AEPA Mathematics (NT304)

A candidate estimates 48.6% of 398 by using 50% of 400. Which statement best describes the estimate?

• AIt is about 200 and is reasonable because both numbers were rounded to convenient nearby…
• BIt is about 100 and is reasonable because 50% means divide both numbers by 4.
• CIt is about 400 and is reasonable because percent values near 50% double the original num…
• DIt cannot be estimated without first converting 48.6% to an exact fraction.

What is 3/4 divided by 2/3?

• A1/2
• B9/8
• C8/9
• D5/7

A class has a ratio of 3 juniors to 5 seniors. If there are 64 students in all, how many are seniors?

• A24
• B32
• C40
• D48

Which number is the greatest common factor of 84 and 120?

• A6
• B12
• C24
• D36

What is the product (4 + 3i)(4 - 3i)?

• A7
• B16 - 9i
• C25
• D25i

Which statement is the contrapositive of "If a figure is a square, then it is a rectangle"?

• AIf a figure is a rectangle, then it is a square.
• BIf a figure is not a square, then it is not a rectangle.
• CIf a figure is not a rectangle, then it is not a square.
• DIf a figure is a square, then it is not a rectangle.

A cyclist travels 18 miles in 1.5 hours and then 10 miles in 0.5 hour. What is the cyclist's average speed for the entire trip?

• A14 miles per hour
• B16 miles per hour
• C18 miles per hour
• D20 miles per hour

A price is increased by 20% and then the new price is decreased by 20%. What is the final price compared with the original price?

• A4% lower than the original
• BThe same as the original
• C4% higher than the original
• D20% lower than the original

For which truth values of p and q is the implication p -> q false?

• Ap is true and q is true
• Bp is true and q is false
• Cp is false and q is true
• Dp is false and q is false

A student claims that n^2 + n + 11 is prime for every positive integer n after checking n = 1, 2, 3, and 4. Which response best addresses the reasoning?

• AThe claim is proven because several examples support it.
• BThe claim is false because n = 11 gives a composite value.
• CThe claim is true because all quadratic expressions generate primes.
• DThe claim cannot be evaluated because n is not specified.

Two buses leave a station at 6:00 a.m. One bus leaves every 18 minutes and the other leaves every 24 minutes. At what time will they next leave together?

• A6:36 a.m.
• B6:42 a.m.
• C7:12 a.m.
• D7:24 a.m.

A line representing a gym membership has equation C = 35m + 60, where C is total cost in dollars and m is the number of months. What does the 60 represent?

• AThe monthly fee
• BThe number of months included
• CThe one-time starting fee
• DThe total cost after 35 months

What is (3 + 4i) / (1 - 2i) in standard a + bi form?

• A-1 + 2i
• B1 + 2i
• C11 - 2i
• D-5 + 10i

If p and q are prime numbers and p^2 q^3 = 108, what is p + q?

• A5
• B6
• C7
• D9

Which statement about irrational numbers is always true?

• AThe sum of two irrational numbers is irrational.
• BThe product of two irrational numbers is irrational.
• CThe sum of a rational number and an irrational number is irrational.
• DThe quotient of two irrational numbers is irrational.

A grocer mixes 12 pounds of nuts costing $4 per pound with x pounds of nuts costing $7 per pound. If the mixture costs $5.50 per pound, what is x?

• A6
• B8
• C10
• D12

For how many rows of the truth table is (p -> q) AND (q -> p) true?

• A1
• B2
• C3
• D4

What is the least common multiple of 391 and 299?

• A299
• B391
• C5,083
• D116,909

Which argument proves that if a^2 is divisible by 3, then a is divisible by 3?

• AAssume a is not divisible by 3; then a is congruent to 1 or 2 mod 3, so a^2 is congruent…
• BAssume a is divisible by 3; then a^2 is divisible by 9, which proves the original implica…
• CCheck a = 3 and a = 6; both work, so the statement is proven for all integers.
• DSince 3 is odd, every square divisible by 3 must be odd.

If f(x) = 2x^2 - 3, what is f(4)?

• A13
• B25
• C29
• D35

What is the solution of 3x - 7 = 20?

• Ax = 7
• Bx = 9
• Cx = 13
• Dx = 27

Which expression is equivalent to x^2 - 9?

• A(x - 9)(x + 1)
• B(x - 3)(x + 3)
• C(x - 3)^2
• D(x + 9)(x - 1)