Integrated Math 1 Tutoring: Integrated Math I Help Online

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Q: 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.

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.

IT / 01

Algebra foundations

Linear and exponential functions, equations and systems.

Open the syllabus →

IT / 02

High school math

All three integrated years, including the geometry units.

Open the syllabus →

IT / 03

Middle school math

Grade 8 functions and equations, if gaps show up.

Open the syllabus →

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.

What different states call the first integrated course (state documents read 31 October 2026)
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 (page 84), Utah State Board of Education mathematics core and NC DPI Standard Course of 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."

Secondary Mathematics I critical areas (Utah Core State Standards for Mathematics, High School, read 31 October 2026; the summary column is ours)
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.

Two savings plans (ours): Plan A starts at 50 and adds 20 each week; Plan B starts at 5 and doubles each week
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.

More worked examples (ours)
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

Residuals (ours): data (1, 52), (2, 55), (3, 61), (4, 62) with the fitted line y = 3.5x + 48.5
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.

Integrated Math I practice written by us, answers in the final column
#	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

August to September: expressions and equations. Modeling with quantities and units, and justified solving.
October to November: functions. Notation, domain and range, sequences, and the linear-exponential contrast.
December to January: systems and inequalities. Graphing, substitution, elimination, and solution regions.
February: data. Scatter plots, lines of fit, residuals and correlation.
March to April: congruence. Rigid motions, triangle congruence criteria and constructions.
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.

The integrated pathway in Utah (Utah State Board of Education, Graduation Pathways PDF, 2021)
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

IT / R / 02

Math through coding

Sequences in Python.

Open the syllabus

IT / R / 03

Competition math

For extra challenge.

Open the syllabus

II

Integrated Math I

Grade 9

IT / Y / 01

Algebra foundations

The algebra half.

Open the syllabus

IT / Y / 02

High school math

Geometry units too.

Open the syllabus

IT / Y / 03

Statistics

For the data unit.

Open the syllabus

III

The years after

Grades 10 to 12

IT / N / 01

AP Precalculus

After Integrated Math III.

Open the syllabus

IT / N / 02

SAT math

Linear and exponential models.

Open the syllabus

IT / N / 03

ACT math

Mixed algebra and geometry.

Open the syllabus

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.

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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

For the traditional Algebra 1 route.

Geometry tutoring

Congruence and proof in depth.

Ninth grade math

The usual Integrated Math I year.

Common Core math tutor

The standards both pathways share.

Math placement tests

How students are placed into grade 9 math.

Math tutor cost

How tutoring is usually priced.

Related pages in this guide

Part of the guide: US math placement and college readiness tests

High school math courses

School placement and growth tests

PSAT and PreACT

College placement and credit

More guides: US state math tests by state · US gifted and selective school tests · Homeschool and school math curricula guide · US math and coding competitions guide

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Three courses for Integrated Math I

Algebra foundations

High school math

Middle school math

What is Integrated Math 1, and how is it different from Algebra 1?

Two sequences, one set of standards

What the integrated order changes

What topics are in Integrated Math 1?

Functions as objects

Sequences hide inside functions

How do you tell linear growth from exponential growth?

Integrated Math 1 practice problems with answers

Is Integrated Math 1 the same as Algebra 1?

Moving from Algebra 1 into Integrated Math

Moving from Integrated Math I into Geometry

Math courses for the integrated pathway

Getting ready

Middle school math

Math through coding

Competition math

Integrated Math I

Algebra foundations

High school math

Statistics

The years after

AP Precalculus

SAT math

ACT math

Integrated Math I lessons in step with school

Your course map

Tables, graphs, rules

Justified steps

Geometry by motion

Transfer bridges

Batch or one to one

Work from our students

NutriLife

Misti

GuardianX

SkyCast

Fees

Rated 4.9 across 547 Google reviews

Integrated Math 1: common questions

What is taught in Integrated Math 1?

Is Integrated Math 1 the same as Algebra 1?

Is Integrated Math 1 harder than Algebra 1?

What grade takes Integrated Math 1?

Which states use Integrated Math?

Where can I find an Integrated Math 1 practice test?

My child moved from Algebra 1 to Integrated Math. What will they have missed?

Can you check my child's Integrated Math homework answers?

When are your Integrated Math 1 classes?

Are you connected with any state or textbook publisher?

Related pages

Algebra tutoring

Geometry tutoring

Ninth grade math

Common Core math tutor

Math placement tests

Math tutor cost

Related pages in this guide

High school math courses

School placement and growth tests

PSAT and PreACT

College placement and credit

Book a free first class

Want a class sooner? Book a priority demo

Keep exploring Modern Age Coders

More maths tuition

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