Math Practice Problems and How to Review Them
These problems are written for study and are not drawn from any official examination. Figures in them are invented for illustration; day-count conventions and calculator rules are set by your jurisdiction and its exam vendor and appear in the current candidate handbook.
Working problems is only half of the exercise. The half that moves a score is the review afterward, because a missed calculation has at least three possible causes and each one calls for a different response.
Below are eight original problems drawn from the patterns licensing exams reuse, each solved in full, followed by the method for sorting your own misses.
The Patterns Calculation Items Keep Returning To
Calculation items are not a random sample of arithmetic. They cluster into a handful of families: a part taken as a percentage of a whole, a commission and its splits, a loan measured against a value, an annual charge divided across days, income converted to value, and an assessment converted to tax.
Naming the family is the part being tested. Once a candidate stops reading a problem as a pile of numbers and starts reading it as a member of a family, the wording becomes a routing instruction rather than an obstacle.
Working an Item When the Clock Is Running
Read to the end of the question before touching a figure. The last line states the unknown, and the unknown decides which relationship you need; numbers gathered before that point tend to steer you toward whatever pattern they resemble.
Then write the relationship down with its variables labeled and substitute one line at a time. Multi-step items are where candidates lose the thread, and a written line lets you find your place again instead of restarting. Before moving on, ask whether the size of the answer is plausible for the scenario; a commission larger than a sale price or a value smaller than its own income is a conversion error announcing itself.
Eight Problems, Solved in Full
Original practice written for this page. Cover the solution, work the problem on paper, and compare your setup line to the one shown rather than only the final figure.
Question 1
A listing carried an asking price of $525,000 and closed at 92 percent of that figure. What was the closing price?
Convert the percentage before multiplying: 525,000 x 0.92 = $483,000. The family here is a part taken from a whole, and the only place it goes wrong is a rate left as 92 instead of 0.92, which returns a figure near forty-eight million and should be caught on sight.
Question 2
A lender requires 15 percent of the purchase price in cash on a $340,000 property. How much cash is required, and what is the loan amount?
Cash = 340,000 x 0.15 = $51,000. The loan is the remainder: 340,000 - 51,000 = $289,000, which is also 340,000 x 0.85. Down payment items are percentage items with a second half, and candidates who stop after the first multiplication answer a question that was not asked.
Question 3
A sale at $465,000 carries a 5 percent commission divided evenly between the two brokerage sides. What does each side receive before any internal split?
Total dollars = 465,000 x 0.05 = $23,250. Each side = 23,250 x 0.50 = $11,625. Keeping the percentage step and the split step on separate lines matters more here than the arithmetic, because every further split multiplies whatever base you wrote last.
Question 4
A borrower received a $232,000 loan representing 80 percent of the value the lender used. What was that value?
Run the relationship backward: 232,000 / 0.80 = $290,000. Division is the step under time pressure that candidates skip, multiplying instead and producing $185,600, a figure smaller than the loan it is supposed to support.
Question 5
An income property produces $58,500 of net operating income and is being valued at a 9 percent capitalization rate. What value does that indicate?
Value = 58,500 / 0.09 = $650,000. Note what the income figure already is: net of operating expenses and before any loan payment. A problem that also lists a monthly mortgage payment is testing whether the payment stays out of the numerator.
Question 6
Annual property taxes of $5,840 are being prorated on a 365-day basis. What is the daily amount, and what is the charge for 45 days?
Daily amount = 5,840 / 365 = $16.00. For 45 days, 45 x 16.00 = $720.00. The arithmetic is trivial; proration items are missed on the inputs instead, meaning the day count, the convention the question specifies, and which party carries the closing date.
Question 7
Two problems both mention a property value and a rate. One asks for annual tax and the other for indicated value. Why does the shared wording not make them the same problem?
Because the unknown differs, and the unknown selects the relationship. The tax item multiplies an assessed figure by a levy; the valuation item divides income by a rate. Classification is scored more often than computation, which is why the unknown should be named in plain words before any relationship is written down.
Question 8
A property has a market value of $620,000 in a jurisdiction applying a 45 percent assessment ratio. What figure will the levy be applied to?
Assessed value = 620,000 x 0.45 = $279,000. Apply the ratio first and only then any levy. Ratios, exemptions and levy formats are set locally and vary widely, so use the ratio the item supplies and never carry one over from a previous question.
Sorting a Missed Problem Into Its Cause
Every missed calculation belongs in one of these bins. Log the bin, not the question number, and the next session aims at something specific.
Conversion. A percentage entered whole, or a monthly figure meeting an annual rate. Cheap to fix, and it responds to a short drill of the same step repeated.
Setup. The right relationship arranged wrong, such as dividing where the item called for multiplying. The fix is writing the relationship with labeled variables before substituting anything.
Classification. The wrong relationship entirely. This is a concept gap rather than a math gap, and more arithmetic practice will not close it; go back to the topic itself.
Reading. The unknown was misidentified, or a stated condition was skipped. Fixed by reading to the final line before gathering figures.
Pace. The setup was correct and unfinished. Worth separating from the others, because it calls for more timed exposure rather than more instruction.
Questions About Practicing Calculation Items
Are these problems taken from a real licensing exam?
No. Everything on this page was written for study. Official exam items are secure, and any source offering them is offering something it should not have. These reproduce the patterns, not the questions.
Are short sets better than long ones?
For calculation work, yes, at the start. A short set followed by a real review tells you which bin your misses fall into. A long set produces a score and little else, and the diagnosis is the reason you are practicing.
Percentages still freeze me. What do I do?
Drill the conversion alone, away from any real problem, until moving a stated rate to decimal form is automatic. Once that step stops consuming attention, the problems built on top of it get noticeably easier.
Should calculation practice be timed?
Once your setup is stable, yes. Timing an unstable setup just rehearses the error faster. Add the clock after the misses stop clustering in the setup and classification bins.
How do I know when calculation work is finished?
When misses no longer cluster in one family and the remaining errors are scattered and rare. A readiness check makes that visible: your PassPulse Score shows whether the improvement holds across attempts, and PassMap™ moves your time to whatever is now costing more.
Where to go next: Related Pages
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