DoAssignment study guide
Ontario Grade 10 Applied Math (MFM2P) curriculum and lessons
Browse the complete MFM2P topic map, with starter examples and practice. Written lessons are added only after quality review and publication.
Course overview
Grade 10 Ontario Applied Math (MFM2P) course overview
This independent guide covers Grade 10 Applied Mathematics (MFM2P). Its 3 course sections lead to the complete topic map below; open a written lesson where one has been published. Read the official Ontario curriculum for exact requirements.
این راهنمای مستقل دربارهٔ ریاضی کاربردی پایه دهم انتاریو (MFM2P) است. از بخش‌های زیر برای پیدا کردن موضوع مورد نظر و درس‌های منتشرشده استفاده کنید. برنامهٔ درسی رسمی انتاریو
Course pathway: Applied
مسیر تحصیلی: کاربردی
- M · Measurement and Trigonometry (اندازه‌گیری و مثلثات)
- G · Modelling Linear Relations (مدل‌سازی روابط خطی)
- Q · Quadratic Relations (روابط درجه دوم)
Course questions
Studying MFM2P: topics, lessons, and official requirements
The course map includes Measurement and Trigonometry, Modelling Linear Relations, Quadratic Relations. Follow the complete section list above for the full study path.
درس ریاضی کاربردی پایه دهم انتاریو (MFM2P) چه مباحثی دارد؟ از جمله مباحث این درس اندازه‌گیری و مثلثات، مدل‌سازی روابط خطی، روابط درجه دوم است. فهرست کامل بخش‌ها در بالای صفحه قرار دارد.
32 of 34 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 کاربردی پایه دهم انتاریو را از کجا پیدا کنم؟ اکنون 32 درس از 34 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.
Publication status
32 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.
Start with a reviewed lesson
Quadratic tables and graphs
Open the published MFM2P lesson for Recognize quadratic tables by constant second differences and graph the parabola. Then return to the course map to choose your next topic.
Read the free Quadratic tables and graphs lesson
درس جدول‌ها و نمودارهای درجه دوم را بخوانید و سپس موضوع بعدی را از فهرست درس انتخاب کنید.
Free published lessons
Start learning MFM2P
These lessons are public, free to read, and connected to the full course map below.
A triangle can help you measure something that is too tall or difficult to reach. For example, you can compare the shadow of a tree…
Suppose two services charge different amounts as you use them. At first, one may cost less. Later, the other may cost less. The point…
You already know that a straight-line graph goes up or down by the same amount every step — that is a linear relationship. But what…
A small road sign and a larger version can have different side lengths but the same shape. Triangles can work the same way. In this…
An equation says that two expressions have the same value. Solving it means finding the value of the variable that makes the…
You already know how to multiply a monomial by a bracket — that is Grade 9 work. This lesson takes the next step: multiplying a…
Suppose a triangle is enlarged without changing its shape. Each side becomes longer by the same multiplier. The enlarged triangle is…
A formula is a rule that connects quantities. For example, the formula for the perimeter of a rectangle uses its length and width.…
MFM2P
Topics by strand
Similarity, right-triangle trigonometry, measurement systems, surface area, and volume.
- M1 · Solve practical problems with similar triangles (published written lesson)
- M2 · Investigate properties of similar triangles (published written lesson)
- M3 · Find corresponding side lengths in similar triangles (published written lesson)
- M4 · Define sine, cosine, and tangent from similar right triangles (published written lesson)
- M5 · Find right-triangle sides and angles using ratios and Pythagoras (published written lesson)
- M6 · Solve real measurement problems with right-triangle trigonometry (published written lesson)
- M7 · Describe how trigonometry is used in an occupation (published written lesson)
- 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 (published written lesson)
- M11 · Solve surface-area and volume problems with combined solids (published written lesson)
- M12 · Develop the sphere-volume formula using cylinder and cone relationships (published written lesson) (2022 transition addendum)
Equations, slope, graphs, and systems of linear relations.
- G1 · Find where two linear models have the same value (published written lesson)
- G2 · Solve first-degree equations including fractional coefficients (published written lesson)
- G3 · Isolate and evaluate a variable in a formula (published written lesson)
- G4 · Convert a line equation to slope-intercept form (published written lesson)
- G5 · Connect rate of change to slope as rise over run (published written lesson)
- G6 · Identify slope-intercept form and horizontal or vertical lines (published written lesson)
- G7 · Explain the meanings of slope and intercept on a graph (published written lesson)
- G8 · Investigate slope direction, steepness, and parallel lines (published written lesson)
- G9 · Graph lines by hand using slope or intercepts (published written lesson)
- G10 · Write a line equation from a graph, point, or slope (published written lesson)
- G11 · Find a linear-system intersection graphically (published written lesson)
- G12 · Solve linear systems by substitution or elimination (published written lesson)
Quadratic expressions, parabolas, and interpretation of graphs.
- Q1 · Recognize quadratic tables by constant second differences and graph the parabola (published written lesson)
- Q2 · Expand products and squares of binomials (published written lesson)
- Q3 · Factor quadratics using a common factor (published written lesson)
- Q4 · Factor simple trinomials of the form x² + bx + c (published written lesson)
- Q5 · Factor a difference of squares (published written lesson)
- Q6 · Collect quadratic data and draw a curve of best fit (published written lesson)
- Q7 · Identify the vertex, axis, intercepts, and extrema of a parabola (published written lesson)
- Q8 · Connect expanded and factored quadratic forms to one graph (published written lesson)
- Q9 · Solve real problems by interpreting quadratic graphs (published written lesson)
- Q10 · Interpret quadratic graph features in experimental data (published written lesson)
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 published written lessons or a substitute for official course materials and assignments. The 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. Titles are concise study-guide paraphrases; consult the official source for exact requirements. Compare both Grade 10 paths.
Sources and editorial process
Curriculum-aligned and reviewed before publication
This independent study guide follows the official course source. It is not an official government, school, or university publication.
Lessons may be AI-assisted or editorially prepared. Published content is checked for structure, notation, calculations, course boundaries, and readability before release. Because corrections can still be necessary, readers can report a problem.
Related courses and next steps
Review a prerequisite or explore a related course. Follow your school or university requirements when choosing your next course.
پیش‌نیازها و درس‌های مرتبط را مرور کنید و برای انتخاب درس بعدی، مقررات مدرسه یا دانشگاه را بررسی کنید.
- MPM2D · Grade 10 Academic Mathematics (Ontario) ریاضی نظری پایه دهم انتاریو
- MBF3C · Grade 11 Foundations for College Mathematics (Ontario) مبانی ریاضی کالج پایه یازدهم انتاریو
- MCF3M · Grade 11 Functions and Applications (Ontario) تابع‌ها و کاربردهای پایه یازدهم انتاریو
- MTH1W · Grade 9 Mathematics (Ontario) ریاضی پایه نهم انتاریو
Get help while studying MFM2P
Use the MFM2P lessons and topic map first, then try a question on your own. For example, bring an attempt from Measurement and Trigonometry and Modelling Linear Relations and mark the first step you cannot explain. A live tutor can help you show each step of your attempt and compare it with a worked example; ask them to confirm they can support your particular course before booking a regular session.
Explore math tutoring · Request an eligible free 30-minute introduction. Requests go to approved tutors who list the selected subject and language; a session is confirmed only if one accepts.
ابتدا درس‌ها و فهرست مباحث MFM2P را بخوانید و یک سؤال را خودتان حل کنید. نخستین گام مبهم را مشخص کنید تا در جلسه بتوانید گام‌های تلاش خود را نشان دهید و آن را با یک نمونهٔ حل‌شده مقایسه کنید. راهنمای معلم ریاضی را ببینید یا جلسهٔ معارفهٔ رایگان ۳۰ دقیقه‌ای درخواست کنید. دربارهٔ امکان تدریس همین درس از معلم تأیید بگیرید.