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Free Math Worksheets — Over 100k free practice problems on Khan Academy

Looking for free math worksheets.

You’ve found something even better!

That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!

Just choose your grade level or topic to get access to 100% free practice questions:

Kindergarten, basic geometry, pre-algebra, algebra basics, high school geometry.

  • Trigonometry

Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

  • Addition and subtraction
  • Place value (tens and hundreds)
  • Addition and subtraction within 20
  • Addition and subtraction within 100
  • Addition and subtraction within 1000
  • Measurement and data
  • Counting and place value
  • Measurement and geometry
  • Place value
  • Measurement, data, and geometry
  • Add and subtract within 20
  • Add and subtract within 100
  • Add and subtract within 1,000
  • Money and time
  • Measurement
  • Intro to multiplication
  • 1-digit multiplication
  • Addition, subtraction, and estimation
  • Intro to division
  • Understand fractions
  • Equivalent fractions and comparing fractions
  • More with multiplication and division
  • Arithmetic patterns and problem solving
  • Quadrilaterals
  • Represent and interpret data
  • Multiply by 1-digit numbers
  • Multiply by 2-digit numbers
  • Factors, multiples and patterns
  • Add and subtract fractions
  • Multiply fractions
  • Understand decimals
  • Plane figures
  • Measuring angles
  • Area and perimeter
  • Units of measurement
  • Decimal place value
  • Add decimals
  • Subtract decimals
  • Multi-digit multiplication and division
  • Divide fractions
  • Multiply decimals
  • Divide decimals
  • Powers of ten
  • Coordinate plane
  • Algebraic thinking
  • Converting units of measure
  • Properties of shapes
  • Ratios, rates, & percentages
  • Arithmetic operations
  • Negative numbers
  • Properties of numbers
  • Variables & expressions
  • Equations & inequalities introduction
  • Data and statistics
  • Negative numbers: addition and subtraction
  • Negative numbers: multiplication and division
  • Fractions, decimals, & percentages
  • Rates & proportional relationships
  • Expressions, equations, & inequalities
  • Numbers and operations
  • Solving equations with one unknown
  • Linear equations and functions
  • Systems of equations
  • Geometric transformations
  • Data and modeling
  • Volume and surface area
  • Pythagorean theorem
  • Transformations, congruence, and similarity
  • Arithmetic properties
  • Factors and multiples
  • Reading and interpreting data
  • Negative numbers and coordinate plane
  • Ratios, rates, proportions
  • Equations, expressions, and inequalities
  • Exponents, radicals, and scientific notation
  • Foundations
  • Algebraic expressions
  • Linear equations and inequalities
  • Graphing lines and slope
  • Expressions with exponents
  • Quadratics and polynomials
  • Equations and geometry
  • Algebra foundations
  • Solving equations & inequalities
  • Working with units
  • Linear equations & graphs
  • Forms of linear equations
  • Inequalities (systems & graphs)
  • Absolute value & piecewise functions
  • Exponents & radicals
  • Exponential growth & decay
  • Quadratics: Multiplying & factoring
  • Quadratic functions & equations
  • Irrational numbers
  • Performing transformations
  • Transformation properties and proofs
  • Right triangles & trigonometry
  • Non-right triangles & trigonometry (Advanced)
  • Analytic geometry
  • Conic sections
  • Solid geometry
  • Polynomial arithmetic
  • Complex numbers
  • Polynomial factorization
  • Polynomial division
  • Polynomial graphs
  • Rational exponents and radicals
  • Exponential models
  • Transformations of functions
  • Rational functions
  • Trigonometric functions
  • Non-right triangles & trigonometry
  • Trigonometric equations and identities
  • Analyzing categorical data
  • Displaying and comparing quantitative data
  • Summarizing quantitative data
  • Modeling data distributions
  • Exploring bivariate numerical data
  • Study design
  • Probability
  • Counting, permutations, and combinations
  • Random variables
  • Sampling distributions
  • Confidence intervals
  • Significance tests (hypothesis testing)
  • Two-sample inference for the difference between groups
  • Inference for categorical data (chi-square tests)
  • Advanced regression (inference and transforming)
  • Analysis of variance (ANOVA)
  • Scatterplots
  • Data distributions
  • Two-way tables
  • Binomial probability
  • Normal distributions
  • Displaying and describing quantitative data
  • Inference comparing two groups or populations
  • Chi-square tests for categorical data
  • More on regression
  • Prepare for the 2020 AP®︎ Statistics Exam
  • AP®︎ Statistics Standards mappings
  • Polynomials
  • Composite functions
  • Probability and combinatorics
  • Limits and continuity
  • Derivatives: definition and basic rules
  • Derivatives: chain rule and other advanced topics
  • Applications of derivatives
  • Analyzing functions
  • Parametric equations, polar coordinates, and vector-valued functions
  • Applications of integrals
  • Differentiation: definition and basic derivative rules
  • Differentiation: composite, implicit, and inverse functions
  • Contextual applications of differentiation
  • Applying derivatives to analyze functions
  • Integration and accumulation of change
  • Applications of integration
  • AP Calculus AB solved free response questions from past exams
  • AP®︎ Calculus AB Standards mappings
  • Infinite sequences and series
  • AP Calculus BC solved exams
  • AP®︎ Calculus BC Standards mappings
  • Integrals review
  • Integration techniques
  • Thinking about multivariable functions
  • Derivatives of multivariable functions
  • Applications of multivariable derivatives
  • Integrating multivariable functions
  • Green’s, Stokes’, and the divergence theorems
  • First order differential equations
  • Second order linear equations
  • Laplace transform
  • Vectors and spaces
  • Matrix transformations
  • Alternate coordinate systems (bases)

Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

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What are teachers saying about Khan Academy’s interactive math worksheets?

“My students love Khan Academy because they can immediately learn from their mistakes, unlike traditional worksheets.”

Is Khan Academy free?

Khan Academy’s practice questions are 100% free—with no ads or subscriptions.

What do Khan Academy’s interactive math worksheets cover?

Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

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Khan Academy is a nonprofit with a mission to provide a free, world-class education to anyone, anywhere.

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Free Math Printable Worksheets with Answer Keys and Activities

Other free resources.

Feel free to download and enjoy these free worksheets on functions and relations. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

  • Long Division with Remainders
  • Long Division with Remainders #2 (Zeros in the Quotient)
  • Long Division with 2 Digit Divisors
  • Whole Number by Unit Fraction
  • Equation of Circle
  • Simplify Imaginary Numbers
  • Adding and Subtracting Complex Numbers
  • Multiplying Complex Numbers
  • Dividing Complex Numbers
  • Dividing Complex Number (Advanced)
  • End of Unit, Review Sheet
  • Distance Formula
  • Simplify Rational Exponents (Algebra 2)
  • Solve Equations with Rational Exponents (Algebra 2)
  • Solve Equations with variables in Exponents (Algebra 2)
  • Exponential Growth (no answer key on this one, sorry)
  • Compound Interest Worksheet #1 (No logs)
  • Compound Interest Worksheet (Logarithms required)
  • Factor Trinomials Worksheet
  • Factor by Grouping
  • Domain and Range (Algebra 1)
  • Functions vs Relations (Distinguish function from relation, state domain etc..) (Algebra 2)
  • Evaluating Functions (Algebra 2)
  • 1 to 1 Functions (Algebra 2)
  • Composition of Functions (Algebra 2)
  • Inverse Functions Worksheet (Algebra 2)
  • Operations with Functions (Algebra 2)
  • Functions Review Worksheet (Algebra 2)
  • Logarithmic Equations
  • Properties of Logarithms Worksheet
  • Product Rule of Logarithms
  • Power Rule of Logarithms
  • Quotient Rule of Logarithms
  • Solve Quadratic Equations by Factoring
  • Quadratic Formula Worksheets (3 different sheets)
  • Quadratic Formula Worksheet (Real solutions)
  • Quadratic Formula (Complex solutions)
  • Quadratic Formula (Both real and complex solutions)
  • Discriminant and Nature of the Roots
  • Solve Quadratic Equations by Completing the Square
  • Sum and Product of Roots
  • Radical Equations
  • Mixed Problems on Writing Equations of Lines
  • Slope Intercept Form Worksheet
  • Standard Form Worksheet
  • Point Slope Worksheet
  • Write Equation of Line from the Slope and 1 Point
  • Write Equation of Line From Two Points
  • Equation of Line Parallel to Another Line and Through a Point
  • Equation of Line Perpendicular to Another Line and Through a Point
  • Slope of a Line
  • Perpendicular Bisector of Segment
  • Write Equation of Line Mixed Review
  • Word Problems
  • Multiplying Monomials Worksheet
  • Multiplying and Dividing Monomials Sheet
  • Adding and Subtracting Polynomials worksheet
  • Multiplying Monomials with Polynomials Worksheet
  • Multiplying Binomials Worksheet
  • Multiplying Polynomials
  • Simplifying Polynomials
  • Factoring Trinomials
  • Operations with Polynomials Worksheet
  • Dividing Radicals
  • Simplify Radicals Worksheet
  • Adding Radicals
  • Multiplying Radicals Worksheet
  • Radicals Review (Mixed review worksheet on radicals and square roots)
  • Rationalizing the Denominator (Algebra 2)
  • Radical Equations (Algebra 2)
  • Solve Systems of Equations Graphically
  • Solve Systems of Equations by Elimination
  • Solve by Substitution
  • Solve Systems of Equations (Mixed Review)
  • Activity on Systems of Equations (Create an advertisement for your favorite method to Solve Systems of Equations )
  • Real World Connections (Compare cell phone plans)
  • Identifying Fractions

Trigonomnetry

  • Law of Sines and Cosines Worksheet (This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for a single triangle's side or angle)
  • Law of Sines
  • Ambiguous Case of the Law of Sines
  • Law of Cosines
  • Vector Worksheet
  • Sine, Cosine, Tangent, to Find Side Length
  • Sine, Cosine, Tangent Chart
  • Inverse Trig Functions
  • Real World Applications of SOHCATOA
  • Mixed Review
  • Unit Circle Worksheet
  • Graphing Sine and Cosine Worksheet
  • Sine Cosine Graphs with Vertical Translations
  • Sine, Cosine, Tangent Graphs with Phase Shifts
  • Sine, Cosine, Tangent Graphs with Change in Period, Amplitude and Phase Shifts (All Translations)
  • Tangent Equation, Graph Worksheet
  • Graphing Sine, Cosine, Tangent with Change in Period
  • Cumulative, Summative Worksheet on Periodic Trig Functions - period, amplitude, phase shift, radians, degrees,unit circle
  • Ratio and Proportion
  • Similar Polygons
  • Area of Triangle
  • Interior Angles of Polygons
  • Exterior Angles of Polygons

maths paper assignment

Arcs and Angles formed by Intersecting Chords

diagram

Angles and arcs formed by tangents and secants

Farc Narc Formula

Tangents, Secants and Side Lengths

Math Worksheet on the Angle formed by the intersection of a Tangent and a Chord

Angle Tangent Chord

Cumulative Review Problems of All Formulas

Big Circle

  • Associated Powerpoint
  • Associated PowerPoint
  • System of Linear Equations Worksheet
  • System of Linear Equations - Real World Application
  • Compositions of Reflections. Reflections Over Intersecting Lines as Rotations

All of these worksheets and activities are available for free so long as they are used solely for educational, noncommercial purposes and are not distributed outside of a specific teacher's classroom.

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

Popular pages @ mathwarehouse.com.

Surface area of a Cylinder

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Home » GRADE 7 WORKSHEETS, TESTS, ASSIGNMENTS, INVESTIGATIONS AND PROJECTS

GRADE 7 WORKSHEETS, TESTS, ASSIGNMENTS, INVESTIGATIONS AND PROJECTS

GRADE 7 WORKSHEETS, TESTS, ASSIGNMENTS, INVESTIGATIONS AND PROJECTS

Download and print Grade 7 worksheets, assignments, investigations, tests and projects for all subjects.

These Cross-curricular resources will help your learners begin to make deeper connections between concepts, connect famous people to history and literature, and understand real-world applications for maths and all other grade 7 subjects.

ARTS AND CULTURE

ECONOMICS AND MANAGEMENT SCIENCES (EMS)

LIFE ORIENTATION (LO)

MATHEMATICS

NATURAL SCIENCES

SOCIAL SCIENCES

Home

Reading & Math for K-5

  • Kindergarten
  • Learning numbers
  • Comparing numbers
  • Place Value
  • Roman numerals
  • Subtraction
  • Multiplication
  • Order of operations
  • Drills & practice

Measurement

  • Factoring & prime factors

Proportions

  • Shape & geometry
  • Data & graphing
  • Word problems
  • Children's stories
  • Leveled Stories
  • Context clues
  • Cause & effect
  • Compare & contrast
  • Fact vs. fiction
  • Fact vs. opinion
  • Main idea & details
  • Story elements
  • Conclusions & inferences
  • Sounds & phonics
  • Words & vocabulary
  • Reading comprehension
  • Early writing
  • Numbers & counting
  • Simple math
  • Social skills
  • Other activities
  • Dolch sight words
  • Fry sight words
  • Multiple meaning words
  • Prefixes & suffixes
  • Vocabulary cards
  • Other parts of speech
  • Punctuation
  • Capitalization
  • Cursive alphabet
  • Cursive letters
  • Cursive letter joins
  • Cursive words
  • Cursive sentences
  • Cursive passages
  • Grammar & Writing

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Math Workbooks for Grade 6

Download & Print From only $2.60

Sixth Grade Math Worksheets

Free grade 6 worksheets from k5 learning.

Our printable grade 6 math worksheets delve deeper into earlier grade math topics (4 operations, fractions, decimals, measurement, geometry) as well as introduce exponents, proportions, percents and integers .

Choose your grade 6 topic:

4 operations.

Place Value & Scientific Notation

Add & Subtract

Multiply & Divide

Decimals & Percents

Fractions to / from Decimals

Decimals - Add and Subtract

Decimals  - Multiply

Decimals - Divide

Add & Subtract Fractions

Multiply & Divide Fractions

Converting Fractions

maths paper assignment

Sample Grade 6 Math Worksheet

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Early math review

Kindergarten, basic geometry and measurement, pre-algebra, algebra basics, high school geometry, trigonometry, statistics and probability, high school statistics, ap®︎/college statistics, college algebra, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra, 6th grade (illustrative mathematics), 7th grade (illustrative mathematics), 8th grade (illustrative mathematics), algebra 1 (illustrative mathematics), 3rd grade (eureka math/engageny), 4th grade (eureka math/engageny), 5th grade (eureka math/engageny), 6th grade (eureka math/engageny), 7th grade (eureka math/engageny), 8th grade (eureka math/engageny), algebra 1 (eureka math/engageny), geometry (eureka math/engageny), algebra 2 (eureka math/engageny), precalculus (eureka math/engageny), 3rd grade foundations (eureka math/engageny), 4th grade foundations (eureka math/engageny), 5th grade foundations (eureka math/engageny), 6th grade foundations (eureka math/engageny), 7th grade foundations (eureka math/engageny), 8th grade foundations (eureka math/engageny), integrated math 1, integrated math 2, integrated math 3, arithmetic (all content), algebra (all content), geometry (all content), get ready for 3rd grade, get ready for 4th grade, get ready for 5th grade, get ready for 6th grade, get ready for 7th grade, get ready for 8th grade, get ready for algebra 1, get ready for geometry, get ready for algebra 2, get ready for precalculus, map recommended practice, get ready for ap® calculus, get ready for ap® statistics, grade 6 math (fl b.e.s.t.), grade 7 math (fl b.e.s.t.), grade 8 math (fl b.e.s.t.), algebra 1 (fl b.e.s.t.), geometry (fl b.e.s.t.), algebra 2 (fl b.e.s.t.), grade 6 (virginia), grade 7 (virginia), grade 8 (virginia), grade 3 (fl b.e.s.t.), grade 4 math (fl b.e.s.t.), grade 5 math (fl b.e.s.t.), class 9 (od), class 10 (od).

maths paper assignment

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Homework Guidelines for Mathematics

Mathematics is a language, and as such it has standards of writing which should be observed. In a writing class, one must respect the rules of grammar and punctuation, one must write in organized paragraphs built with complete sentences, and the final draft must be a neat paper with a title. Similarly, there are certain standards for mathematics assignments.

How should I format my homework?

Write your name and class number clearly at the top of at least the first page, along with the assignment number, the section number(s), or the page number(s). If you are not stapling or paper-clipping the pages together, then put your name (or at least your initials) on all the pages.

Use standard-sized paper (8.5" × 11" for North Americans; A4 for others), with no "fringe" running down the side as a result of the paper’s having been torn out of a spiral notebook. Do not use sticky-notes, scented stationery, or other nonstandard types of paper.

Use standard-weight paper , not onion skin, construction paper, or otherwise abnormally thin or heavy paper.

Attach your pages with a paper clip or staple. Do not fold, tear, spit on, or otherwise "dog-ear" the pages. It is better that the pages be handed in loose (with your name on each sheet) than that the corners be folded or shredded.

Clearly indicate the number of the exercise you are doing. If you accidentally do a problem out of order, or separate one part of the problem from the rest, then include a note to the grader, directing the grader to the missed problem or work.

Write out the original exercise (except in the case of word problems, which are too long).

Do your work in pencil, with mistakes cleanly erased, not crossed or scratched out. If you work in ink, use "white-out" to correct mistakes.

Write legibly (that is, suitably large and suitably dark) ; if the grader can't read your answer, it's wrong.

Write neatly across the page , with each succeeding problem below the preceding one, not off to the right. Do not work in multiple columns down the page (like a newspaper); your page should contain only one column.

Keep work within the margins . If you run out of room at the end of a problem, continue onto the next page; do not try to squeeze lines together at the bottom of the sheet. Do not lap over the margins on the left or right; do not wrap writing around the notebook-paper holes.

Do not squeeze the problems together, with one problem running into the next. Use sufficient space for each problem, with at least one blank line between the end of one problem and the beginning of the next.

Do "scratch work," but do it on scratch paper ; hand in only the "final draft." Show your steps, but any work that is scribbled in the margins belongs on scratch paper, not on your hand-in homework.

Show your work . This means showing your steps, not just copying the question from the assignment, and then the answer from the back of the book. Show everything in between the question and the answer. Use complete English sentences if the meaning of the mathematical sentences is not otherwise clear. For your work to be complete, you need to explain your reasoning and make your computations clear.

For tables and graphs, use a ruler to draw the straight lines , and clearly label the axes, the scale, and the points of interest. Use a consistent scale on the axes, and do a T-chart, unless instructed otherwise. Also, make your table or graph large enough to be clear. If you can fit more than three or four graphs on one side of a sheet of paper, then you're drawing them too small.

Do not invent your own notation and abbreviations, and then expect the grader to figure out what you meant. For instance, do not use "#" in your sentence if you mean "pounds" or "numbers". Do not use the "equals" sign ("=") to mean "indicates", "stands for", "leads to", "is related to", or anything else in a sentence; use actual words. The equals sign should be used only in equations , and only to mean "is equal to".

Do not do magic. Plus/minus signs ("±"), "= 0", radicals, and denominators should not disappear in the middle of your calculations, only to mysteriously reappear at the end. Each step should be complete.

If the problem is of the "Explain" or "Write in your own words" type, then copying the answer from the back of the book, or the definition from the chapter, is unacceptable. Write the answer in your words, not the text's.

Remember to put your final answer at the end of your work, and mark it clearly by, for example, underlining it or drawing a box around it. Label your answer appropriately; if the question asks for measured units, make sure to put appropriate units on the answer. If the question is a word problem, the answer should be in words.

In general, write your homework as though you're trying to convince someone that you know what you're talking about.

You should use your instructor or grader as a study aid, in addition to the text, study guides, study groups, and tutoring services. Your work is much easier to grade when you have made your work and reasoning clear, and any difficulties you have in completing the assignment can be better explained by the grader. More importantly, however, completely worked and corrected homework exercises make excellent study guides for the Final. Also, if you develop good habits while working on the homework, you will generally perform better on the tests.

In summary, schools today have made the development of essential skills, the provision of significant and meaningful learning experiences, and the development of the workforce some of its primary goals for student success. As such, they want their instructors to guide the students toward a higher level of confidence and competence. In math, that translates into a greater need for clarity in mathematical writing. The intention on these "Homework Guidelines" is that you and your instructor communicate better, and that you succeed both in your present mathematics courses and in future mathematical communication with co-workers and clients.

For further information, review these examples of acceptable and unacceptable solutions, and this sheet showing neat and messy papers.

Instructors: These "Homework Guidelines" are copyrighted by Elizabeth Stapel.

You are welcome to use these "Homework Guidelines," in part or in whole, as an asset in teaching your own classes. The only conditions of use are that distribution, if any, of the Homework Guidelines be made at no cost to the recipient(s), that the original copyright notice be retained on copies of this page, and that the following notice be included on all derivative works:

Based on "Homework Guidelines" http://www.purplemath.com/guidline.htm Copyright Elizabeth Stapel Used By Permission

These "Guidelines" are also available as a printer-friendly PDF .

If you would like an example sheet for your students (displaying the differences between acceptable and unacceptable formatting), try this PDF .

URL: https://www.purplemath.com/guidline.htm

Standardized Test Prep

College math, homeschool math.

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  • Prof. Haynes Miller
  • Dr. Nat Stapleton
  • Saul Glasman

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Learning resource types, project laboratory in mathematics.

Next: Revision and Feedback »

In this section, Prof. Haynes Miller and Susan Ruff describe the criteria for good mathematical writing and the components of the writing workshop .

A central goal of the course is to teach students how to write effective, journal-style mathematics papers. Papers are a key way in which mathematicians share research findings and learn about others’ work. For each research project, each student group writes and revises a paper in the style of a professional mathematics journal paper. These research projects are perfect for helping students to learn to write as mathematicians because the students write about the new mathematics that they discover. They own it, they are committed to it, and they put a lot of effort into writing well.

Criteria for Good Writing

In the course, we help students learn to write papers that communicate clearly, follow the conventions of mathematics papers, and are mathematically engaging.

Communicating clearly is challenging for students because doing so requires writing precisely and correctly as well as anticipating readers’ needs. Although students have read textbooks and watched lectures that are worded precisely, they are often unaware of the care with which each word or piece of notation was chosen. So when students must choose the words and notation themselves, the task can be surprisingly challenging. Writing precisely is even more challenging when students write about insights they’re still developing. Even students who do a good job of writing precisely may have a different difficulty: providing sufficient groundwork for readers. When students are deeply focused on the details of their research, it can be hard for them to imagine what the reading experience may be like for someone new to that research. We can help students to communicate clearly by pointing out places within the draft at which readers may be confused by imprecise wording or by missing context.

For most students, the conventions of mathematics papers are unfamiliar because they have not read—much less written—mathematics journal papers before. The students’ first drafts often build upon their knowledge of more familiar genres: humanities papers and mathematics textbooks and lecture notes. So the text is often more verbose or explanatory than a typical paper in a mathematics journal. To help students learn the conventions of journal papers, including appropriate concision, we provide samples and individualized feedback.

Finally, a common student preconception is that mathematical writing is dry and formal, so we encourage students to write in a way that is mathematically engaging. In Spring 2013, for example, one student had to be persuaded that he did not have to use the passive voice. In reality, effective mathematics writing should be efficient and correct, but it should also provide motivation, communicate intuition, and stimulate interest.

To summarize, instruction and feedback in the course address many different aspects of successful writing:

  • Precision and correctness: e.g., mathematical terminology and notation should be used correctly.
  • Audience awareness: e.g., ideas should be introduced with appropriate preparation and motivation.
  • Genre conventions: e.g., in most mathematics papers, the paper’s conclusion is stated in the introduction rather than in a final section titled “Conclusion.”
  • Style: e.g., writing should stimulate interest.
  • Other aspects of effective writing, as needed.

To help students learn to write effective mathematics papers, we provide various resources, a writing workshop, and individualized feedback on drafts.

Writing Resources

Various resources are provided to help students learn effective mathematical writing.

The following prize-winning journal article was annotated to point out various conventions and strategies of mathematical writing. (Courtesy of Mathematical Association of America. Courtesy of a Creative Commons BY-NC-SA license.)

An Annotated Journal Article (PDF)

This document introduces the structure of a paper and provides a miscellany of common mistakes to avoid.

Notes on Writing Mathematics (PDF)

LaTeX Resources

The following PDF, TeX, and Beamer samples guide students to present their work using LaTeX, a high-quality typesetting system designed for the production of technical and scientific documentation. The content in the PDF and TeX documents highlights the structure of a generic student paper.

Sample PDF Document created by pdfLaTeX (PDF)

Sample TeX Document (TEX)

Beamer template (TEX)

The following resources are provided to help students learn and use LaTeX.

LaTeX-Project. “ Obtaining LaTeX .” August 28, 2009.

Downes, Michael. “Short Math Guide for LaTeX.” (PDF) American Mathematical Society . Version 1.09. March 22, 2002.

Oetiker, Tobias, Hubert Partl, et al. “The Not So Short Introduction to LaTeX 2ε.” (PDF) Version 5.01. April 06, 2011.

Reckdahl, Keith. “Using Imported Graphics in LaTeX and pdfLaTeX.” (PDF) Version 3.0.1. January 12, 2006.

Writing Workshop

Each semester there is a writing workshop, led by the lead instructor, which features examples to stimulate discussion about how to write well. In Spring 2013, Haynes ran this workshop during the third class session and used the following slide deck, which was developed by Prof. Paul Seidel and modified with the help of Prof. Tom Mrowka and Prof. Richard Stanley.

The 18.821 Project Report (PDF)

This workshop was held before students had begun to think about the writing component of the course, and it seemed as if the students had to be reminded of the lessons of the workshop when they actually wrote their papers. In future semesters, we plan to offer the writing workshop closer to the time that students are drafting their first paper. We may also focus the examples used in the workshop on the few most important points rather than a broad coverage.

  • Download video

This video features the writing workshop from Spring 2013 and includes instruction from Haynes as well as excerpts of the class discussion.

MIT Open Learning

  • MATHEMATICS INVESTIGATION GRADE 12 - 2022 ASSIGNMENTS

MATHEMATICS (INVESTIGATION: 2022) GRADE 12 NATIONAL SENIOR CERTIFICATE 23 FEBRUARY 2022

INSTRUCTIONS

  • The question paper consists of 5 questions.
  • Answer ALL the questions on the spaces provided on the question paper.
  • Clearly show ALL calculations.
  • Write neatly and legibly.

QUESTION 1: TRANSPORT Mr Dlamini transports people between Butterworth and East London using a bus which has a capacity of 100 people. The transport charge starts with a minimum charge of R8 and thereafter it was increased by R2 for each kilometre. On a particular day the bus was full with passengers from Butterworth. In each and every kilometre there was a passenger getting off while no new passenger entered in the bus. Mr Dlamini was calculating total money in his hand after each passenger was getting out. The total amount he has after each stop can be written as a series as follows: S n = 8 + 10 + 12 + 14 +... Use the series to calculate the following questions: 1.1

  • Term 2 (T2) =…………….. Sum of first two terms (S2) =…………………(2)
  • Express T2 in terms of S1 and S2. ………………………………… (1)
  • Term 3 (T3) =…………….. Sum of first three terms (S3) =…………………(2)
  • Express T3 in terms of S3 and S2. ………………………………… (1)
  • Term 4 (T4) =…………….. Sum of first four terms (S4) =…………………(2)
  • Express T4 in terms of S3 and S4. ………………………………… (1)

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1.4 Write the general formula to find the sum of the above series ………………………………………………… (2) 1.5 Did you observe any pattern from the answers in question 1.1, 1.2 and 1.3. Explain your observation with respect to relation between term and sum of the terms. ……………………………………………………………………………………... ……………………………………………………………………………………… (2) 1.6 Use your deduction in activity question 1.5 to develop a formula between Tn, Sn and Sn-1 where n > 1 and n ∈ ℕ. ………………………………………………………………………………………... (2) 1.7 Calculate T70 using formula identified in question 1.6. ………………………………………………………………………………………… (2) [17]

  • Draw a pattern of roses by means of chords connecting the points given in the circles provided.
  • Connect each point to each other point on the circle by a chord and write the sequence you identified by counting the number of chords (3)

2.2 Write down the general formula for the nth term of sequence. ………………………………………………………………………………………….. …………………………………………………………………………………………. …………………………………………………………………………………………. …………………………………………………………………………………………. (3) 2.3 Hence find the number of lines in the circle with 10 dots ………………………………………………………………………………………….. ………………………………………………………………………………………….. (2) 2.4 Calculate the value of T9 using the formula identified question 1.6 T9=……………………………………………………………………………………… ………………………………………………………………………………….............. (3) 2.5 Describe your findings from activity question 2.3 and 2.4 ………………………………………………………………………………………….. ………………………………………………………………………………………….. (1) [12]

QUESTION 3: POCKET MONEY Mr Reyan made an agreement with his son Smith who is studying in grade 12 as follows. Smith will get pocket money after he finishes all his homework every day. The amount of pocket money will be double the amount previous day. He will start first day with R1. He can use this saving for his matric dance. 3.1 Write the information as a sequence …………………………………………………………………………………………. (1) 3.2 Write the formula for the nth term of above sequence Tn = …………………………………………………………………………………….. (2) 3.3 Write the formula for the sum of n terms of the above series Sn= ……………………………………………………………………………………... (2) 3.4 How much will Smith get on the 20th day if he successfully completed his homework. ………………………………………………………………………………………….. …………………………………………………………………………………………. (2) 3.5 Calculate T20 using the formula identified in question 1.6 T20=…………………………………………………………………………………….. …………………………………………………………………………………………. (2) 3.5 Describe your findings from activity question 3.4 and 3.5 ………………………………………………………………………………………….. …………………………………………………………………………………………. (1) [10]

QUESTION 4: EXPANSION QUESTION: Application 4. Given Sum of an arithmetic series is Sn = 𝑛 2 − 2𝑛 . Determine the equation of Tn of this arithmetic sequence using the findings from previous activities Tn= …………………………………………………………………………………………… ……………………………………………………………………………………………….. (3) [3]

QUESTION 5 : EXPANSION QUESTION : Sum Of Series t is an even number in the series  1 / t +  3 / t +  5 / t + ... t-1 / t 5.1 Determine the number of terms in the series in terms of t. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. (2) 5.2 Determine the sum of the series in terms of t. ………………………………………………………………………………………….. …………………………………………………………………………………………. …………………………………………………………………………………………. …………………………………………………………………………………………. (2) 5.3 Hence, or otherwise, evaluate: (¼ + 3 / 4 ) + ( 1 / 6 +  3 / 6 +  5 / 6 ) + ( 1 / 8 +  3 / 8 +  5 / 8 +  7 / 8 )+ ...  +( 1 / 50 +  3 / 50 + 5 / 50 + ... +  49 / 50  ) ………………………………………………………………………………………….. …………………………………………………………………………………………. …………………………………………………………………………......................... …………………………………………………………………………………………. ………………………………………………………………………………………… ………………………………………………………………………………………… (4) [8] TOTAL: 50

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ISC Class 12 Maths Paper Analysis 2024: Student Feedback, Difficulty Level and Question Paper PDF

Isc 12th maths paper analysis 2024: check the detailed paper analysis, students’ reactions, and teachers' feedback on the difficulty level of today’s isc class 12 maths exam 2024. also, find the link to download the isc 12th maths question paper and answer key 2024..

Gurmeet Kaur

ISC Class 12 Maths  Exam 2024 Highlights

Isc class 12 maths  exam paper analysis 2024.

  • Section A was compulsory.
  • Candidates had to choose any one of the sections C and B.

ISC Class 12 Maths  Paper Analysis 2024: Student Reactions

Students had mixed reactions on the difficulty level of the ISC Maths paper. The majority of students rated the paper medium on the difficulty level. They found certain sections of the paper challenging. The general feedback from students is as follows:

  • Out of the last two optional sections, Section C was easier
  • All questions were from the prescribed syllabus.
  • MCQs were diverse and fairly easy.
  • Questions on integrals were intricate.

ISC Class 12 Maths  Paper Analysis 2024: Expert Review

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maths paper assignment

maths paper assignment

Original EdwardsMaths Papers

Grade 12 Model Assignments

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Grade 12 Eastern Cape Maths June 2023 P2

Grade 12 eastern cape maths june 2023 p1, grade 11 eastern cape maths november 2022 p2, grade 11 eastern cape maths november 2022 p1.

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    Assignment 9 (PDF) Assignment 10 (PDF) Assignment 11 (PDF) Assignment 12 (PDF) Midterm Exam (PDF) Final Assignment (PDF) MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity.

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    Writing. In this section, Prof. Haynes Miller and Susan Ruff describe the criteria for good mathematical writing and the components of the writing workshop. A central goal of the course is to teach students how to write effective, journal-style mathematics papers. Papers are a key way in which mathematicians share research findings and learn ...

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  17. Mathematics Investigation Grade 12

    INSTRUCTIONS The question paper consists of 5 questions. Answer ALL the questions on the spaces provided on the question paper. Clearly show ALL calculations. Write neatly and legibly. QUESTION 1: TRANSPORT Mr Dlamini transports people between Butterworth and East London using a bus which has a capacity of 100 people.

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