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Questions and Answers
What is the slope of the line represented by the equation -4x + 8y = 32?
What is the slope of the line represented by the equation -4x + 8y = 32?
Find the slope of the line through the points (-7, -9) and (9, -9).
Find the slope of the line through the points (-7, -9) and (9, -9).
Which equation describes a horizontal line?
Which equation describes a horizontal line?
Which of the following equations has a slope of -4 and contains the point (2, 3)?
Which of the following equations has a slope of -4 and contains the point (2, 3)?
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Determine whether the graphs of the equations 3x - 4y = 4 and 8x + 6y = 4 are parallel, perpendicular, or neither.
Determine whether the graphs of the equations 3x - 4y = 4 and 8x + 6y = 4 are parallel, perpendicular, or neither.
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What is the slope of the line represented by the equation if rewritten as y = mx + b?
What is the slope of the line represented by the equation if rewritten as y = mx + b?
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Write the equation of a line that contains the points (2, 0) and (-7, 5).
Write the equation of a line that contains the points (2, 0) and (-7, 5).
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Express x^(-6) using positive exponents.
Express x^(-6) using positive exponents.
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What are six multiples of 22?
What are six multiples of 22?
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Which of the following numbers is 738 divisible by?
Which of the following numbers is 738 divisible by?
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Determine the factors of 42.
Determine the factors of 42.
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What is the prime factorization of 36?
What is the prime factorization of 36?
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Which of the following represents the prime factorization of 30?
Which of the following represents the prime factorization of 30?
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What is the result of simplifying the expression 56x/8x?
What is the result of simplifying the expression 56x/8x?
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What is the least common multiple (LCM) of 7 and 9?
What is the least common multiple (LCM) of 7 and 9?
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Which of the following numbers is 735 divisible by?
Which of the following numbers is 735 divisible by?
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What is the result of rounding 4.17553 to the nearest tenths?
What is the result of rounding 4.17553 to the nearest tenths?
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What is the median of the numbers 52, 72, 279, 250, 405, 471?
What is the median of the numbers 52, 72, 279, 250, 405, 471?
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Estimate the sum of 0.06, 57.37, by rounding to the nearest one.
Estimate the sum of 0.06, 57.37, by rounding to the nearest one.
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Calculate the average of the numbers: 67, 77, 53, 73, 50, 77, 51.
Calculate the average of the numbers: 67, 77, 53, 73, 50, 77, 51.
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What percentage of students in the college do not attend soccer or basketball matches?
What percentage of students in the college do not attend soccer or basketball matches?
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How many fewer CDs are projected to be sold in 2009 than in 2011?
How many fewer CDs are projected to be sold in 2009 than in 2011?
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What is the perimeter of a polygon with sides measuring 32 m, 15 m, 15 m, and 26 m?
What is the perimeter of a polygon with sides measuring 32 m, 15 m, 15 m, and 26 m?
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Round 7.11563 to the nearest hundredths.
Round 7.11563 to the nearest hundredths.
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What is the result of multiplying $8x^2y^2$ and $4x^3y$?
What is the result of multiplying $8x^2y^2$ and $4x^3y$?
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Which inequality is correct when comparing $-3/5$ and $-2/7$?
Which inequality is correct when comparing $-3/5$ and $-2/7$?
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What is the simplified result of adding $\frac{3x}{8}$ and $\frac{5x}{7}$?
What is the simplified result of adding $\frac{3x}{8}$ and $\frac{5x}{7}$?
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When subtracting $\frac{1x}{5}$ from $\frac{7x}{10}$, what is the simplified form?
When subtracting $\frac{1x}{5}$ from $\frac{7x}{10}$, what is the simplified form?
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What is the mixed number equivalent of $\frac{34}{3}$?
What is the mixed number equivalent of $\frac{34}{3}$?
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When adding $71x$ and $65x$, what is the mixed numeral result?
When adding $71x$ and $65x$, what is the mixed numeral result?
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What is the result when multiplying $2\frac{1}{5}$ by $31/4$?
What is the result when multiplying $2\frac{1}{5}$ by $31/4$?
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What is the result of dividing $2$ by $17$?
What is the result of dividing $2$ by $17$?
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What is the result of simplifying the expression $(-5x^4y)^2$?
What is the result of simplifying the expression $(-5x^4y)^2$?
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What is the degree of the polynomial $15x^8yz - 4x^6y^2 + x^5yz^3$?
What is the degree of the polynomial $15x^8yz - 4x^6y^2 + x^5yz^3$?
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Evaluate the polynomial $-2x^2 - y^2 + xy$ for $x = -2$ and $y = 4$. What is the result?
Evaluate the polynomial $-2x^2 - y^2 + xy$ for $x = -2$ and $y = 4$. What is the result?
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What is the scientific notation of the number 0.000637?
What is the scientific notation of the number 0.000637?
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If you collect like terms from $-4x^7 + 7x^9 - 3x^8 - 2x^7 + 8x^8 + 9x^9$, what is the simplified form?
If you collect like terms from $-4x^7 + 7x^9 - 3x^8 - 2x^7 + 8x^8 + 9x^9$, what is the simplified form?
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What is the result when adding the polynomials $(3 + 9x^5 + 9x^2) + (2x^5 - 4x^2 + 8)$?
What is the result when adding the polynomials $(3 + 9x^5 + 9x^2) + (2x^5 - 4x^2 + 8)$?
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Convert the number 25657 into scientific notation. What is the correct representation?
Convert the number 25657 into scientific notation. What is the correct representation?
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What is the simplified result of the polynomial expression $b^{-2} b^{10}$?
What is the simplified result of the polynomial expression $b^{-2} b^{10}$?
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Study Notes
Multiples
- A multiple of a number is the product of that number and an integer.
- The multiples of 22 are 22, 44, 66, 88, 110, 132, and so on.
Divisibility Rules
- A number is divisible by 2 if it is even.
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 5 if its units digit is a 0 or a 5.
- A number is divisible by 6 if it is divisible by both 2 and 3.
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- A number is divisible by 10 if its units digit is a 0.
Factors
- Factors of a number are the numbers that divide evenly into that number.
- The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
- The factors of 28 are 1, 2, 4, 7, 14, and 28.
Prime Factorization
- Prime factorization is the process of expressing a number as a product of prime numbers.
- The prime factorization of 36 is 2 x 2 x 3 x 3.
- The prime factorization of 30 is 2 x 3 x 5.
Multiplication and Division of Fractions
- To multiply fractions, multiply the numerators and the denominators.
- To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
Simplifying Fractions
- To simplify a fraction, divide both the numerator and the denominator by their greatest common factor.
Least Common Multiple (LCM)
- The least common multiple of two or more numbers is the smallest number that is a multiple of all of the numbers.
- The LCM of 7 and 9 is 63.
- When finding the LCM of expressions with variables, the LCM must include the highest power of each variable.
Inequalities
- To write a true sentence using < or >, compare the absolute values of the numbers.
- The number with the smaller absolute value is less than the number with the larger absolute value.
Adding and Subtracting Fractions
- To add or subtract fractions, they must have the same denominator. Find a common denominator and simplify the expression.
Mixed Numbers
- A mixed number is a number expressed as a whole number and a fraction.
- To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. Keep the same denominator.
Adding and Multiplying Mixed Numbers
- To add mixed numbers, add the whole numbers and then add the fractions.
- To multiply mixed numbers, convert them to improper fractions and then multiply.
Rounding Decimals
- To round a decimal to the nearest tenth, look at the digit in the hundredths place. If it is 5 or greater, round the tenths digit up. If it is less than 5, keep the tenths digit the same.
- To round a decimal to the nearest hundredth, look at the digit in the thousandths place. If it is 5 or greater, round the hundredths digit up. If it is less than 5, keep the hundredths digit the same.
- To round a decimal to the nearest thousandth, look at the digit in the ten-thousandths place. If it is 5 or greater, round the thousandths digit up. If it is less than 5, keep the thousandths digit the same.
Estimating
- To estimate, round each number to the nearest one, tenth, or hundredth and then perform the calculation.
Average
- The average of a set of numbers is the sum of the numbers divided by the number of numbers in the set.
Median
- The median of a set of numbers is the middle number when the numbers are arranged in order from least to greatest.
- If there are an even number of numbers, the median is the average of the two middle numbers.
Mode
- The mode of a set of numbers is the number that appears most often in the set.
Circle Graphs
- A circle graph shows the percentage of a whole that is represented by each part of the whole.
- To find the percentage of the circle graph that does not represent a certain category, subtract the percentage of the given categories from 100%.
Pictographs
- A pictograph uses symbols to represent data.
- Each symbol represents a certain quantity.
- To find the number of symbols to represent a certain quantity, divide the quantity by the value that each symbol represents.
Perimeter
- The perimeter of a polygon is the total distance around the polygon.
- To find the perimeter of a polygon, add up the lengths of all of its sides.
Area
- The area of a polygon is the amount of surface that it covers.
- Formulas for calculating the area of different polygons are needed.
Linear Equations
- A linear equation is an equation that can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
- The slope of a line is the ratio of the rise to the run.
- The y-intercept of a line is the point where the line crosses the y-axis.
Graphing Linear Equations
- To graph a linear equation, plot the y-intercept and then use the slope to find other points on the line.
- The slope tells you how many units to move up or down and how many units to move right or left.
Parallel and Perpendicular Lines
- Parallel lines have the same slope.
- Perpendicular lines have slopes that are negative reciprocals of each other.
Exponents
- A positive exponent indicates the number of times a base is multiplied by itself.
- A negative exponent indicates the number of times a base is divided by itself.
Scientific Notation
- Scientific notation is a way of writing very large or very small numbers in a compact form.
- A number in scientific notation is expressed as a number between 1 and 10 multiplied by a power of 10.
Polynomials
- A polynomial is an expression that consists of one or more terms.
- Each term in a polynomial is a product of a coefficient and one or more variables raised to non-negative integer powers.
- The degree of a polynomial is the highest power of the variable in the polynomial.
Adding and Subtracting Polynomials
- To add polynomials, combine like terms.
- To subtract polynomials, change the sign of each term in the second polynomial and then combine like terms.
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Description
This quiz covers key concepts like multiples, divisibility rules, factors, and prime factorization. Test your understanding of how to identify multiples of numbers and the rules that determine divisibility. Additionally, explore the process of prime factorization and its significance in mathematics.