Illinois exam math practice
How to practice real estate math without scratch paper
Read the requested result first, choose the relationship, align the units and estimate the answer. Then work in short steps, giving each subtotal a name before using it again. This method can reduce what you need to hold in memory. Test it under confirmed exam conditions; it does not guarantee that remote delivery will suit you.
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Start with the actual testing conditions
The PSI Illinois booklet dated June 24, 2026 permits a physical calculator and supplies paper and pencil at a test center. Standard remote testing prohibits physical calculators and scratch paper. The scored national Real Estate Calculations category is 7 percent; numbers can also appear in other topics, so that is not a cap on all numerical work.
The live Illinois PSI program FAQ gives test-center calculator feature criteria. The exact digital calculator, whiteboard, memory functions and shortcuts for a remote booking remain unconfirmed in the public sources inspected. The calculator-policy guide separates those confirmed rules from the open tool questions.
PSI's current system requirements direct Secure Browser candidates to the assigned tutorial in My Tests after booking. Ask whether that tutorial demonstrates the same math tools as the actual Illinois exam. A compatibility check, generic demo or app exercise does not answer that question.
Practice with paper while learning a new relationship, then compare work without it. Use a calculator display only when that tool is authorized and confirmed. Never substitute a personal notes app, spreadsheet, physical whiteboard or hidden paper.
Use a smaller-step method instead of holding the whole problem
| Step | What to decide | Example of a useful label |
|---|---|---|
| Name the target | What result and unit does the question ask for? | Monthly payment, not annual cost |
| Choose the relationship | Which facts belong in that equation? | Loan amount times points rate |
| Align units and estimate | Do the rates and periods match, and what size should the result be? | One percent of the loan |
| Complete a short stage | What does this new subtotal mean? | Monthly tax: $600 |
| Check the result | Does it satisfy the original relationship and requested unit? | Dollar cost, not an interest-rate reduction |
If you have an authorized calculator display, it can hold a subtotal while you remember its meaning. Without one, choose simple percentage or fraction anchors where they fit. Return to the stem for a fact rather than trying to retain every number at once.
Do not silently change a problem to make it easier. A 360-day denominator does not always mean every month has 30 days, and a loan's value basis is not automatically the purchase price. Use the actual assumptions in the question. The day-count guide explains why those proration details matter.
Worked examples: keep the label with the number
1. A percentage amount
A stated compensation base is $360,000 and the stated rate is 4.5 percent. Five percent is $18,000. Half of one percent is $1,800. Subtract: $18,000 - $1,800 = $16,200. The label is total compensation under the stated terms, before any other split or expense. No standard commission rate is implied.
2. Put PITI components on the same monthly basis
Monthly principal and interest are $1,900, annual property tax is $7,200 and annual homeowners insurance is $1,800. Convert first: tax is $600 per month and insurance is $150 per month. Then $1,900 + $600 + $150 = $2,650 monthly PITI.
The CFPB PITI explanation defines the four components. This example is not a complete household budget and does not claim that HOA charges, utilities or every insurance cost are included.
3. Calculate points on the loan base
A $240,000 loan has a stated 1.5-point charge. One percent is $2,400 and half a percent is $1,200, for $3,600. The CFPB points guide explains that a point equals one percent of the loan amount. That does not mean one point always lowers the interest rate by one percentage point.
4. Use a complement only when the facts allow it
A practice purchase gives both price and the loan's value basis as $400,000. A single loan is 80 percent of that basis, and the question excludes other financing, credits and closing costs. The down-payment share is 20 percent, so the down payment is $80,000. If the value basis or sources change, return to the actual amounts rather than reusing that shortcut.
5. Keep a longer calculation in named stages
A simplified practice stem gives potential income of $100,000, vacancy loss of $5,000, other income of $2,000 and operating expenses of $37,000. It defines effective income as potential income minus vacancy plus other income, NOI as effective income minus those expenses, and value as NOI divided by a stated 8 percent capitalization rate.
Work in stages: effective income is $97,000; annual NOI is $60,000; the indicated value under the supplied formula is $60,000 ÷ 0.08 = $750,000. Check backward: eight percent of $750,000 is $60,000. These are a simplified practice model and supplied expense categories, not a complete appraisal or lending calculation.
The down payment in that simplified example is not the full cash needed at closing. A question about total cash can add closing costs, deposits already paid, credits or other specified sources. Identify the requested result before using the 20 percent shortcut.
A longer problem may still need several stages. Name those stages, return to given facts as needed and stop when a subtotal loses its meaning. If the exam interface permits returning to the item, follow its navigation instructions and leave enough time to revisit it. No particular flag, hotkey or portion-to-portion time transfer is promised here.
Try four original paper-free questions
Choose an answer before opening the explanation. The calculations use the stated assumptions. These are original exercises, not recalled or released PSI questions.
1. Which answer is monthly PITI?
Monthly P&I is $1,900, annual tax is $7,200 and annual homeowners insurance is $1,800. Find monthly PITI using only those components.
- $2,050
- $2,650
- $9,100
- $10,900
Show answer and every-choice explanation
B is correct. Annual tax converts to $600 monthly, and insurance to $150: $1,900 + $600 + $150 = $2,650. A leaves out tax. C adds annual tax to monthly P&I and leaves out insurance. D adds both annual figures to the monthly payment. If annual tax becomes $8,400 with other facts unchanged, monthly PITI becomes $2,750.
2. Which amount is the points charge?
The purchase price is $300,000, the loan is $240,000 and the stated charge is 1.5 points on that loan.
- $4,500
- $2,400
- $360
- $3,600
Show answer and every-choice explanation
D is correct. $240,000 × 0.015 = $3,600. A uses the purchase price instead of the loan. B charges one point, leaving out the half point. C is ten times too small. If the charge becomes two points on the same loan, it is $4,800. The question calculates a dollar charge, not the amount of any interest-rate reduction.
3. Which amount is the down payment?
Price and the loan's value basis are both $400,000. One loan supplies 80 percent of that basis. There is no other financing or credit, and the question excludes closing costs.
- $80,000
- $320,000
- $64,000
- $500,000
Show answer and every-choice explanation
A is correct. The loan is $320,000, leaving $80,000 of the price; equivalently, 20 percent of $400,000 is $80,000. B is the loan amount. C applies 20 percent to the loan instead of the stated price/value base. D divides price by 0.80 and answers a different question. With a 90 percent loan and the same simplifying facts, the down payment becomes $40,000.
4. Which answer fits the stated fee?
A 0.5 percent fee applies to a stated $420,000 base. Find the fee.
- $210
- $21,000
- $2,100
- $4,200
Show answer and every-choice explanation
C is correct. One percent is $4,200, so half of one percent is $2,100. A uses 0.05 percent, ten times too little. B uses five percent, ten times too much. D uses one percent, twice the stated rate. If the stated rate becomes one percent, D becomes correct at $4,200.
Compare practice conditions before choosing delivery
Use comparable mixed sets rather than repeating a memorized question. Record accuracy and elapsed time with the permitted tools you expect to use. If comparing paper and paper-free work, use similar difficulty and review the mistakes, since different sets can change the result.
| Error | What to check | Next practice task |
|---|---|---|
| Wrong base | Loan, price or another stated amount? | Name the base before calculating points or a fee |
| Wrong period | Are annual and monthly amounts mixed? | Convert each component before adding PITI |
| Lost subtotal | What did the previous number represent? | Restart the short stage and keep its label |
| Decimal placement | Does the answer fit a one-percent estimate? | Check 0.5 percent and 5 percent on the same base |
If written setup or a qualifying physical calculator materially helps, consider a test center, where those standard tools are documented. For remote delivery, resolve the digital-tool questions before relying on a particular setup. An approved accommodation is a separate arrangement; follow the official accommodation process and written instructions.
Paper-free Illinois exam math questions
Can I use scratch paper on the Illinois broker exam?
The June 24, 2026 PSI Illinois booklet supplies a piece of scratch paper and a pencil at a test center, to be returned at checkout. Standard remote proctoring prohibits scratch paper and physical calculators. A digital calculator or writing tool is a separate availability question; this guide does not promise one.
Does paper-free practice mean I must do every calculation mentally?
No. Use only the tools actually authorized and available for your exam. If an approved digital calculator exists, a labeled display value can reduce the subtotals you must remember. If it has not been confirmed, do not build your format decision around it. A test center is an option when permitted physical tools materially improve your work.
What should I do when I lose a subtotal?
Return to the given facts and restart that short step. Do not keep calculating from a number whose meaning you have lost. If the interface permits returning to the item, use that navigation as instructed and come back after shorter work. A flagging feature, hotkey or transfer of time between portions is not assumed here.
Can answer choices help me solve a math question?
Use them after choosing the relationship and expected units. Estimate the likely size or substitute a plausible option back into the stated equation. Reject an option because its calculation or units fail, rather than assuming the largest, smallest or middle choice must be right.
Will these exercises prove I can pass remotely?
No. They are original instructional exercises, not official PSI items or a validated readiness test. Compare representative mixed practice under the confirmed conditions you expect to use, then consider accuracy, time and repeat errors. Follow approved accommodation arrangements where applicable.
Want another set of original math practice?
You can download Pass Illinois to practice the setup and arithmetic before exam day. The app does not reproduce or certify PSI's interface, and it is not an authorized tool to use during the secure exam.