--- title: "Integrated Math 3 Tutoring: Integrated Math III Help Online" description: "Integrated Math 3 tutoring online: what is taught in Integrated Math III, from polynomials and logarithms to the Laws of Sines and Cosines and data inference." canonical: https://learn.modernagecoders.com/integrated-math-3-tutoring source: src/pages/integrated-math-3-tutoring.html --- > Integrated Math 3 tutoring online: what is taught in Integrated Math III, from polynomials and logarithms to the Laws of Sines and Cosines and data inference. In short Integrated Math III is the third course of the integrated sequence, usually taken in grade 11. Utah's Secondary Mathematics III groups it into four areas: inference from data; polynomial, rational and radical functions; trigonometry of general triangles and radians; and modeling with functions, including logarithms. Our High School Mathematics course teaches it live online, to a group of 15 to 20 students or one to one. Integrated Math III ## Three courses for Integrated Math III The high school course covers the year itself; AP Precalculus and the statistics course carry its two biggest threads further. [![High School Mathematics course thumbnail](/images/high-school-maths.webp) GAO / 01 High school math Polynomials, logarithms, trigonometry and modeling. Open the syllabus →](/courses/complete-high-school-mathematics-mastery)[![AP Precalculus course thumbnail](/images/ap-precalculus.webp) GAO / 02 AP Precalculus The usual next step for calculus-bound juniors and seniors. Open the syllabus →](/courses/ap-precalculus-exam-prep-course)[![Statistics & Probability course thumbnail](/images/statistics-probability-maths.webp) GAO / 03 Statistics and probability For the inference unit and a statistics senior year. Open the syllabus →](/courses/statistics-probability-maths-course) The course ## What is taught in Integrated Math 3? Integrated Math III gathers up the first two years and adds four new areas. Utah describes it as the course where "students pull together and apply the accumulation of learning that they have from their previous courses." Utah's description continues in four sentences that serve as a map of the year: "They apply methods from probability and statistics to draw inferences and conclusions from data. Students expand their repertoire of functions to include polynomial, rational, and radical functions. They expand their study of right triangle trigonometry to include general triangles. And, finally, students bring together all of their experience with functions and geometry to create models and solve contextual problems." | Version of the course | Listed topics | | --- | --- | | Secondary Math III (standard) | Polynomial, Rational, and Radical Functions; Trigonometry; Logarithms; Data Collection and Analysis | | Secondary Math III Plus (extended) | Everything above, plus Composition of Functions; Inverse Functions / Trig Functions; Polar Coordinates; Arithmetic and Geometric Series | Sources: Utah State Board of Education [Core State Standards for Mathematics, High School](https://www.schools.utah.gov/curr/mathematics/_mathematics_/_core/_utah_core_standards_tab_/CoreStandardsHighSchool.pdf) and [Graduation Pathways](https://www.schools.utah.gov/curr/mathematics/_mathematics_/_core/CoreStandardsGraduationPathways.pdf). North Carolina's equivalent course is NC Math 3. ### Why the year feels heavier Integrated Math I and II each had one main function family, linear and exponential, then quadratic. Integrated Math III adds several families at once and expects students to choose between them. A student who is shaky on factoring quadratics or on exponent rules will feel it here first, because polynomial division and logarithms both rest on them. ### Why it matters for what comes next In North Carolina, NC Math 3 is the last of three required integrated courses, and the state then asks for a fourth math course matched to what the student plans after graduation. Here, as in most states, this year decides which fourth course is realistic. Utah's own overview says that after Secondary Math III, "In precalculus (or college algebra), students will expand their solving to all types of equations including complex number systems, vectors, matrices, and polar coordinates." Four areas ## What are the four units of Integrated Math III? Utah organizes Secondary Mathematics III into four critical areas. Each line below quotes Utah, then says in our words what the student practices. | Area | Utah's wording, shortened | Practice in our lessons | | --- | --- | --- | | 1. Inference | Ways of collecting data, "including sample surveys, experiments, and simulations", and "the role that randomness and careful design play in the conclusions that can be drawn" | Normal-model estimates, study design, simulation | | 2. Polynomials and rational expressions | "structural similarities between the system of polynomials and the system of integers"; "The unit culminates with the fundamental theorem of algebra" | Long division, the remainder idea, zeros and factors | | 3. Trigonometry of general triangles | The Laws of Sines and Cosines; whether three measures define "0, 1, 2, or infinitely many triangles"; radian measure; simple periodic phenomena | Ambiguous cases, radians, sinusoidal graphs | | 4. Mathematical modeling | Solving exponential equations with logarithms; transformations that have "the same effect regardless of the type of the underlying functions"; choosing and adjusting models | Pick a function family, fit it, judge the fit | ### Polynomials are a lot like whole numbers Utah's Area 2 asks students to connect "multiplication of polynomials with multiplication of multi-digit integers, and division of polynomials with long division of integers." It adds that "A central theme of this unit is that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers." Students who see the parallel stop memorizing steps and start reusing ones they know. ### Modeling is the point of the course Area 4 quotes the definition of modeling as "the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions." That is why a test question in this course often gives data and asks which kind of function fits, rather than giving the function and asking for a value. Worked examples ## How do you divide polynomials and solve with the Law of Sines? With the same habits as integer long division, and by checking how many triangles the measurements allow. All examples here are ours, written for this page. | Step | 1573 divided by 11 | (x^3 + 5x^2 + 7x + 3) divided by (x + 1) | | --- | --- | --- | | First term | 11 goes into 15 once: 1, remainder 4 | x goes into x^3 by x^2; subtract x^3 + x^2, leaving 4x^2 + 7x | | Second term | 11 into 47: 4, remainder 3 | x into 4x^2 by 4x; subtract 4x^2 + 4x, leaving 3x + 3 | | Third term | 11 into 33: 3, remainder 0 | x into 3x by 3; subtract 3x + 3, leaving 0 | | Quotient | 143 | x^2 + 4x + 3, which factors as (x + 1)(x + 3) | | Meaning | 1573 = 11 x 143 | The cubic is (x + 1)^2 (x + 3): zeros -1 (twice) and -3, three in all, as the fundamental theorem of algebra predicts for degree 3 | | Step | Working | | --- | --- | | 1. Find the height | b sin A = 10 x 0.5 = 5 | | 2. Count triangles | 5 < 6 < 10, so side a can swing to meet the base in two places: two triangles | | 3. Law of Sines | sin B = b sin A / a = 5/6, about 0.833 | | 4. Two angles | B is about 56.4 degrees, or 180 minus that, about 123.6 degrees | | 5. Check both | Both leave room for angle C (93.6 or 26.4 degrees), so both triangles exist | | Problem | Reasoning | Result | | --- | --- | --- | | Simplify (x^2 - 9)/(x^2 + 3x) | Factor: (x - 3)(x + 3) over x(x + 3); cancel x + 3, as with a common factor in a fraction | (x - 3)/x, with x not 0 or -3 | | Two sides 7 and 8 meet at 60 degrees. Find the third side. | Law of Cosines: c^2 = 49 + 64 - 2 x 7 x 8 x 0.5 = 57 | c = root 57, about 7.55 | | Convert 150 degrees to radians | Multiply by pi/180 | 5 pi / 6 | | Solve 3 x 2^x = 48 | Divide by 3: 2^x = 16 = 2^4 | x = 4 | | Solve 5^x = 20 | Take logs: x log 5 = log 20 | x = log 20 / log 5, about 1.861 | | Scores are roughly normal, mean 70, standard deviation 6. About what share score above 82? | 82 is two standard deviations above the mean; about 95% lie within two, so about 5% lie outside, split between both tails | About 2.5% | Practice ## Integrated Math 3 practice problems with answers A dozen problems our teachers wrote across the four areas. Students looking for Integrated Math 3 help can use them to find which unit needs work first. | # | Area | Problem | Answer | | --- | --- | --- | --- | | 1 | Inference | A school surveys only students in the library. What is the flaw? | Not a random sample of the school | | 2 | Inference | Mean 100, standard deviation 15, roughly normal. About what percent lie between 85 and 115? | About 68% | | 3 | Polynomials | Remainder when x^3 - 2x + 4 is divided by x - 2 | 8 | | 4 | Polynomials | How many complex zeros does a degree 5 polynomial have, counted with multiplicity? | 5 | | 5 | Polynomials | Zeros of (x - 1)(x^2 + 4) | 1, 2i and -2i | | 6 | Rational | Add 1/x + 2/(x + 1) | (3x + 1)/(x(x + 1)) | | 7 | Radical | Solve the square root of (x + 5) = 3 | x = 4 | | 8 | Trigonometry | Convert pi/4 to degrees | 45 degrees | | 9 | Trigonometry | Period of y = sin(2x) | pi | | 10 | Trigonometry | A = 40 degrees, B = 60 degrees, a = 10. Find b to one decimal. | About 13.5 | | 11 | Logarithms | Solve log base 2 of x = 5 | x = 32 | | 12 | Modeling | Data double every 3 years. Linear, quadratic or exponential model? | Exponential | 1. **Fall, first half: statistics and inference.** Distributions, the normal model, sampling, experiments and simulation. 2. **Fall, second half: polynomials.** Long and synthetic division, zeros and factors, end behavior and the fundamental theorem of algebra. 3. **Winter: rational and radical functions.** Simplifying, adding and solving, with attention to excluded values and extraneous roots. 4. **Early spring: trigonometry.** Laws of Sines and Cosines, the ambiguous case, radians and the unit circle, and periodic graphs. 5. **Late spring: logarithms and modeling.** Inverses of exponentials, solving with logs, transformations, and choosing models for data. 6. **Before the summer: the bridge.** A preview of whichever fourth course comes next. This order is our reading of Utah's four areas; schools often teach trigonometry earlier or split polynomials across the year. We never write a student's graded work for them. We teach the method and leave the work to the student. After Math III ## What math comes after Integrated Math 3? A fourth course chosen around the student's plans. Utah's pathways chart, from 2021, sets out the options most clearly; your own district will name its courses differently. | Option | What Utah says about it | | --- | --- | | Pre-Calculus | A high school class; "doesn't award college credit" but prepares for calculus | | Math 1050 and Math 1060 | Concurrent enrollment; "most of the same topics as Precalculus" | | College Statistics or AP Statistics | College mathematics credit choices for statistics | | Math 1010 | Does not give the quantitative literacy credit a bachelor's degree needs | | An alternative selection instead | Allowed, but "not usually recommended" | ### Opting out of Math III Utah answers this directly: "You are allowed to take one of the Alternate Selections in place of Secondary Math III and still receive a high school diploma. This is not usually recommended." Families weighing that choice should first check what the student's likely college majors expect. ### Skipping ahead Utah is just as direct about skipping: "If you skip a step on the chart you may not be ready for the next class, so it is never advised students to skip classes." Students who want to move faster can take extended versions or summer classes instead, which Utah also mentions. The catalogue ## Courses for Integrated Math III and after Live courses for the year itself, the tests juniors sit, and the fourth math course. I ### Shoring up Skills from Math I and II GAO / S / 01 #### Algebra foundations Exponents and factoring. [Open the syllabus](/courses/algebra-foundations-masterclass) GAO / S / 02 #### Math through coding Model data in Python. [Open the syllabus](/courses/maths-through-coding) GAO / S / 03 #### Statistics The inference unit. [Open the syllabus](/courses/statistics-probability-maths-course)II ### Junior year The course and the tests GAO / J / 01 #### High school math All four areas. [Open the syllabus](/courses/complete-high-school-mathematics-mastery) GAO / J / 02 #### SAT math Advanced math questions. [Open the syllabus](/courses/sat-math-prep-course) GAO / J / 03 #### ACT math Trig and logs appear. [Open the syllabus](/courses/act-math-prep-course)III ### The fourth course Senior year and beyond GAO / F / 01 #### AP Precalculus Functions in depth. [Open the syllabus](/courses/ap-precalculus-exam-prep-course) GAO / F / 02 #### AP Statistics For the data route. [Open the syllabus](/courses/ap-statistics-maths-exam-prep-course) GAO / F / 03 #### College placement For dual enrollment entry. [Open the syllabus](/courses/college-math-placement-test-prep-course) How lessons run ## Integrated Math III lessons for busy juniors Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Weekdays Evening slots around sports and jobs. Weekends Longer review before unit tests. 1-on-1 Planned around SAT or ACT dates too. ### Integer parallels Polynomial steps tied to number facts. ### Triangle counting Ambiguous cases drawn first. ### Logs as inverses Never a rule without its reason. ### Model choice Which family fits, and why. ### Fourth-course plan Advice on what to take next. ### Batch or private Fifteen to twenty, or one to one. Student work ## Work from our students Older students fit models to real data in their own code. See examples on [student labs](/student-labs). ![NutriLife AI nutrition coach project screenshot](/images/projects/nutrilife.webp) AI and ML #### NutriLife An AI nutrition coach that reads what you eat and works you toward a target. by Bhavya · [Open it](https://nutrilife-bhavya.lovable.app) ![Misti AI chatbot for maths and coding screenshot](/images/projects/misti.webp) AI and ML #### Misti A chatbot that answers mathematics and programming questions, built and deployed by a student. by Harshit · [Open it](https://misti.modernagecoders.com) ![GuardianX AI internet safety assistant screenshot](/images/projects/guardianx.webp) AI and ML #### GuardianX An assistant that helps a young person recognise unsafe situations online. by Vivaan · [Open it](https://guardianx-cybersaver.lovable.app) ![SkyCast weather forecast application screenshot](/images/projects/skycast.webp) Web app #### SkyCast A weather forecasting site with live conditions for any location. by Krish Fees ## Fees The fee is monthly, in US dollars, with no minimum term. Many juniors join for one semester, then decide whether to continue into the fourth course with us. Free first class USD 0 no card required - Free first lesson - Bring a recent unit test - No card at sign-up Book it Group batch USD 100 a month, billed in US dollars - Group of 15 to 20 - Consistent teacher - Pick a time - Billed each month Start here One to one USD 150 a month, billed in US dollars - One-to-one teaching - Matched to the school calendar - Choose your hours Enquire What families say ## Rated 4.9 across 547 Google reviews Reviews from Google, reproduced exactly as families posted them. ★★★★★ "The one step solution for my son. Modern Age Coders make learning coding so simple that kids love it. The teachers explain complex concepts clearly with practical exercises and interactive content." Ria Mukherjee Parent ★★★★★ "Modern Age Coders has been a game-changer for me. I struggled to grasp IT concepts and coding before joining, but their classes transformed everything. I can now confidently write complex programs with ease." Samriddha Mondal Student ★★★★★ "One of the most wonderful education centres out there. Education is not limited to school syllabus but focuses on skill development." Vansh Agarwal Student ★★★★★ "My child Dhairya is really enjoying the Modern Age Coders classes. This is his first online class and he eagerly looks forward to it. I can already see his improvement, and the teachers are very cooperative." Sonam Oswal Parent of Dhairya ★★★★★ "Modern Age Coders have wonderful teachers who teach in a clear, easy and practical way. The teacher boosts students' confidence and inspires them to learn without hesitation." Sonu Goyal Parent ★★★★★ "I highly recommend this computer coding class! The teachers are incredibly knowledgeable and passionate about coding." Ritu Kedia Parent Questions families ask ## Integrated Math 3: common questions ### What is taught in Integrated Math 3? Integrated Math III covers inference from data, polynomial, rational and radical functions, trigonometry of general triangles with radians and periodic functions, and modeling with function families including logarithms. Utah's Secondary Mathematics III groups these into four critical areas. ### Is Integrated Math 3 the same as Algebra 2? They overlap heavily on polynomials, rational functions and logarithms. Integrated Math III also includes the Laws of Sines and Cosines and a statistics unit, so a student switching from Algebra 2 may need help with those. ### Is Integrated Math 3 hard? It asks for more combining of ideas than the earlier courses, because several function families appear at once. Students with secure factoring and exponent skills usually cope well; gaps from Integrated Math II show up quickly. ### What grade takes Integrated Math 3? Grade 11 for most students, after Integrated Math I and II. Accelerated students may take it in grade 10, which leaves room for precalculus and calculus later. ### What comes after Integrated Math 3? Usually precalculus, a statistics course, or a college algebra course taken for dual or concurrent enrollment credit. Utah's pathways chart lists Pre-Calculus, Math 1050 and 1060, a college Statistics course and AP Statistics among the options. ### Can my child skip Integrated Math 3? Utah allows an alternative course in its place for the diploma but says this is not usually recommended, because the alternatives do not prepare students for college math credit. Ask your school counselor how your district handles it. ### Where can I find Integrated Math 3 practice problems? Use the school textbook first, since tests follow it, then our twelve-problem set on this page. We do not copy state test items or textbook answer keys. ### Do you help with modeling projects in Integrated Math 3? We teach how to choose a model, fit it and judge the fit, and we review the student's reasoning. We do not write or edit the project for a grade. ### When are your Integrated Math 3 classes? Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. ### Are you affiliated with any state or school? No. Modern Age Coders runs independently of every state education agency, district and publisher. State documents are quoted here only to describe the course accurately. Elsewhere on this site ## Related pages More pages for juniors and the courses that follow. ### [Precalculus tutoring](/precalculus-tutoring-online) The most common fourth course. ### [Algebra 2 tutoring](/algebra-2-tutoring-online) For the traditional route. ### [Trigonometry tutoring](/trigonometry-tutoring-online) The unit circle and beyond. ### [AP Statistics tutoring](/ap-statistics-tutoring-online) A data-focused senior year. ### [Eleventh grade math](/online-math-tutor-11th-grade) The usual Integrated Math III year. ### [Calculus tutoring](/calculus-tutoring-online) Where the pathway is heading. ## Related pages in this guide Part of the guide: [US math placement and college readiness tests](/us-math-placement-and-college-readiness-tests) ### High school math courses - [Integrated Math 1 tutoring](/integrated-math-1-tutoring) - [Integrated Math 2 tutoring](/integrated-math-2-tutoring) - [Trigonometry tutoring online](/trigonometry-tutoring-online) - [Statistics tutoring online](/statistics-tutoring-online) - [AP Precalculus tutoring online](/ap-precalculus-tutoring-online) ### School placement and growth tests - [MAP Growth math test prep](/map-growth-math-test-prep) - [i-Ready math help](/i-ready-math-help) - [Middle school math placement test prep](/middle-school-math-placement-test-prep) - [Accelerated math program online](/accelerated-math-program-online) ### PSAT and PreACT - [PSAT 8/9 and PSAT 10 math prep](/psat-8-9-math-prep) - [PSAT math prep](/psat-math-prep) - [PreACT math prep](/preact-math-prep) - [SAT math tutoring online](/sat-math-tutoring-online) - [ACT math tutoring online](/act-math-tutoring-online) ### College placement and credit - [ACCUPLACER math prep](/accuplacer-math-prep) - [ALEKS math placement test prep](/aleks-math-placement-test-prep) - [TSIA2 math prep](/tsia2-math-prep) - [CLEP College Algebra prep](/clep-college-algebra-prep) - [CLEP Calculus prep](/clep-calculus-prep) - [Dual enrollment math help](/dual-enrollment-math-help) More guides: [US state math tests by state](/us-state-math-tests-by-state) · [US gifted and selective school tests](/us-gifted-and-selective-school-tests-guide) · [Homeschool and school math curricula guide](/homeschool-math-curriculum-guide-usa) · [US math and coding competitions guide](/us-math-and-coding-competitions-guide) Start here ## Book a free first class Let us know the unit your child is studying, the fourth course they are considering and any SAT or ACT date. 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[Book a priority demo](/book-demo) ## Keep exploring Modern Age Coders ### More maths tuition - [Cayley, Hamilton and Maclaurin Preparation](/intermediate-mathematical-olympiad-cayley-hamilton-maclaurin-preparation) - [IOI and Informatics Olympiad Training](/ioi-olympiad-informatics-training) - [Iowa Assessments Math Prep (ITBS) for Grades 1 to 5](/iowa-assessments-math-prep) - [Indian Computing Olympiad Prep: ZIO, ZCO and INOI, Live Online](/indian-computing-olympiad-preparation) - [Junior Mathematical Olympiad Preparation](/junior-mathematical-olympiad-preparation) - [IB MYP Maths Tutor Online](/ib-myp-maths-tutor-online) - [VCE General Maths Tutoring](/vce-general-maths-tutoring) - [Math Tutor Ottawa](/math-tutor-ottawa) - [Maths Tutor in Parramatta](/maths-tutor-parramatta) ### Learn more - [Ontario Grade 12 University Math](/courses/ontario-grade-12-university-math-mhf4u-mcv4u-course) - [Western Canada Grade 12 Math: Pre-calculus 12 and Math 30-1](/courses/western-canada-grade-12-math-pre-calculus-12-math-30-1-course) - [GRE & GMAT Quantitative Prep: Live Maths Coaching](/courses/gre-gmat-quant-maths-prep-course) - [Early Math Foundations: Playful, Concrete Math (Ages 4-7)](/courses/early-math-foundations) ### From the blog - [Maths Learning Guides](/blog/topic/maths) - [How Coding and Mathematics Work Together in Engineering & Science](/blog/coding-mathematics-engineering-science) - [Custom Software vs Ready-Made Software: What Is Right for Your Business?](/blog/custom-software-vs-ready-made-software) - [How to Get a 5 in AP Computer Science A (2026)](/blog/how-to-get-a-5-in-ap-computer-science-a) ### Start here - [Try a free trial class with a Modern Age Coders mentor](/free-trial) - [About Modern Age Coders, teaching since 2020](/about) Free class[Priority demo](/book-demo)[Call us](tel:+919123366161) --- *Canonical: https://learn.modernagecoders.com/integrated-math-3-tutoring*