Free California Math Practice Test — LicenseIQ

Question 1

A lender approves a $276,000 loan and the buyer wants to keep an 80% LTV. What is the maximum purchase price?

Accepted Answer

Purchase price = loan / LTV = $276,000 / 0.80 = $345,000. ($220,800 wrongly multiplies by 0.80.)

Question 2

A seller proves that her listing broker's negligence cost her $12,000. Which remedy can the Real Estate Commissioner provide directly?

Accepted Answer

The Commissioner protects the public by acting against licenses. Money damages come from courts or arbitration. The Recovery Account pays only after a final judgment, award, or restitution order based on fraud or conversion, so it cannot pay without a judgment.

Question 3

A home sells for $520,000 with a 5% commission. The listing broker pays 2.5% to the buyer's broker and splits the listing side 60/40 with the listing salesperson (salesperson gets 60%). How much does the listing salesperson earn?

Accepted Answer

Total = $520,000 x 0.05 = $26,000. Buyer broker gets 2.5% = $13,000, leaving $13,000 for the listing side. Salesperson = $13,000 x 0.60 = $7,800.

Question 4

A house with only one bathroom and very small closets in a market expecting more suffers from:

Accepted Answer

Functional obsolescence is outdated design or layout inside the property. External obsolescence comes from outside the property and is usually incurable.

Question 5

A house is L-shaped: one section is 40 ft by 30 ft and the other is 20 ft by 15 ft. At $185 per square foot, what is the estimated cost to build?

Accepted Answer

Area = (40 x 30) + (20 x 15) = 1,200 + 300 = 1,500 sq ft; 1,500 x $185 = $277,500.

Question 6

A 275-gallon heating oil tank costs $168 to fill at $4.20 per gallon. The buyer will credit the seller for the oil remaining in the tank. What is the credit?

Accepted Answer

Gallons needed = $168 / $4.20 = 40; remaining = 275 - 40 = 235 gallons; credit = 235 x $4.20 = $987.

Question 7

A buyer purchases a $275,000 home with an 80% LTV loan and pays 2.5 discount points. What do the points cost?

Accepted Answer

Loan = $275,000 x 0.80 = $220,000; points = $220,000 x 0.025 = $5,500. ($6,875 wrongly applies points to the price.)

Question 8

At a 1.1% total tax rate, how much does the full homeowners' exemption save the owner each year?

Accepted Answer

The exemption reduces assessed value by $7,000. $7,000 × 0.011 = $77. At exactly 1% the savings would be $70.

Question 9

Who appoints California's Real Estate Commissioner?

Accepted Answer

The Commissioner heads the DRE and is appointed by the Governor. The Commissioner is a state officer. Trade associations such as C.A.R. have no appointment role.

Question 10

Annual taxes are $3,650. Using a 365-day year, what is the daily proration amount?

Accepted Answer

$3,650 / 365 = $10 per day. (The course's default convention is a 360-day year; this question specifies 365.)

Question 11

On a $250,000 loan, how much is 2 discount points?

Accepted Answer

1 point = 1% of the loan. 2 points = 0.02 x $250,000 = $5,000.

Question 12

A rectangular lot is 100 ft by 150 ft. How many square feet is it?

Accepted Answer

Area = length x width = 100 x 150 = 15,000 square feet. (250 is the sum of two sides.)

Question 13

A property sells for $545,000. The buyer assumes the seller's existing $245,000 loan. What is the county documentary transfer tax?

Accepted Answer

Liens remaining on the property are excluded: $545,000 − $245,000 = $300,000. $300,000 ÷ $500 = 600 units. 600 × $0.55 = $330.

Question 14

Broker Ortega hires a newly licensed salesperson on June 1. Under the Commissioner's Regulations, by when must the broker notify the DRE?

Accepted Answer

Reg. 2752 requires the responsible broker to notify the Commissioner within five days of employing a salesperson. The ten-day figure applies to the predecessor broker's optional notice of termination.

Question 15

A lender offers a 95% LTV loan. The buyer has $18,000 for the down payment. What is the maximum purchase price?

Accepted Answer

At 95% LTV the down payment is 5% of price. Price = $18,000 / 0.05 = $360,000; loan = $342,000.

Question 16

A seller wants to net $250,000 after paying a 6% commission and $6,000 in other closing costs. To the nearest dollar, what must the sale price be?

Accepted Answer

Net + other costs = $256,000, which equals 94% of the price (100% - 6%). Price = $256,000 / 0.94 = $272,340.43, about $272,340. Adding 6% to $256,000 ($271,360) understates the price.

Question 17

A buyer purchases a $300,000 home with a $60,000 down payment. What is the loan-to-value (LTV) ratio?

Accepted Answer

Loan = $300,000 - $60,000 = $240,000; $240,000 / $300,000 = 80% LTV. (20% is the down payment percentage.)

Question 18

A listing agreement in which the broker earns a commission regardless of who sells the property is a(n):

Accepted Answer

In an exclusive right-to-sell listing, the listing broker earns a commission no matter who procures the buyer, even the owner. (Reclassified to section 6 / CORE.)

Question 19

A borrower pays $4,500 for 1.5 discount points. What is the loan amount?

Accepted Answer

Loan = cost of points / points as a percentage = $4,500 / 0.015 = $300,000.

Question 20

Taxable consideration is $410,250. What is the county documentary transfer tax at $0.55 per $500 or fractional part?

Accepted Answer

$410,250 ÷ $500 = 820.5. A fractional part counts as a full unit, so there are 821 units. 821 × $0.55 = $451.55.

Question 21

A printed listing form for a single-family home must include which notice in at least 10-point boldface type?

Accepted Answer

Section 10147.5 requires the 'not fixed by law' notice in 10-point boldface immediately before the compensation clause for 1–4 unit residential property and mobilehomes.

Question 22

A covered unit rents for $2,800. The lowest rent in the past 12 months was $2,800, and the regional CPI change is 6.5%. What is the maximum new rent under the Tenant Protection Act?

Accepted Answer

5% + 6.5% = 11.5%, which exceeds the 10% ceiling, so 10% applies. $2,800 × 1.10 = $3,080. The tempting $3,122 applies 11.5% and ignores the ceiling.

Question 23

A new highway interchange built next to a residential subdivision lowers home values. This is:

Accepted Answer

Loss in value caused by factors outside the property boundaries is external obsolescence.

Question 24

A broker collects a commission under an exclusive right-to-sell listing that says it lasts 'until the property is sold.' Which statute did the broker violate?

Accepted Answer

Claiming or collecting compensation under an exclusive agreement that lacks a definite, specified termination date is grounds for discipline under §10176(f).

Question 25

A broker's earned commission has been sitting in the trust account. Under Reg. 2835, what is the latest it may remain there?

Accepted Answer

Earned commissions and other broker-owned funds in the trust account must be disbursed within 25 days. Holding them longer is commingling.

California real estate math practice test

1. A lender approves a $276,000 loan and the buyer wants to keep an 80% LTV. What is the maximum purchase price?

2. A seller proves that her listing broker's negligence cost her $12,000. Which remedy can the Real Estate Commissioner provide directly?

3. A home sells for $520,000 with a 5% commission. The listing broker pays 2.5% to the buyer's broker and splits the listing side 60/40 with the listing salesperson (salesperson gets 60%). How much does the listing salesperson earn?

4. A house with only one bathroom and very small closets in a market expecting more suffers from:

5. A house is L-shaped: one section is 40 ft by 30 ft and the other is 20 ft by 15 ft. At $185 per square foot, what is the estimated cost to build?

6. A 275-gallon heating oil tank costs $168 to fill at $4.20 per gallon. The buyer will credit the seller for the oil remaining in the tank. What is the credit?

7. A buyer purchases a $275,000 home with an 80% LTV loan and pays 2.5 discount points. What do the points cost?

8. At a 1.1% total tax rate, how much does the full homeowners' exemption save the owner each year?

9. Who appoints California's Real Estate Commissioner?

10. Annual taxes are $3,650. Using a 365-day year, what is the daily proration amount?

11. On a $250,000 loan, how much is 2 discount points?

12. A rectangular lot is 100 ft by 150 ft. How many square feet is it?

13. A property sells for $545,000. The buyer assumes the seller's existing $245,000 loan. What is the county documentary transfer tax?

14. Broker Ortega hires a newly licensed salesperson on June 1. Under the Commissioner's Regulations, by when must the broker notify the DRE?

15. A lender offers a 95% LTV loan. The buyer has $18,000 for the down payment. What is the maximum purchase price?

16. A seller wants to net $250,000 after paying a 6% commission and $6,000 in other closing costs. To the nearest dollar, what must the sale price be?

17. A buyer purchases a $300,000 home with a $60,000 down payment. What is the loan-to-value (LTV) ratio?

18. A listing agreement in which the broker earns a commission regardless of who sells the property is a(n):

19. A borrower pays $4,500 for 1.5 discount points. What is the loan amount?

20. Taxable consideration is $410,250. What is the county documentary transfer tax at $0.55 per $500 or fractional part?

21. A printed listing form for a single-family home must include which notice in at least 10-point boldface type?

22. A covered unit rents for $2,800. The lowest rent in the past 12 months was $2,800, and the regional CPI change is 6.5%. What is the maximum new rent under the Tenant Protection Act?

23. A new highway interchange built next to a residential subdivision lowers home values. This is:

24. A broker collects a commission under an exclusive right-to-sell listing that says it lasts 'until the property is sold.' Which statute did the broker violate?

25. A broker's earned commission has been sitting in the trust account. Under Reg. 2835, what is the latest it may remain there?

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