Becoming an Agent

Woman studying real estate exam math at a desk in a bright Scottsdale home, using a calculator and open notebook with handwritten formulas.

Real Estate Math Questions: The Complete Arizona Exam Guide (2026)

Becoming an Agent

By: Arizona School of Real Estate 8 minutes June 22, 2026

Math is the part of the Arizona real estate exam most candidates dread—and the part most within your control. Unlike the vocabulary and statutory sections, every math question on the Pearson VUE exam follows a predictable format with a finite set of formulas. Learn the formulas, practice the question types, and math becomes a reliable source of guaranteed points.

This guide covers every math category tested on the Arizona exam—with the formula, a worked example using real Scottsdale market numbers, and two practice questions each. It also includes a printable cheat sheet covering every formula you need, and the Memory Circle—ASREB's proven shortcut for solving any real estate math problem.

Arizona-specific note: As of January 1, 2026, the Arizona salesperson exam was split into two parts—the General exam ($70) and the State exam ($60), bookable back-to-back for a $75 combo. Math appears in both. The Arizona-specific rules on proration day-count and property tax assessment differ from national prep guides—the sections below cover them explicitly.

How Much Math Is on the Arizona Real Estate Exam?

The national/general exam includes a dedicated Math Calculations section with seven categories, one question each. The Arizona state exam adds further math across its content areas, bringing the combined total to approximately 11 math questions across the full 180-question scored exam.

To pass: 75—135 of 180 scored questions correct. For context on how candidates typically find the exam, see our guide: How Difficult Is It to Get a Real Estate License in Arizona?.

The Memory Circle (Memory T)—One Framework for Almost Every Math Problem

The Memory Circle—sometimes called Memory T or T-math—is the single most useful shortcut for real estate math. ASREB instructors teach it because it handles the majority of exam questions across every category: commission, interest, property tax, proration, LTV.

The formula is simple: Part = Whole × Percentage. The circle is divided into three sections. Cover the section you want to find and the remaining two tell you what to do.

Find the PART (small $$): cover Part → multiply Whole × Percent
Find the WHOLE (large $$): cover Whole → divide Part ÷ Percent
Find the PERCENT: cover Percent → divide Part ÷ Whole

Convert Before You Calculate—Every Time

The most common arithmetic error on the exam: entering a percentage as a whole number. 6% into your calculator is 0.06, not 6. Enter it wrong and your answer is off by a factor of 100.

To convert	Do this	Example
% → decimal	Divide by 100	6% → 0.06
Decimal → %	Multiply by 100	0.0725 → 7.25%
Fraction → decimal	Divide top by bottom	3/8 → 0.375

Commission rate of 5.5% → enter 0.055 in your calculator, not 5.5.

Area Conversions—Memorize These (Not Given on the Exam)

1 acre = 43,560 square feet 1 square mile = 640 acres 1 mile = 5,280 feet

Example: These are not provided at the Pearson VUE test center.

1. Commission Calculations

Commission is the most practical math skill you'll use from day one as a licensed agent. In Scottsdale—where the median sale price is around $969,000 (Redfin, April 2026)—commission math isn't just exam prep, it's the arithmetic of your future income. Once you're licensed, use ASREB's free real estate commission calculator.

Commission Formula

Sale Price × Commission Rate = Total Commission Total Commission × Split % = Party's Commission Working backwards: Agent's Commission ÷ Split % ÷ Rate = Sale Price

Example: A $969,000 Scottsdale home at 5.5% commission.

Worked example—Scottsdale single-family home

A Scottsdale home sells for $969,000. The commission rate is 5.5%, split 50/50 between the listing broker and the buyer's broker. That means each broker receives 50% of the total commission. The listing agent then receives 60% of their broker's 50% share—not 60% of the total commission.

Total commission: $969,000 × 0.055 = $53,295
Listing broker's side (50% of total): $53,295 ÷ 2 = $26,647.50
Listing agent's share (60% of their broker's side): $26,647.50 × 0.60 = $15,988.50

Watch for backwards commission problems: the exam gives you the agent's commission and asks for the sale price. Reverse the steps—commission ÷ split % ÷ commission rate = sale price.

Practice Question 1

A Scottsdale condo sells for $575,000. The commission rate is 5%, split 50/50 between listing and buyer's broker. The listing agent receives 55% of the listing broker's share. What is the listing agent's commission?

Answer: $575,000 × 0.05 = $28,750 total. ÷ 2 = $14,375 listing side. × 0.55 = $7,906.25.

Practice Question 2

A broker received a commission check for $18,700. The commission rate was 5.5% and the broker kept 100% with no agent split. What was the sale price of the property?

Answer: $18,700 ÷ 0.055 = $340,000.

2. Prorations—Splitting Property Taxes at Closing

Proration questions split a prepaid or accrued expense between buyer and seller based on days of ownership. They appear on both exam parts and require careful attention to the day-count rules—the most common source of errors in this category.

In Scottsdale, the median annual property tax bill is approximately $2,573. Here's how the exam tests it:

Proration Formula

Annual Amount ÷ Days in Year = Daily Rate Daily Rate × Days Owned = Party's Share 360-day (banker's) year: 12 months × 30 days each 365-day (calendar) year: actual days

Example: The exam ALWAYS tells you which year and who owns closing day.

Important rule for Arizona: The Pearson VUE candidate handbook is explicit—every proration question specifies (a) 360 or 365 days, and (b) whether the day of closing belongs to the buyer or seller. Never assume either. Both change your answer.

Worked example—360-day year, buyer owns closing day

Taxes for the year are $1,824 and have not yet been paid. Closing is June 7. Assume a 360-day year and the buyer is responsible for the day of closing.

Step 1: Draw a timeline — seller owes from January 1 through June 6 (buyer takes over on June 7).

Step 2: Find days used.

January through May = 150 days (30 days/month × 5 months)
June 1 through June 6 = +6 days (buyer owns closing day, so seller pays through June 6)
Total: 156 days used

Step 3: Find the cost per day.

$1,824 ÷ 360 = $5.0667 per day

Step 4: Find the prorated amount.

$5.0667 × 156 = $790.40—charged to the seller and credited to the buyer

Worked example—365-day year, seller owns closing day

Annual property taxes are $3,650 and have not yet been paid. Closing is September 15. The seller is responsible through and including the day of closing. Use a 365-day year.

Step 1: Draw a timeline — seller owes from January 1 through September 15 (inclusive).

Step 2: Find days used.

January through August = 243 days (31+28+31+30+31+30+31+31)
September 1 through September 15 = +15 days (seller owns closing day)
Total: 258 days used

Step 3: Find the cost per day.

$3,650 ÷ 365 = $10.00 per day

Step 4: Find the prorated amount.

$10.00 × 258 = $2,580.00 — charged to the seller and credited to the buyer

Using the wrong day-count method or misreading who owns closing day are the two most common proration errors. Read the full question before picking up your calculator.

Practice Question 3

Annual HOA dues on a Scottsdale townhome are $3,600. The seller has prepaid the full year. Closing is August 1. The buyer's ownership begins on closing day. Using a 360-day year, how much does the buyer owe the seller?

Answer: Aug 1 through Dec 31 = 5 months × 30 = 150 days. $3,600 ÷ 360 = $10.00/day. $10.00 × 150 = $1,500.

Practice Question 4

Scottsdale property taxes are $3,285/year and have not been paid. Closing is May 1. The seller pays through but NOT including closing day. Use a 365-day year.

Answer: Jan 1 through Apr 30 = 31+28+31+30 = 120 days. $3,285 ÷ 365 = $9.00/day. $9.00 × 120 = $1,080.

3. Loan Financing Costs—LTV, Interest, and Discount Points

This category covers three related concepts: loan-to-value ratio, simple interest, and discount points. They're tested separately but all follow the Memory Circle logic—Part = Whole × Percent.

Loan Financing Formulas

LTV = Loan Amount ÷ Property Value Down Payment = (1 − LTV) × Property Value Simple Interest: I = Principal × Rate × Time Monthly interest = P × R × (1/12) Discount Points: 1 point = 1% of LOAN AMOUNT (not purchase price) Points cost = Loan Amount × (Points × 0.01)

Example: Points are on the loan, not the sale price—the most common trap in this category.

Worked example—discount points on a Scottsdale purchase

A buyer purchases a Scottsdale home for $850,000 with 10% down. The lender offers a rate buydown requiring 2 discount points. How much will the buyer pay in points at closing?

Down payment: $850,000 × 0.10 = $85,000
Loan amount: $850,000 − $85,000 = $765,000
2 points: $765,000 × 0.02 = $15,300 paid at closing

The trap: some candidates calculate points on $850,000 (purchase price) instead of $765,000 (loan amount). Points are always based on the loan amount.

Practice Question 5

A buyer purchases a Scottsdale home for $725,000 with 20% down. The lender requires 1.5 discount points. How much will the buyer pay in points?

Answer: Loan: $725,000 × 0.80 = $580,000. Points: $580,000 × 0.015 = $8,700.

Practice Question 6

A buyer closes on a Scottsdale property on April 15. The loan is $640,000 at 7% annual interest. First mortgage payment is due June 1. The buyer owns closing day. Use a 360-day year. How much prepaid interest is collected at closing?

Answer: Daily interest: $640,000 × 0.07 ÷ 360 = $124.44/day. Apr 15–30 = 16 days. $124.44 × 16 = $1,991.11.

4. Property Area Calculations—Square Footage and Acreage

Area questions test square footage, acreage conversions, and price-per-square-foot. In Scottsdale, where the median price per square foot is around $429 (Redfin, April 2026), this math maps directly to real listing valuations. If you want to model income from specific transaction sizes once you're licensed, use ASREB's free real estate commission calculator.

Property Area Formulas

Area = Length × Width (result in square feet) Acres = Square Feet ÷ 43,560 Price per sq ft = Total Value ÷ Square Footage Total Value = Price per sq ft × Square Footage Irregular (L-shaped) lots: Break into rectangles → calculate each → add or subtract

Example: 43,560 sq ft per acre—memorize this. It's not on the exam sheet.

Worked example—standard rectangular lot

A rectangular lot in North Scottsdale is 150 feet wide and 290 feet deep. What is the lot size in acres?

Area: 150 × 290 = 43,500 sq ft
Acres: 43,500 ÷ 43,560 = 0.999 acres (essentially 1 acre)

Worked example—irregular L-shaped lot

A lot in Scottsdale's DC Ranch area has an L-shape. The full rectangle would be 200 feet wide by 150 feet deep, but a 60×80 foot corner is cut out. What is the total square footage and acreage?

Full rectangle: 200 × 150 = 30,000 sq ft
Cut-out: 60 × 80 = 4,800 sq ft
Total: 30,000 − 4,800 = 25,200 sq ft
Acres: 25,200 ÷ 43,560 = 0.578 acres

Practice Question 7

A buyer is purchasing a Scottsdale lot at $429/sq ft. The lot measures 120 ft wide by 180 ft deep. What is the total purchase price?

Answer: 120 × 180 = 21,600 sq ft. 21,600 × $429 = $9,266,400.

Practice Question 8

A Scottsdale property contains 130,680 square feet. How many acres is this? If listed at $200,000 per acre, what is the asking price?

Answer: 130,680 ÷ 43,560 = 3 acres. 3 × $200,000 = $600,000.

5. Settlement and Closing Costs

Settlement cost questions test what each party owes or receives at closing. The most frequently tested types are prepaid interest (the partial first month collected at closing) and prorated tax or HOA credits. These questions always specify the day-count method and who owns closing day.

Prepaid Interest at Closing

The lender collects interest from closing day through end of that month. The first full mortgage payment is due the 1st of the SECOND month after closing. Daily interest = Loan × Annual Rate ÷ 360 (or ÷ 365 per question) Prepaid interest = Daily Rate × Days remaining in month

Example: Buyer closes March 10 → first payment due May 1 → lender collects March 10–31 at closing.

Worked example—prepaid interest, Scottsdale closing

A buyer closes on a Scottsdale home on March 10. The loan is $750,000 at 6% annual interest. First payment is due May 1. The buyer owns closing day. Use a 360-day year.

Daily interest: $750,000 × 0.06 ÷ 360 = $125.00/day
Days March 10–31 (buyer owns Mar 10): 22 days
Prepaid interest: $125.00 × 22 = $2,750.00

Practice Question 9

A buyer closes on a Scottsdale condo on September 20. Loan: $480,000 at 7.5% annual interest. First payment due November 1. Buyer owns closing day. 360-day year. How much prepaid interest is collected at closing?

Answer: Daily interest: $480,000 × 0.075 ÷ 360 = $100.00/day. Sep 20–30 = 11 days. $100.00 × 11 = $1,100.

Practice Question 10

Annual property taxes on a Scottsdale home are $4,745. The seller has not paid them. Closing is June 30. Seller pays through but not including closing day. 365-day year. What does the seller owe at closing?

Answer: Jan 1 to Jun 29 = 31+28+31+30+31+29 = 180 days. $4,745 ÷ 365 = $13.00/day. $13.00 × 180 = $2,340.

6. Property Tax Calculations—Arizona's Assessment Method

Property tax questions require two steps: finding the assessed value from market value, then applying the tax rate. Arizona's system differs from many states—residential properties are assessed at 10% of their Limited Property Value (LPV). The exam will give you the rate; what you need is the sequence.

Arizona Property Tax Formula

Step 1: Market Value × Assessment Rate = Assessed Value (AZ residential default: 10% of LPV) Step 2: Assessed Value × Mill Rate = Annual Tax (1 mill = $0.001 per $1 of assessed value) (Scottsdale combined rate: ~$0.9124 per $100 AV) Alternatively: AV × (Rate per $100 ÷ 100)

Example: $969,000 market value × 10% = $96,900 AV. $96,900 × 0.009124 = $884.12/yr.

Practice Question 11

A Scottsdale property has an assessed value of $85,000. The combined mill rate is 91.24 mills. What are the annual property taxes?

Answer: $85,000 × 0.09124 = $7,755.40.

Practice Question 12

A homeowner pays $2,573/year in property taxes. The mill rate is 91.24 mills. Working backwards, what is the assessed value?

Answer: $2,573 ÷ 0.09124 = $28,202.54.

7. Investment and Property Management Calculations

Investment math covers GRM and cap rate. Property management covers the 28/36 qualifying rule. Both appear in the national exam.

Investment and Property Management

GRM = Property Price ÷ Gross Annual Rent Cap Rate = NOI ÷ Property Value 28/36 Rule: Gross Income × 0.28 = Max monthly housing cost (PITI) Gross Income × 0.36 = Max monthly total debt

Example: GRM uses gross rent. Cap rate uses NOI (net, after expenses).

Practice Question 13

A Scottsdale rental property generates $72,000/year in gross rents and is listed at $1,100,000. What is the GRM?

Answer: $1,100,000 ÷ $72,000 = 15.28.

Practice Question 14

A buyer's gross monthly income is $12,500. Using the 28/36 rule, what is the maximum monthly housing cost (PITI) to qualify for most loans?

Answer: $12,500 × 0.28 = $3,500.

Practice Question 15

A residential building cost $310,000. Land value is $60,000. Using straight-line depreciation over 27.5 years, what is the annual depreciation?

Answer: ($310,000 − $60,000) ÷ 27.5 = $9,090.91/year.

Arizona Real Estate Exam Math—Formula Cheat Sheet

Every formula category on the Arizona Pearson VUE exam. Save it, print it, use it.

Category	Formula	Key to memorize
Commission	Sale Price × Rate = Total Commission Party's Cut = Total × Split %	Use Memory Circle
Proration	Annual ÷ Days × Days Owned = Amount Due	360 OR 365 — exam tells you
Property Area	L × W = Sq Ft \| Sq Ft ÷ 43,560 = Acres	43,560 sq ft = 1 acre
Loan / Points	P × R × T = Interest 1 point = 1% of LOAN (not price)	Points on loan, not purchase price
Property Tax	MV × Assessment % = AV AV × Mill Rate = Annual Tax	AZ residential: 10% of LPV
Investment (GRM)	Property Price ÷ Gross Annual Rent = GRM	Lower GRM = better deal
28/36 Rule	Income × 0.28 = Max housing Income × 0.36 = Max total debt	Housing ≤28%; All debt ≤36%
Depreciation	(Cost − Land) ÷ 27.5 = Annual dep.	Residential 27.5 yrs; commercial 39

5 Exam Day Tips for the Math Section

Bring an approved calculator. Battery-operated, non-printing, no alphabetic keypad. Approved models include the HP 10BII, HP 12C, and Real Estate Qualifier Plus IIIX. Smartphones are not permitted.
Convert percentages before every calculation. 6% = 0.06. 5.5% = 0.055. Enter the decimal, not the whole number.
Read every proration question in full before starting. It will specify 360 or 365 days AND whose day closing is. Don't start calculating until you've identified both.
Use scratch paper. Pearson VUE provides it at the test center. Write out every step. A wrong answer takes seconds to find on scratch paper; recalculating from memory takes minutes.
Flag and return. Complete the questions you're confident about first. Flag math questions needing extra time and come back. Don't let one proration problem derail your time budget.

Ready to Put This Into Practice?

The math formulas above are a start. The exam covers much more—contracts, agency, Arizona statutes, property rights, and 170+ additional questions. Here are the resources to take you from formula practice to exam-day ready:

New to the process? How to Become a Real Estate Agent in Arizona—the complete step-by-step from eligibility through license application.
Wondering what you'd earn? How Much Do Real Estate Agents Make in Arizona?—Use the free commission calculator to model your income based on deal volume and price point.
Studying in Scottsdale? ASREB's Scottsdale pre-licensing courses—classroom, livestream, and online options with flexible scheduling.
Ready to prep for the actual exam? ASREB Exam Prep—powered by CompuCram with simulated practice exams that mirror the Pearson VUE format.

Start Your Arizona Real Estate Career with ASREB

You've done the hardest part of the math prep. The next step is a pre-licensing program that delivers the rest—and stands behind it with a guarantee no other Arizona real estate school offers.

Pass or Don't Pay Guarantee

Follow ASREB's recommended study plan and pass the Arizona state exam on your first attempt—or ASREB refunds your first state exam fee. No hoops, no asterisks. Just send your Pearson VUE score report to ASREB.

You've just spent time learning every math formula on the exam. The next step is a pre-licensing program that makes sure you show up to the test center ready to use them.

ASREB students have a 74% first-time pass rate on the Arizona real estate exam—well above the statewide average of around 60%. That gap comes from how ASREB prepares students, not just which students enroll.

55+ years of Arizona real estate education. ASREB has been Arizona's leading real estate school since 1969. The instructors are licensed Arizona real estate professionals—they teach from real-world market experience, not textbooks.

CompuCram exam prep—86.5% first-time pass rate. ASREB students get access to CompuCram: practice tests, a simulated exam that mirrors Pearson VUE's format, a readiness indicator to show you when you're ready, and math review specifically for the calculation sections. Value: $105.

The Crammer Course. An instructor-led live exam prep session reviewing exam questions, testing strategies, and key terminology—including every math category in this guide. Value: $99.

Your format, your schedule. Self-paced online, livestream, or in-person classroom. Mix and match as you go. Complete the 90-hour pre-licensing requirement on a timeline that works around your current job and life.

Career support beyond the exam. Career Nights, the Broker Marketplace, a Broker Interviewing Skills Workshop, and 18 hours of continuing education included at no extra charge for the first renewal cycle.

Get started: View ASREB pre-licensing course options | Explore exam prep

Frequently Asked Questions

How many math questions are on the Arizona real estate exam?

The national/general portion includes 7 dedicated math questions (one per category). The Arizona state exam adds further math, bringing the combined total to approximately 11 math questions across the full 195-question exam (180 scored, 15 unscored pretest items).

Can you use a calculator on the Arizona real estate exam?

Yes. Pearson VUE allows a battery-operated, non-printing, silent calculator without an alphabetic keypad. Approved models include the HP 10BII, HP 10, HP 12C, Real Estate Qualifier Plus IIIX, and Real Estate Mortgage Qualifier Plus. Smartphones are not permitted.

What is the difference between a 360-day and 365-day year in proration?

The 360-day banker's year treats every month as exactly 30 days. The 365-day calendar year uses actual day counts. The Arizona Pearson VUE exam will always specify which method to use within the question. Using the wrong method gives a different answer even with perfect arithmetic.

How does Arizona calculate property tax differently from other states?

Arizona assesses residential properties at 10% of their Limited Property Value (LPV), which is capped at a maximum 5% annual increase regardless of market appreciation. This means assessed values can be significantly below market value in fast-appreciating areas like Scottsdale. On the exam, you'll be given the assessed value or assessment rate—the calculation sequence is the same.

What are discount points and how are they calculated?

Discount points are upfront fees paid to reduce a loan's interest rate. One point equals 1% of the loan amount—not the purchase price. Calculate the loan amount first (purchase price minus down payment), then multiply by the number of points as a percentage. Calculating on the purchase price instead of the loan amount is the most common error in this category.

What is ASREB's Pass or Don't Pay Guarantee?

If you follow ASREB's recommended study plan and don't pass the Arizona state exam on your first attempt, ASREB refunds your first state exam fee. Send your Pearson VUE score report to ASREB to claim the refund. Learn more about our Pass or Don't Pay Guarantee.

What is the passing score for the Arizona real estate exam?

75%—135 of 180 scored questions correct.

Does ASREB's exam prep cover math?

Yes. ASREB's pre-licensing and exam prep courses cover all math categories tested by Pearson VUE, with AZ-specific worked examples and practice problems through the CompuCram platform. There is also a dedicated math review session available. View exam prep options.