Mathematics Knowledge Practice Test 1

Correct answer: A — 24

According to the order of operations (PEMDAS):

First, solve inside the parentheses: $$(5 + 2) = 7$$ and $$(4 - 2) = 2$$.

The equation becomes $$7 \times 4 - 8 \div 2$$.

Next, perform multiplication and division from left to right: $$7 \times 4 = 28$$ and $$8 \div 2 = 4$$.

The equation becomes $$28 - 4$$. Finally, subtract: $$28 - 4 = 24$$

Correct answer: A — $$\frac{1}{3}$$

To compare the fractions, convert them to decimals: $$\frac{1}{3} \approx 0.333$$, $$\frac{2}{5} = 0.400$$, $$\frac{3}{8} = 0.375$$, and $$\frac{4}{11} \approx 0.363$$. The smallest decimal value is 0.333, which corresponds to $$\frac{1}{3}$$

Correct answer: B — 71.65

Follow the order of operations (PEMDAS) and perform the multiplication first: $$12.3 \times 2.1 = 25.83$$. Then, add this result to 45.82: $$45.82 + 25.83 = 71.65$$

Correct answer: B — $$\frac{29}{8}$$

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. This becomes the new numerator, placed over the original denominator. $$(3 \times 8) + 5 = 24 + 5 = 29$$. Therefore, the improper fraction is $$\frac{29}{8}$$

Correct answer: A — 34, 33, 66

The pattern alternates between multiplying the previous number by 2 and then subtracting 1.

$$3 \times 2 = 6$$

$$6 - 1 = 5$$

$$5 \times 2 = 10$$

$$10 - 1 = 9$$

$$9 \times 2 = 18$$

$$18 - 1 = 17$$

Following this pattern, the next operations are: $$17 \times 2 = 34$$; $$34 - 1 = 33$$; $$33 \times 2 = 66$$

Correct answer: A — $$\frac{2}{3}$$

To divide by a fraction, you multiply by its reciprocal. The reciprocal of $$\frac{9}{10}$$ is $$\frac{10}{9}$$. Multiply: $$\frac{3}{5} \times \frac{10}{9} = \frac{(3 \times 10)}{(5 \times 9)} = \frac{30}{45}$$. Simplifying the fraction by dividing both the numerator and denominator by 15 gives $$\frac{2}{3}$$

Correct answer: B — 349.5

To round to the nearest tenth, look at the hundredths digit. The number in the tenths place is 5, and the number in the hundredths place is 4. Since 4 is less than 5, you keep the tenths digit the same and drop the remaining digits. The result is 349.5.

Correct answer: C — 6

First, convert the mixed numbers to improper fractions: $$2 \frac{1}{3} = \frac{7}{3}$$, and $$1 \frac{4}{5} = \frac{9}{5}$$. Multiply these fractions: $$\frac{7}{3} \times \frac{9}{5} = \frac{63}{15}$$, which simplifies to $$\frac{21}{5}$$. Next, divide by $$\frac{7}{10}$$ by multiplying by its reciprocal $$(\frac{10}{7})$$: $$\frac{21}{5} \times \frac{10}{7} = \frac{(21 \times 10)}{(5 \times 7)} = \frac{210}{35}$$. Dividing 210 by 35 equals exactly 6.

Correct answer: C — A number that can be divided evenly only by 1 and itself, and is greater than 1.

A prime number is a natural number strictly greater than 1 that cannot be formed by multiplying two smaller natural numbers. Therefore, it has exactly two distinct positive divisors: 1 and the number itself.

Correct answer: B — 1

First, solve inside the parentheses. Convert $$\frac{1}{4}$$ to 0.25. Then, $$0.5 + 0.25 = 0.75$$. For the second set of parentheses, dividing by $$\frac{1}{2}$$ is the same as multiplying by 2, so $$3 \div \frac{1}{2} = 6$$. Now substitute these back into the expression: $$0.75 \times 8 \div 6$$. Following order of operations from left to right: $$0.75 \times 8 = 6$$. Finally, $$6 \div 6 = 1$$