--- title: "Integrated Math 1 Tutoring: Integrated Math I Help Online" description: "Integrated Math 1 tutoring online: what Integrated Math I covers, how it differs from Algebra 1, worked examples on linear and exponential models, and practice." canonical: https://learn.modernagecoders.com/integrated-math-1-tutoring source: src/pages/integrated-math-1-tutoring.html --- > Integrated Math 1 tutoring online: what Integrated Math I covers, how it differs from Algebra 1, worked examples on linear and exponential models, and practice. In short Integrated Math I is the first course of the Common Core integrated sequence (Mathematics 1, 2 and 3), taught in states such as Utah, as Secondary Mathematics I, and North Carolina, as NC Math 1. It covers linear and exponential functions, equations and systems, linear models of data, and congruence. Modern Age Coders teaches it live online, in a batch of 15 to 20 or 1-on-1, through our Algebra Foundations course. Integrated Math I ## Three courses for Integrated Math I Algebra Foundations carries the algebra and functions half of the course; the other two cover geometry and the years ahead. [![Algebra Foundations course thumbnail](/images/algebra-foundations.webp) IT / 01 Algebra foundations Linear and exponential functions, equations and systems. Open the syllabus →](/courses/algebra-foundations-masterclass)[![High School Mathematics course thumbnail](/images/high-school-maths.webp) IT / 02 High school math All three integrated years, including the geometry units. Open the syllabus →](/courses/complete-high-school-mathematics-mastery)[![Middle School Mathematics Mastery course thumbnail](/images/middle-school-maths.webp) IT / 03 Middle school math Grade 8 functions and equations, if gaps show up. Open the syllabus →](/courses/comprehensive-middle-school-mathematics-mastery) What it is ## What is Integrated Math 1, and how is it different from Algebra 1? It is the same Common Core high school content as the traditional pathway, cut into courses a different way. Algebra 1 keeps geometry for a separate year; Integrated Math I mixes a share of it in from the start. ### Two sequences, one set of standards The Common Core's note on courses says its high school standards "do not mandate the sequence of high school courses." It names two model sequences: "a traditional course sequence (Algebra I, Geometry, and Algebra II)" and "an integrated course sequence (Mathematics 1, Mathematics 2, Mathematics 3)." The same note says "The standards themselves do not dictate curriculum, pedagogy, or delivery of content." That is why course names and textbooks differ from state to state while the underlying standards match. ### What the integrated order changes A student in Algebra 1 spends most of grade 9 on equations, functions and quadratics. A student in Integrated Math I stops after linear and exponential functions, then studies data and congruence before quadratics arrive in Integrated Math II. Neither order is easier. Moving between them mid-sequence is what causes trouble, because a transferring student can miss a topic or meet one twice. | State | Course name | What the state publishes | | --- | --- | --- | | Utah | Secondary Mathematics I | Core standards with six critical areas; a graduation pathways chart | | North Carolina | NC Math 1 | Graduation requires "NC Math 1, 2, and 3 and a fourth mathematics course to be aligned with the student's post high school plans" | | Many districts elsewhere | Integrated Math I or Math I | District course guides; check yours for the exact unit order | Sources: [Common Core State Standards for Mathematics](https://corestandards.org/wp-content/uploads/2023/09/Math_Standards1.pdf) (page 84), [Utah State Board of Education mathematics core](https://www.schools.utah.gov/curr/mathematics/core.php) and [NC DPI Standard Course of Study supporting resources](https://www.dpi.nc.gov/districts-schools/classroom-resources/office-teaching-and-learning/standard-course-study/mathematics/standard-course-study-supporting-resources). Test makers follow the integrated names too. NWEA's MAP Growth features page says "Every license of MAP Growth includes tests for Algebra 1 and 2, Integrated Math 1, 2 and 3, and Geometry", so a district can measure growth inside the course itself. The units ## What topics are in Integrated Math 1? Utah's core standards set the course out in six critical areas. They give a clear picture of a typical Integrated Math I year, even outside Utah. Utah opens its course description with the purpose: "THE FUNDAMENTAL PURPOSE OF SECONDARY MATHEMATICS I is to formalize and extend the mathematics that students learned in the middle grades." It deepens linear relationships "in part by contrasting them with exponential phenomena", and "The final unit in the course ties together the algebraic and geometric ideas studied." | Area | Utah's focus | In plain terms (ours) | | --- | --- | --- | | 1 | Using quantities to model and analyze situations, interpreting expressions, creating equations | Writing an equation from a word problem, and saying what each part means | | 2 | Function notation, domain and range; comparing linear and exponential functions, "distinguishing between additive and multiplicative change" | Adding the same amount each step, or multiplying by the same factor | | 3 | Solving linear equations and inequalities, justifying each step, systems of equations, simple exponential equations | Explaining why each move is allowed, not just doing it | | 4 | Regression for approximately linear data; "With linear models, they look at residuals to analyze the goodness of fit" | Fitting a line and checking how far points miss it | | 5 | Triangle congruence criteria from rigid motions and formal constructions | Why SSS, SAS and ASA work, through slides, flips and turns | | 6 | Coordinate geometry: special triangles and quadrilaterals, "slopes of parallel and perpendicular lines" | Proving a shape is a square with slopes and distances | ### Functions as objects In Area 2, Utah says students "move beyond viewing functions as processes that take inputs and yield outputs, and start viewing functions as objects in their own right." That is the step that trips up many ninth graders. A student can plug numbers into f(x) = 3x + 2 yet still struggle to compare two functions given as a table and a graph. ### Sequences hide inside functions Utah's wording is that students "interpret arithmetic sequences as linear functions and geometric sequences as exponential functions." Once a student sees that 7, 11, 15, 19 is a line sampled at whole numbers, half of the course's sequence questions become questions they already know how to answer. Worked examples ## How do you tell linear growth from exponential growth? Look at what happens from one step to the next. Linear quantities change by the same amount; exponential quantities change by the same factor. These examples are ours, written for this page. | Week w | Plan A: 50 + 20w | Plan B: 5 x 2^w | Which is ahead | | --- | --- | --- | --- | | 0 | 50 | 5 | A | | 2 | 90 | 20 | A | | 4 | 130 | 80 | A | | 5 | 150 | 160 | B, just | | 6 | 170 | 320 | B, by a lot | Plan A grows by a constant difference of 20, so its graph is a line. Plan B grows by a constant ratio of 2, so its graph curves upward. A fair conclusion, written the way Integrated Math I expects it: "an exponential function with a growth factor above 1 eventually passes any linear function, however far behind it starts." Here that happens between week 4 and week 5. | Problem | Reasoning | Result | | --- | --- | --- | | Write 7, 11, 15, 19, ... as a function of the term number n | Common difference 4, first term 7: a(n) = 7 + 4(n - 1) | a(n) = 4n + 3, a linear function | | Write 3, 6, 12, 24, ... as a function of n | Common ratio 2, first term 3 | g(n) = 3 x 2^(n - 1), exponential | | Solve 3x + 2y = 16 and x - y = 2 | From the second, x = y + 2 (adding y to both sides keeps the equation true). Substitute: 3(y + 2) + 2y = 16, so 5y = 10 | y = 2, x = 4 | | Is the quadrilateral A(0,0), B(4,1), C(3,5), D(-1,4) a square? | Slope AB = 1/4 and slope BC = -4; the product is -1, so AB is perpendicular to BC. Each side has length the square root of 17. | Yes: four equal sides and a right angle | | x | Actual y | Predicted y | Residual (actual minus predicted) | | --- | --- | --- | --- | | 1 | 52 | 52 | 0 | | 2 | 55 | 55.5 | -0.5 | | 3 | 61 | 59 | 2 | | 4 | 62 | 62.5 | -0.5 | Small residuals scattered on both sides of zero, with no curved pattern, suggest a linear model fits. If the residuals had run negative, then positive, then negative again, the data would be bending away from a line, perhaps toward an exponential. Practice ## Integrated Math 1 practice problems with answers Twelve problems we wrote, covering all six areas. Students searching for an Integrated Math 1 practice test can use these as a first check, then go to their own textbook's review. | # | Area | Problem | Answer | | --- | --- | --- | --- | | 1 | Expressions | In C = 15 + 4h for a bike rental, what does 4 mean? | The cost added per hour | | 2 | Functions | Domain of f(x) = 2x - 1 for x in {0, 1, 2}? Range? | Domain {0, 1, 2}; range {-1, 1, 3} | | 3 | Functions | Does 2, 6, 18, 54 grow linearly or exponentially? | Exponentially, factor 3 | | 4 | Functions | Average rate of change of f(x) = x^2 from x = 1 to x = 3? | 4 | | 5 | Equations | Solve 5 - 2x > 11 | x < -3 | | 6 | Equations | Solve 2^x = 32 | x = 5 | | 7 | Systems | Solve y = 2x + 1 and y = -x + 7 | x = 2, y = 5 | | 8 | Data | A residual is -3. Was the actual value above or below the line? | Below | | 9 | Data | Correlation r = 0.95. Strong or weak? Direction? | Strong, positive | | 10 | Congruence | Reflect (2, 1) across the y-axis | (-2, 1) | | 11 | Congruence | Two sides and the included angle match. Which criterion? | SAS | | 12 | Coordinates | Slope of a line perpendicular to y = 3x - 4? | -1/3 | 1. **August to September: expressions and equations.** Modeling with quantities and units, and justified solving. 2. **October to November: functions.** Notation, domain and range, sequences, and the linear-exponential contrast. 3. **December to January: systems and inequalities.** Graphing, substitution, elimination, and solution regions. 4. **February: data.** Scatter plots, lines of fit, residuals and correlation. 5. **March to April: congruence.** Rigid motions, triangle congruence criteria and constructions. 6. **May: coordinate geometry and review.** Slopes, distances and coordinate proofs, then the end-of-course review. The calendar above is our own estimate for a school that follows Utah's unit order. Districts reorder units, so the teacher lines lessons up with your child's actual course map in the first week. Integrated or traditional ## Is Integrated Math 1 the same as Algebra 1? Not quite. It covers much of Algebra 1 plus some geometry and statistics, and leaves quadratics for the next year. Utah's pathways chart lists what each integrated course carries. | Course | Topics Utah lists | | --- | --- | | Secondary Math I | Linear and Exponential Functions; Congruence; Descriptive Statistics | | Secondary Math I Plus (extended) | Adds Matrices and Vectors | | Secondary Math II | Quadratic Functions; Similarity; Right Angle Trigonometry; Conditional Probability | | Secondary Math III | Polynomial, Rational, and Radical Functions; Trigonometry; Logarithms; Data Collection and Analysis | ### Moving from Algebra 1 into Integrated Math A student arriving after Algebra 1 usually knows quadratics already but may have missed congruence and descriptive statistics. Those units are where we start. Utah notes that "Taking all three Extended courses is equivalent to taking Pre-Calculus", which matters for students aiming at calculus in grade 12. ### Moving from Integrated Math I into Geometry A student leaving after Integrated Math I has seen congruence early but not quadratics. A short bridge on factoring and graphing parabolas usually closes the gap. Ask the new school for its course map before the first week, so the bridge can start straight away. The catalogue ## Math courses for the integrated pathway Live courses for the grade before, the year itself and the two integrated years that follow. I ### Getting ready Grade 8 and before IT / R / 01 #### Middle school math Grade 8 functions. [Open the syllabus](/courses/comprehensive-middle-school-mathematics-mastery) IT / R / 02 #### Math through coding Sequences in Python. [Open the syllabus](/courses/maths-through-coding) IT / R / 03 #### Competition math For extra challenge. [Open the syllabus](/courses/olympiad-competition-mathematics-mastery)II ### Integrated Math I Grade 9 IT / Y / 01 #### Algebra foundations The algebra half. [Open the syllabus](/courses/algebra-foundations-masterclass) IT / Y / 02 #### High school math Geometry units too. [Open the syllabus](/courses/complete-high-school-mathematics-mastery) IT / Y / 03 #### Statistics For the data unit. [Open the syllabus](/courses/statistics-probability-maths-course)III ### The years after Grades 10 to 12 IT / N / 01 #### AP Precalculus After Integrated Math III. [Open the syllabus](/courses/ap-precalculus-exam-prep-course) IT / N / 02 #### SAT math Linear and exponential models. [Open the syllabus](/courses/sat-math-prep-course) IT / N / 03 #### ACT math Mixed algebra and geometry. [Open the syllabus](/courses/act-math-prep-course) How lessons run ## Integrated Math I lessons in step with school 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 After school, a step ahead of class. Weekends Catch-up on a missed unit. 1-on-1 For students switching pathway mid-year. ### Your course map Lessons follow the district's unit order. ### Tables, graphs, rules Every function seen three ways. ### Justified steps Each move in an equation explained. ### Geometry by motion Congruence through transformations. ### Transfer bridges Gaps closed for students who moved. ### Batch or one to one Fifteen to twenty, or private. Student work ## Work from our students Students who enjoy patterns often go on to code them. Browse [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 We charge a monthly fee in US dollars and there is no fixed term, so a family can book help for a single hard unit or for the whole year. Free first class USD 0 no card required - A free first class - Bring the current homework - No payment details Book it Group batch USD 100 a month, billed in US dollars - Fifteen to twenty students - A regular teacher - Choose the batch - Month to month Start here One to one USD 150 a month, billed in US dollars - Private lessons - Built on your school's unit order - Flexible slots Enquire What families say ## Rated 4.9 across 547 Google reviews Google reviews from families, copied word for word. ★★★★★ "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 1: common questions ### What is taught in Integrated Math 1? Integrated Math I usually covers expressions and equations, linear and exponential functions, systems, linear models of data with residuals, triangle congruence through rigid motions, and coordinate geometry. Utah's Secondary Mathematics I sets these out in six critical areas. ### Is Integrated Math 1 the same as Algebra 1? No, though they overlap a great deal. Integrated Math I shares most of the Algebra 1 work on linear and exponential functions but adds geometry and statistics units, and leaves quadratics for Integrated Math II. ### Is Integrated Math 1 harder than Algebra 1? Not by design. Both follow the same Common Core high school standards in a different order. Students sometimes find it harder because the course switches between algebra and geometry within one year. ### What grade takes Integrated Math 1? Most students take it in grade 9. Some take it in grade 8 as an accelerated course, and others begin in grade 10, depending on district placement. ### Which states use Integrated Math? Utah (Secondary Mathematics I to III) and North Carolina (NC Math 1 to 3) are two states whose documents we checked. Many districts in other states also offer an integrated pathway alongside or instead of Algebra 1, Geometry and Algebra 2. ### Where can I find an Integrated Math 1 practice test? Your child's textbook and teacher are the first place, since school tests follow them. This page has twelve practice problems we wrote, with answers. We do not reproduce state test items or publisher answer keys. ### My child moved from Algebra 1 to Integrated Math. What will they have missed? Usually congruence through transformations and descriptive statistics, and sometimes coordinate proofs. A few focused lessons on those units usually close the gap. ### Can you check my child's Integrated Math homework answers? We go through the thinking with the student and check that their method is right, but we do not hand over answers to graded work. The aim is that they can do the next problem alone. ### When are your Integrated Math 1 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 connected with any state or textbook publisher? No. Modern Age Coders is an independent online school, not affiliated with any state education department, district or publisher. We teach from the published standards and your school's course. Elsewhere on this site ## Related pages More help for grade 9 math and the courses around it. ### [Algebra tutoring](/algebra-tutoring-online-usa) For the traditional Algebra 1 route. ### [Geometry tutoring](/geometry-tutoring-online-usa) Congruence and proof in depth. ### [Ninth grade math](/online-math-tutor-9th-grade) The usual Integrated Math I year. ### [Common Core math tutor](/common-core-math-tutor) The standards both pathways share. ### [Math placement tests](/middle-school-math-placement-test-prep) How students are placed into grade 9 math. ### [Math tutor cost](/online-math-tutor-cost) How tutoring is usually priced. ## 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 2 tutoring](/integrated-math-2-tutoring) - [Integrated Math 3 tutoring](/integrated-math-3-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 Tell us your district, the unit your child is on, and whether they came from an Algebra 1 course. The teacher will begin with one linear and one exponential table to see where your child stands. See [how we teach](/how-we-teach) or [the full course list](/courses). [WhatsApp us](https://wa.me/919123366161?text=Hello%20Modern%20Age%20Coders%2C%20my%20child%20is%20taking%20Integrated%20Math%201%20and%20needs%20some%20help.%20Could%20we%20book%20a%20free%20first%20class%3F) · [+91 91233 66161](tel:+919123366161) · [connect@modernagecoders.com](mailto:connect@modernagecoders.com) Lessons are taught live by teachers in India, with afternoon and evening slots in Eastern, Central, Mountain and Pacific time. WhatsApp reaches us fastest. ### Want a class sooner? Book a priority demo A priority demo is a full class of about 45 to 60 minutes. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off. [Book a priority demo](/book-demo) ## Keep exploring Modern Age Coders ### More maths tuition - [Indian Computing Olympiad Prep: ZIO, ZCO and INOI, Live Online](/indian-computing-olympiad-preparation) - [IB MYP Maths Tutor Online](/ib-myp-maths-tutor-online) - [Cayley, Hamilton and Maclaurin Preparation](/intermediate-mathematical-olympiad-cayley-hamilton-maclaurin-preparation) - [IB Maths Tuition Online](/ib-maths-tuition-online) - [IOI and Informatics Olympiad Training](/ioi-olympiad-informatics-training) - [IB Maths IA Guidance](/ib-maths-ia-guidance) - [Maths Tuition in Coventry](/maths-tuition-in-coventry) - [TASC Mathematics Methods Tutoring](/tasc-mathematics-methods-tutoring) - [Maths Tutor in Melbourne](/maths-tutor-melbourne) ### Learn more - [Ontario Math Curriculum Coding, Grades 1 to 8, by Grade](/ontario-coding-curriculum-grades-1-to-8) - [College Maths Course: Calculus, Linear Algebra to Analysis](/courses/college-mathematics-complete-masterclass) - [Khan Academy Math vs a Live Tutor: Which Does Your Child Need?](/khan-academy-math-vs-live-tutor) - [Common Core Math vs Traditional Math: A Parent Guide](/common-core-math-vs-traditional-math) ### From the blog - [Maths Learning Guides](/blog/topic/maths) - [How Coding and Mathematics Work Together in Engineering & Science](/blog/coding-mathematics-engineering-science) - [BODMAS Rule Explained: The Left to Right Step](/blog/bodmas-rule-explained) - [Custom Software vs Ready-Made Software: What Is Right for Your Business?](/blog/custom-software-vs-ready-made-software) ### Start here - [Real projects built by Modern Age Coders students](/student-labs) - [Browse every live course at Modern Age Coders](/courses) Free class[Priority demo](/book-demo)[Call us](tel:+919123366161) --- *Canonical: https://learn.modernagecoders.com/integrated-math-1-tutoring*