Mathematics Knowledge Practice Test 4

Correct answer: C — 40

First, find the square root of each number: $$\sqrt{64} = 8$$ and $$\sqrt{25} = 5$$. Then, find their product by multiplying them together: $$8 \times 5 = 40$$

Correct answer: A — 243

When multiplying numbers with the same base, you can simply add their exponents: $$3^3 \times 3^2 = 3^{(3+2)} = 3^5$$. Calculating 3⁵ gives $$3 \times 3 \times 3 \times 3 \times 3 = 243$$. Alternatively, solve each first: $$27 \times 9 = 243$$

Correct answer: B — 13

The square root of a number is a value that, when multiplied by itself, gives the original number. Since $$13 \times 13 = 169$$, the square root of 169 is 13.

Correct answer: C — $$5.12 \times 10^{-9}$$

To write a number in scientific notation, move the decimal point to the right until you have a number between 1 and 10 (which is 5.12). Since you moved the decimal point 9 places to the right to make a very small number into 5.12, the exponent is negative 9. Thus, $$5.12 \times 10^{-9}$$.

Correct answer: B — $$2^3 \times 3 \times 5$$

To find the prime factorization, divide by prime numbers: $$120 = 2 \times 60$$. Then $$60 = 2 \times 30$$. Then $$30 = 2 \times 15$$. Finally, $$15 = 3 \times 5$$. Grouping the factors gives $$2 \times 2 \times 2 \times 3 \times 5$$, which can be written using exponents as $$2^3 \times 3 \times 5$$. Option A contains 4 (not prime), and Option D contains 60 (not prime).

Correct answer: B — $360

Use the simple interest formula: Interest = Principal × Rate × Time in years ($$I = PRT$$). The principal is $4,000, the rate is 0.06 (6%), and the time is 1.5 years (18 months divided by 12). $$I = 4000 \times 0.06 \times 1.5 = 360$$.

Correct answer: C — 48 minutes

First, find the total distance using Distance = Speed × Time. Distance = 80 mph × 4 hours = 320 miles. Next, find the time it would take at the new speed: Time = Distance ÷ Speed = $$320 \div 100 = 3.2$$ hours. The time saved is the original time minus the new time: $$4 - 3.2 = 0.8$$ hours. Convert 0.8 hours to minutes by multiplying by 60: $$0.8 \times 60 = 48$$ minutes.

Correct answer: C — 12.5

Sarah needs to earn $50,000 in interest ($150,000 target - $100,000 deposit). The account earns simple interest on the initial $100,000 at 4% per year, which is $4,000 per year ($100,000 × 0.04). Divide the total interest needed by the annual interest to find the number of years: $50,000 ÷ $4,000 = 12.5 years.

Correct answer: B — 12 miles

Let 'd' be the one-way distance. The time to get to the park is $$\frac{d}{12}$$ and the time to return is $$\frac{d}{8}$$. The total time is 2.5 hours, so $$\frac{d}{12} + \frac{d}{8} = 2.5$$. To add the fractions, find a common denominator (24), yielding $$2d/24 + 3d/24 = 2.5$$. This simplifies to $$5d/24 = 2.5$$. Multiply both sides by 24 to get $$5d = 60$$, then divide by 5 to find $$d = 12$$ miles.

Correct answer: B — 12 hours

Since the ships are moving towards each other, add their speeds to find the relative rate of closure. Their combined speed is $$20 + 15 = 35$$ knots. To find the time it takes to cover the 420 nautical miles separating them, divide the total distance by their combined speed: $$420 \div 35 = 12$$ hours.