesson not published)
- M11 · Solve surface-area and volume problems with combined solids (written lesson not published)
- M12 · Develop the sphere-volume formula using cylinder and cone relationships (written lesson not published) (2022 transition addendum)
Equations, slope, graphs, and systems of linear relations.
- G1 · Find where two linear models have the same value (written lesson not published)
- G2 · Solve first-degree equations including fractional coefficients (written lesson not published)
- G3 · Isolate and evaluate a variable in a formula (written lesson not published)
- G4 · Convert a line equation to slope-intercept form (written lesson not published)
- G5 · Connect rate of change to slope as rise over run (written lesson not published)
- G6 · Identify slope-intercept form and horizontal or vertical lines (written lesson not published)
- G7 · Explain the meanings of slope and intercept on a graph (written lesson not published)
- G8 · Investigate slope direction, steepness, and parallel lines (written lesson not published)
- G9 · Graph lines by hand using slope or intercepts (written lesson not published)
- G10 · Write a line equation from a graph, point, or slope (written lesson not published)
- G11 · Find a linear-system intersection graphically (written lesson not published)
- G12 · Solve linear systems by substitution or elimination (written lesson not published)
Quadratic expressions, parabolas, and interpretation of graphs.
- Q1 · Recognize quadratic tables by constant second differences and graph the parabola (written lesson not published)
- Q2 · Expand products and squares of binomials (written lesson not published)
- Q3 · Factor quadratics using a common factor (written lesson not published)
- Q4 · Factor simple trinomials of the form x² + bx + c (written lesson not published)
- Q5 · Factor a difference of squares (written lesson not published)
- Q6 · Collect quadratic data and draw a curve of best fit (written lesson not published)
- Q7 · Identify the vertex, axis, intercepts, and extrema of a parabola (written lesson not published)
- Q8 · Connect expanded and factored quadratic forms to one graph (written lesson not published)
- Q9 · Solve real problems by interpreting quadratic graphs (written lesson not published)
- Q10 · Interpret quadratic graph features in experimental data (written lesson not published)
Worked examples
Start with worked Grade 10 examples
These original examples introduce selected MFM2P topics. The full topic map is not a complete set of written lessons or a substitute for your teacher’s assignments. The Q, G, T, and M topic labels below are study-guide labels, not official Ontario expectation codes.
A 1.5 m pole casts a 2 m shadow. At the same time, a tree casts an 8 m shadow. How tall is the tree?
Worked method: The sunlight makes the same angle, so height ÷ shadow is the same. Write 1.5 ÷ 2 = h ÷ 8. Multiply: h = 8 × 1.5 ÷ 2 = 6 m. The tree is 6 m tall.
فارسی · توضیح مثال
یک میله 1.5 متری سایه 2 متری دارد. همزمان سایه یک درخت 8 متر است. بلندی درخت چقدر است؟ زاویه تابش خورشید یکسان است، پس نسبت بلندی به سایه برابر است: 1.5 ÷ 2 = h ÷ 8. بنابراین h = 8 × 1.5 ÷ 2 = 6 متر.
Plan A costs CAD 10 plus CAD 5 per visit. Plan B costs CAD 18 plus CAD 3 per visit. After how many visits do they cost the same?
Worked method: Let x be visits. Set 10 + 5x = 18 + 3x. Subtract 3x and 10 to get 2x = 8, so x = 4. Both plans then cost CAD 30.
فارسی · توضیح مثال
طرح A ده دلار ثابت و 5 دلار برای هر بازدید دارد. طرح B هجده دلار ثابت و 3 دلار برای هر بازدید دارد. پس از چند بازدید هزینهها برابر میشوند؟ اگر x شمار بازدیدها باشد، 10 + 5x = 18 + 3x. پس 2x = 8 و x = 4؛ هزینه هر دو طرح 30 دلار است.
The outputs for x = 0, 1, 2, 3, 4 are 0, 3, 4, 3, 0. What does the pattern suggest about the graph?
Worked method: The outputs rise to 4 at x = 2, then fall symmetrically. The graph has a maximum at (2, 4) and crosses the x-axis at x = 0 and x = 4.
فارسی · توضیح مثال
خروجیها برای x = 0, 1, 2, 3, 4 برابر 0، 3، 4، 3، 0 هستند. الگو چه چیزی درباره نمودار نشان میدهد؟ خروجیها تا 4 در x = 2 بالا میروند و سپس بهطور متقارن پایین میآیند. بیشینه نمودار در (2, 4) است و محور x را در 0 و 4 قطع میکند.
Try independently, then check
Write your own solution before opening each answer. If a step is unclear, review the matching topic or a Grade 9 prerequisite.
A 2 m post casts a 3 m shadow. A nearby building casts a 12 m shadow. Find the building height.
Show worked answer
2 ÷ 3 = h ÷ 12, so h = 12 × 2 ÷ 3 = 8 m.
فارسی · تمرین و پاسخ
ستون 2 متری سایه 3 متری و ساختمانی در نزدیکی سایه 12 متری دارد. بلندی ساختمان را بیابید. 2 ÷ 3 = h ÷ 12، پس h = 12 × 2 ÷ 3 = 8 متر.
Plan A costs CAD 12 + CAD 4 per visit; Plan B costs CAD 24 + CAD 2 per visit. When are they equal?
Show worked answer
12 + 4x = 24 + 2x gives x = 6 visits. Both cost CAD 36.
فارسی · تمرین و پاسخ
طرح A برابر 12 دلار ثابت و 4 دلار برای هر بازدید، و طرح B برابر 24 دلار ثابت و 2 دلار برای هر بازدید است. چه زمانی برابرند؟ از 12 + 4x = 24 + 2x به x = 6 بازدید میرسیم. هر دو 36 دلارند.
Mathematical processes across topics
These processes are practised throughout the course, rather than listed as separate lessons.
- Problem solving (حل مسئله)
- Reasoning and proving (استدلال و اثبات)
- Selecting tools and computational strategies (انتخاب ابزار و راهبردهای محاسباتی)
- Reflecting (بازاندیشی)
- Connecting (پیوند دادن مفاهیم)
- Representing (بازنمایی)
- Communicating (بیان و انتقال اندیشه)
Source and coverage
The topic map follows the official Ontario mathematics curriculum and the MFM2P transition addendum. Topic titles are concise study-guide paraphrases; consult the official documents for exact expectations. Compare both Grade 10 paths or review MTH1W prerequisites.