Geometry and Algebra Problem Set

This video tutorial focuses on the math section of the OAT test, specifically the quantitative reasoning part. It covers various topics such as the distance formula, expanding expressions using FOIL, circle geometry, logarithmic expressions, solving linear equations, trigonometry basics, and working with fractions and ratios. The video provides practice problems and solutions to help learners understand and apply these mathematical concepts effectively.

What is the distance between the points (-4, 2) and (8, 7)?

• 16

• 10

• 14

• 12

Which expression is equivalent to (3x - 2y)^2?

• 9x^2 - 12xy + 4y^2

• 9x^2 + 4y^2

• 6x^2 - 8xy + 4y^2

• 9x^2 - 4xy + 4y^2

If the circumference of a circle is 10π, what is its area?

• 10π

• 20π

• 25π

• 50π

If 3x + 7 = 5x + 1, what is the value of 7x + 4?

• 21

• 23

• 19

• 25

If sin(x) = 4/5 and cos(x) > 0, what is tan(x)?

• 3/4

• 4/3

• 5/4

• 4/5

If a product costs $300 and the sales tax is 8%, what is the final price of the product?

• $324

• $330

• $312

• $318

A shirt's final price is $48.15 after a 7% sales tax. What was the original price?

• $47

• $44

• $46

• $45

What is the value of a stock after it rises by 20% and then falls by 20% from an initial price of $100?

• $96

• $100

• $80

• $120

How far apart will a car traveling east at 30 mph and a bus traveling north at 60 mph be after 4 hours?

• 150 miles

• 136 miles

• 180 miles

• 120 miles

Susan bought 5 books for $4 each and 10 books for $8 each. What is the average cost per book?

• $6.00

• $7.00

• $6.67

• $5.33