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Questions and Answers
How many problems did the student answer correctly if they earned a grade of 90% on a test with 30 problems?
How many problems did the student answer correctly if they earned a grade of 90% on a test with 30 problems?
What percent of 30 is 15?
What percent of 30 is 15?
What is the total number of problems on a test if a student answered 40 problems correctly and received a grade of 40%?
What is the total number of problems on a test if a student answered 40 problems correctly and received a grade of 40%?
What number is 30 if 30 is 10% of that number?
What number is 30 if 30 is 10% of that number?
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What percent attendance was recorded if 8 out of 40 carpenters showed up for work?
What percent attendance was recorded if 8 out of 40 carpenters showed up for work?
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What is the correct result of the expression $3 + (5 \times 2) \div 2 + 10$?
What is the correct result of the expression $3 + (5 \times 2) \div 2 + 10$?
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Which of the following represents a prime number?
Which of the following represents a prime number?
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What are the prime factors of 40?
What are the prime factors of 40?
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What is the result of the operation $82 - 32 \times (15 - 12)^{2}$?
What is the result of the operation $82 - 32 \times (15 - 12)^{2}$?
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Which of these choices is a correct example of prime factorization for the number 90?
Which of these choices is a correct example of prime factorization for the number 90?
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In the order of operations, which operation should be performed last?
In the order of operations, which operation should be performed last?
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Which of the following is NOT a prime factor of 225?
Which of the following is NOT a prime factor of 225?
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What is the result of $5 + 3 \times 49 - 7 \times 258 \times 0$?
What is the result of $5 + 3 \times 49 - 7 \times 258 \times 0$?
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What are the three sides of a triangle if the ratio of the sides is 1:2:3 and the total length is 120 cm?
What are the three sides of a triangle if the ratio of the sides is 1:2:3 and the total length is 120 cm?
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How do you convert a percentage of 55% to a decimal?
How do you convert a percentage of 55% to a decimal?
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What is the base if 20% of it equals 140?
What is the base if 20% of it equals 140?
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Which formula correctly defines the relationship between percentage, base, and rate?
Which formula correctly defines the relationship between percentage, base, and rate?
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What percentage does the decimal 0.345 represent?
What percentage does the decimal 0.345 represent?
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What does the term 'base' refer to in percentage calculations?
What does the term 'base' refer to in percentage calculations?
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What is 20% of 700?
What is 20% of 700?
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How do you convert the decimal 25.5 to a percentage?
How do you convert the decimal 25.5 to a percentage?
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What is the simplified form of the ratio of the belt to the handkerchief?
What is the simplified form of the ratio of the belt to the handkerchief?
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What is the ratio of the number of girls to boys in the class?
What is the ratio of the number of girls to boys in the class?
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How many cups of sugar are needed for 6 cups of boiling water?
How many cups of sugar are needed for 6 cups of boiling water?
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If 4 pipes can fill a tank in 20 minutes, how long will it take 8 pipes to fill the tank?
If 4 pipes can fill a tank in 20 minutes, how long will it take 8 pipes to fill the tank?
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In a direct proportion situation with the formula $\frac{x_1}{y_1} = \frac{x_2}{y_2}$, if $x_1 = 2$, $y_1 = 3$, and $x_2 = 6$, what is $y_2$?
In a direct proportion situation with the formula $\frac{x_1}{y_1} = \frac{x_2}{y_2}$, if $x_1 = 2$, $y_1 = 3$, and $x_2 = 6$, what is $y_2$?
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What type of proportion describes a situation where one quantity increases and another decreases?
What type of proportion describes a situation where one quantity increases and another decreases?
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If a triangle has sides in the ratio 1:2:3 and a perimeter of 120 cm, what is the length of the largest side?
If a triangle has sides in the ratio 1:2:3 and a perimeter of 120 cm, what is the length of the largest side?
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Which of the following equations represents a proportion?
Which of the following equations represents a proportion?
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What is the numerical expression for 'a number increased by 5'?
What is the numerical expression for 'a number increased by 5'?
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Which of the following is the correct verbal expression for the numerical expression '8x - 2'?
Which of the following is the correct verbal expression for the numerical expression '8x - 2'?
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What does the equation '5x + 3x + 2 = 42' simplify to when isolating for x?
What does the equation '5x + 3x + 2 = 42' simplify to when isolating for x?
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What is the first step in solving the equation '5x - 3 - x + 2x = 45'?
What is the first step in solving the equation '5x - 3 - x + 2x = 45'?
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What is the final solution for x in the equation '3x + 2x = 30'?
What is the final solution for x in the equation '3x + 2x = 30'?
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What does 'x ÷ 7' represent in verbal terms?
What does 'x ÷ 7' represent in verbal terms?
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Which of the following is a step in solving an algebraic equation?
Which of the following is a step in solving an algebraic equation?
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Which expression translates to 'a number multiplied by 5'?
Which expression translates to 'a number multiplied by 5'?
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Study Notes
Order of Operations
- PEMDAS is the order of operations: Parenthesis, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right).
Prime Factorization
- Prime factorization breaks down a number into its prime factors.
- A prime number is greater than 1 and its only factors are 1 and itself.
- Example:
- Prime factors of 40 are 2, 2, 2, and 5.
- Prime factors of 24 are 2, 2, 2, and 3.
Ratio
- Ratio compares two quantities.
- The ratio is expressed in its simplest form.
- Example:
- The ratio of girls to boys in a class with 15 boys and 33 girls is 11:5.
Proportion
- Proportion is an equality of two ratios.
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Direct proportion means that as one quantity increases, the other increases, or as one decreases, the other decreases.
- Formula: x1/y1 = x2/y2
-
Inverse proportion means that as one quantity increases, the other decreases, and vice versa.
- Formula: (x1)(y1) = (x2)(y2)
- Partitive proportion divides a quantity into unequal parts.
Percent
- Percent means "per hundred".
- Converting percent to decimal: remove the percent symbol and move the decimal point two places to the left.
- Converting decimal to percent: move the decimal point two places to the right and add the percent symbol.
Percentage, Rate, and Base
- Percentage (P): part of the whole.
- Base (B): the whole.
- Rate (R): the number in percent.
-
Formulas:
- P = B × R
- B = P/R
- R = P/B
Algebraic Expressions and Equations
- Algebraic expression: a combination of numbers, variables, and operations.
-
Translating verbal expressions into algebraic expressions:
- Example: "Eight times a number decreased by 2" is translated as 8x - 2.
- Algebraic equation: an equation with two algebraic expressions set equal.
-
Solving algebraic equations:
- Steps: transpose, combine like terms, divide both sides.
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Description
This quiz covers essential mathematical concepts including PEMDAS, prime factorization, ratios, and proportions. Test your knowledge of how to apply these foundational principles in problem-solving. Perfect for students looking to strengthen their understanding of basic math operations.
