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Free randomized Math Coach

Illinois real estate exam math drill

Start a ten-question set drawn from 27 original problems. You are not told the formula in advance. Enter the answer, commit to your setup, and then compare it with a worked explanation. The bank covers the calculation families in the PSI Illinois broker outline effective June 24, 2026, plus the Illinois transfer-tax context candidates need to recognize.

Start your randomized math drill

Each run samples ten problems without repeating a question inside that set. A new run reshuffles the complete bank. Your result links each missed topic to the right guide so review starts with the actual gap instead of a generic formula sheet.

Randomized Math Coach

Ten problems, no formula labels in advance

Your set is drawn from 27 current problems across the calculation families named in the PSI broker outline. Enter the answer yourself. You will see the setup only after you commit.

  • Use numbers only; dollar signs, commas, and percent signs are accepted.
  • Carry precision until the final answer unless the question says otherwise.
  • A fresh set is randomized each time you start again.

What does the 2026 math drill cover?

The national broker outline assigns approximately seven of 100 scored national questions to Real Estate Math. That published weight is smaller than the number of skills named inside the category, so this bank rotates across families rather than showing the same five formulas every time.

Question family
Percent and commission
Skills sampled
Rate conversion, reverse base, split chains
Question family
Illinois tax
Skills sampled
Assessment sequence, mill rate, transfer-tax ceiling
Question family
Proration
Skills sampled
360-day and 365-day methods, party share
Question family
Closing math
Skills sampled
Buyer funds, seller net, credits, deposits, payoff
Question family
Financing
Skills sampled
LTV, equity, PITI, whole and fractional points
Question family
Measurement
Skills sampled
Rectangle subtraction, square feet, acres, aliquot parts
Question family
Value change
Skills sampled
Appreciation and percentage depreciation
Question family
Income valuation
Skills sampled
GRM, EGI, NOI, cap rate, capitalized value

The split-chain item is included to strengthen sequential percentage work. Commission appears in the current math outline, but a brokerage-to-licensee commission split is not a separate published calculation heading. Treat that question as supporting arithmetic, not evidence of an extra PSI category.

Outline source: PSI Illinois Candidate Information Booklet dated June 24, 2026. The outline weight is approximate and does not guarantee the visible number or order of math questions on one exam form.

How should you set up each problem?

  1. Name the target. Write or say the exact answer unit: dollars, percent, acres, days, monthly payment, annual NOI, buyer cash, or seller net.
  2. Select the relationship. State it in words before choosing numbers. For example, points are a percent of loan amount, and cap rate is annual NOI divided by value.
  3. Label the inputs. Several plausible bases may appear. Price, value, loan, taxable EAV, gross rent, and original value are not interchangeable.
  4. Align the units. Convert percent to decimal, annual figures to monthly when required, and square feet to acres only after area is calculated.
  5. Estimate before calculating. A half-percent fee should be far below half the base. An 80% LTV should leave a simple one-loan equity share near 20%.
  6. Reverse-check. Substitute the answer into the original formula, reconcile the closing ledger, or confirm that party-day counts match the stated year.

Do not chase the answer with arithmetic alone

Many distractors are mathematically neat. They use purchase price instead of loan amount, gross income instead of NOI, 5 instead of 0.05, annual tax inside a monthly total, or nearest rounding when a statute says fraction thereof. A visible setup is the defense.

How should you use your score?

Treat the score as a diagnostic, not a pass prediction. Ten questions cannot sample every variation, and a randomized set may lean toward your stronger or weaker families. The missed-topic links are more useful than the total by itself.

9 or 10 correct

Explain every setup, including guessed answers. Repeat on a fresh set. Two strong sets with no recurring error justify spaced maintenance.

7 or 8 correct

Review the linked families, solve five focused questions on each miss, then return to mixed practice where the formula is not announced.

0 to 6 correct

Rebuild the parent formulas, percent conversions, periods, and party ledgers before another timed set. Accuracy comes before speed.

Keep a one-line error log. Classify each miss as target, formula, definition, base, unit, party direction, inclusion, rounding, calculator entry, or timing. If one label repeats, that is the next lesson. Redoing only the same question can test memory of its numbers rather than mastery of the relationship.

Which current rules matter in the drill?

Problems state transaction-specific facts rather than pretending one number fits every file. Compensation rates are negotiable. Illinois property taxes have no single statewide aggregate rate. Cook County classification and preferential assessments can differ from the ordinary one-third example. LTV depends on the required value and included debt. Gross multipliers must use a consistent income period.

A mortgage point is 1% of loan amount, but it does not guarantee one fixed interest-rate change. Illinois state transfer tax is currently $0.50 per $500 or fraction of value, and the county rate is $0.25 per $500 or fraction of value. A question can supply both and can add a municipal rate when relevant. The words or fraction thereof create a ceiling, so a partial $500 unit is raised rather than rounded to nearest.

Worked explanations follow the facts in their question. In a live transaction, the operative contract, loan program, tax records, payoff, invoices, disclosure forms, survey, appraisal, and current law control. This tool teaches exam setup, not transaction advice.

Can you practice without scratch paper?

The current PSI booklet supplies one piece of scratch paper and a pencil at a test center and requires both to be returned. Standard remote proctoring does not allow scratch paper. If you plan to test remotely, use this drill without paper after learning each formula. Keep one labeled subtotal active at a time. Use a calculator only when PSI authorizes it for the delivery setting, and do not assume a particular remote interface tool will be available.

If paper-free accuracy remains materially lower than your test-center-style score, consider whether test-center delivery is the safer fit. Follow current appointment instructions and any approved accommodation. Do not assume a personal sheet, whiteboard, or writing surface is permitted remotely.

See the current scratch-paper rules and calculator policy before choosing your testing format.

Illinois real estate math drill FAQ

Is this Illinois real estate math drill free?

Yes. Each run gives ten questions drawn from the free question bank, worked explanations, a score, and links to the topic guides for anything you miss. Starting a new set reshuffles the bank.

What math is on the Illinois real estate broker exam?

The PSI outline effective June 24, 2026 assigns approximately seven of 100 scored national questions to Real Estate Math. It names basic math, tax, proration, commission, closing funds, transfer fees, PITI, equity, LTV, points, area, acreage, value change, assessment, mill rate, gross multipliers, and capitalization rate.

Are these questions from the live PSI exam?

No. They are original practice problems written from the current outline and primary sources. They are not copied, recalled, reconstructed, or presented as live PSI examination content.

How should I enter money and percentages?

Enter the requested number. Dollar signs, commas, spaces, and percent signs are accepted and removed before scoring. If the label asks for a percentage, enter 80 for 80%, not 0.80. If it asks for dollars, enter the dollar amount rather than a rate.

What score should I aim for?

Aim for at least 9 of 10 on two fresh randomized sets, with a correct setup you can explain for every answer. A single high score can include familiar questions or lucky arithmetic, so use repeated performance and the absence of recurring error types as the readiness signal.

Why does the drill not tell me the formula first?

Formula selection is part of the tested skill. A real question can place price, loan, value, rate, costs, time periods, and distractors in the same stem. Naming the target and selecting the relationship before calculating is more useful than completing a worksheet already labeled LTV or proration.

Does the drill use current Illinois tax rates?

Illinois transfer-tax questions state the rate and use the current state and county structure. Property-tax questions supply their assessment, equalization, exemption, and aggregate-rate facts because Illinois has no single statewide property-tax rate and Cook County and special property types can differ.

Can I use the drill to predict whether I will pass?

No short web drill can predict a PSI result. Use it to find formula and setup gaps. The actual exam covers many non-math domains, contains separate national and Illinois portions, and can include unscored experimental questions.

How many questions are in the randomized math bank?

The current free bank contains 27 original problems, and each run draws ten without repeating a problem inside that set. The mix changes when you start a new set, so repeated attempts are more useful than memorizing one fixed sequence.

Can I use scratch paper or a calculator on the Illinois exam?

Under the current Illinois PSI booklet, a test-center candidate receives one piece of scratch paper and a pencil and may use a qualifying nonprinting, silent, battery-operated calculator. Remote proctoring prohibits scratch paper and a physical calculator. Confirm the current booklet, appointment instructions, proctor directions, and any approved accommodation before testing.

Primary sources

The problem bank was checked against the current PSI outline and the official sources below through August 22, 2026. The official source controls if a study explanation conflicts with it.

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