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Questions and Answers
Write the following as an algebraic expression: the product of five and a number less than two
Write the following as an algebraic expression: the product of five and a number less than two
5(x - 2)
Simplify: 24 ÷ 2 * 4 + 33
Simplify: 24 ÷ 2 * 4 + 33
51
Simplify b² - 4ac if a = 2, b = -4, c = 3
Simplify b² - 4ac if a = 2, b = -4, c = 3
40
Simplify: 11 – 2(-3x + 4) + 2(-4x - 5)
Simplify: 11 – 2(-3x + 4) + 2(-4x - 5)
Evaluate each of the following given: f(x) = 3x + 5 and g(x) = x² – 5 a) f(3) b) g(-2)
Evaluate each of the following given: f(x) = 3x + 5 and g(x) = x² – 5 a) f(3) b) g(-2)
Determine if the following relation is a function: {(-2,7), (6,7), (0,9), (5, -2)}. Yes or No and tell why.
Determine if the following relation is a function: {(-2,7), (6,7), (0,9), (5, -2)}. Yes or No and tell why.
Solve: 2x + 3 = 27
Solve: 2x + 3 = 27
Solve: 6(3x + 1) – 30 = 3(2x - 4)
Solve: 6(3x + 1) – 30 = 3(2x - 4)
Solve: |2x – 4| = 8
Solve: |2x – 4| = 8
Water was leaking from a faucet at a rate of 1.5 gal every 5 minutes. If it took 22 min to stop the leak, how much water was wasted?
Water was leaking from a faucet at a rate of 1.5 gal every 5 minutes. If it took 22 min to stop the leak, how much water was wasted?
Write an absolute value equation for the graph shown below:
Write an absolute value equation for the graph shown below:
Find the perimeter of the square shown.
Find the perimeter of the square shown.
You bought a shirt for $36.99 what will the total cost be if the store offers a 30% discount with a 6% tax?
You bought a shirt for $36.99 what will the total cost be if the store offers a 30% discount with a 6% tax?
You go to dinner and the meal you ordered is $15.99. They add a 6% tax to your bill. How much is the bill BEFORE tip?
You go to dinner and the meal you ordered is $15.99. They add a 6% tax to your bill. How much is the bill BEFORE tip?
A game was $75 and is now $60. Find the percent change of the game.
A game was $75 and is now $60. Find the percent change of the game.
Find three consecutive ODD integers that have a sum of 111.
Find three consecutive ODD integers that have a sum of 111.
Find the value of r given: (r, 7), (10, 8); m = -1/5
Find the value of r given: (r, 7), (10, 8); m = -1/5
Given the sequence: 2, 5, 8,... a) Find the NEXT THREE terms: b) Use the formula: an = a1 + d(n − 1) to find a121.
Given the sequence: 2, 5, 8,... a) Find the NEXT THREE terms: b) Use the formula: an = a1 + d(n − 1) to find a121.
Suppose y varies directly as x. If y = 3 when x = 6. Find y when x = 10.
Suppose y varies directly as x. If y = 3 when x = 6. Find y when x = 10.
Write an equation of a line with m = -3 that passes through the point (-2, 6).
Write an equation of a line with m = -3 that passes through the point (-2, 6).
Write an equation of a line that passes through (-2, 2) and (4, 8)
Write an equation of a line that passes through (-2, 2) and (4, 8)
From 2005 to 2017, the number of airports in the United States increased at a constant rate of 150 airports per year. In 2010 there were 20,245 airports in the United States. Write an equation of the line that gives the number of airports as a function of time since 2005 (Hint: let x = 0 be 2005).
From 2005 to 2017, the number of airports in the United States increased at a constant rate of 150 airports per year. In 2010 there were 20,245 airports in the United States. Write an equation of the line that gives the number of airports as a function of time since 2005 (Hint: let x = 0 be 2005).
Write an equation of a line that is parallel to 3x + 4y = -8 and passes through the point (-4, 6)
Write an equation of a line that is parallel to 3x + 4y = -8 and passes through the point (-4, 6)
Find the inverse of f(x) = -2x + 8
Find the inverse of f(x) = -2x + 8
The graph shows 4 lines A, B, C, D. Write these lines in order from least to greatest according to their slope.
The graph shows 4 lines A, B, C, D. Write these lines in order from least to greatest according to their slope.
Solve if possible: -2x + 4 < 8
Solve if possible: -2x + 4 < 8
Solve if possible: 4x + 15 < 3 and x – 5 > -3
Solve if possible: 4x + 15 < 3 and x – 5 > -3
Solve if possible: |4x – 2| < 4
Solve if possible: |4x – 2| < 4
Use desmos to graph the following system and identify their point of intersection: -3x + 2y = -2 3x + 3y = 12
Use desmos to graph the following system and identify their point of intersection: -3x + 2y = -2 3x + 3y = 12
Flashcards
Write the following as an algebraic expression: the product of five and a number less than two
Write the following as an algebraic expression: the product of five and a number less than two
An expression that represents the product of 5 and a number that is 2 less than another number.
Simplify: 24 ÷ 2 * 4 + 33
Simplify: 24 ÷ 2 * 4 + 33
Simplify the expression by following the order of operations (PEMDAS).
Simplify b² - 4ac if a = 2, b = -4, c = 3
Simplify b² - 4ac if a = 2, b = -4, c = 3
Substitute the values of a, b, and c into the expression and simplify.
Simplify: 11 - 2(-3x + 4) + 2(-4x - 5)
Simplify: 11 - 2(-3x + 4) + 2(-4x - 5)
Simplify the expression by distributing and combining like terms.
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Evaluate f(3) given f(x) = 3x + 5
Evaluate f(3) given f(x) = 3x + 5
Substitute the value of x (3) into the function f(x) and simplify.
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Evaluate g(-2) given g(x) = x² - 5
Evaluate g(-2) given g(x) = x² - 5
Substitute the value of x (-2) into the function g(x) and simplify.
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Determine if the following relation is a function: {(-2, 7), (6, 7), (0, 9), (5, -2)}. Yes or No and tell why.
Determine if the following relation is a function: {(-2, 7), (6, 7), (0, 9), (5, -2)}. Yes or No and tell why.
A function is a relation where each input (x-value) has only one output (y-value).
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Determine if the following is a function. Yes or no and tell why.
Determine if the following is a function. Yes or no and tell why.
A function is a relation where each input (x-value) has only one output (y-value).
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Solve: 2x + 3 = 27
Solve: 2x + 3 = 27
Solve for x by isolating the variable using inverse operations.
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Solve: 6(3x + 1) - 30 = 3(2x - 4)
Solve: 6(3x + 1) - 30 = 3(2x - 4)
Solve for x by simplifying, combining like terms, and isolating the variable.
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Solve: |2x - 4| = 8
Solve: |2x - 4| = 8
Solve for x by considering both positive and negative cases of the absolute value.
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Water was leaking from a faucet at a rate of 1.5 gal every 5 minutes. If it took 22 min to stop the leak, how much water was wasted?
Water was leaking from a faucet at a rate of 1.5 gal every 5 minutes. If it took 22 min to stop the leak, how much water was wasted?
Calculate the amount of water wasted by dividing the total time by the time it takes for 1.5 gallons to leak.
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Write an absolute value equation for the graph shown below:
Write an absolute value equation for the graph shown below:
An absolute value equation represents the distance from zero on a number line.
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Find the perimeter of the square shown.
Find the perimeter of the square shown.
The perimeter of a square is the sum of all its sides.
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You bought a shirt for $36.99 what will the total cost be if the store offers a 30% discount with a 6% tax?
You bought a shirt for $36.99 what will the total cost be if the store offers a 30% discount with a 6% tax?
Calculate the final price by subtracting the discount from the original price and adding the tax.
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You go to dinner and the meal you ordered is $15.99. They add a 6% tax to your bill. How much is the bill BEFORE tip?
You go to dinner and the meal you ordered is $15.99. They add a 6% tax to your bill. How much is the bill BEFORE tip?
Calculate the total cost by adding a 6% tax to the original bill amount.
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A game was $75 and is now $60. Find the percent change of the game.
A game was $75 and is now $60. Find the percent change of the game.
Calculate the percent change by dividing the difference of the new price and the original price by the original price and expressing the result as a percentage.
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Find three consecutive ODD integers that have a sum of 111.
Find three consecutive ODD integers that have a sum of 111.
Three consecutive odd integers can be represented as x, x + 2, and x + 4. Set up an equation that represents the sum of these integers and solve for x.
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Find the value of r given: (r, 7), (10, 8); m=−5
Find the value of r given: (r, 7), (10, 8); m=−5
The slope of a line passing through two points can be found by dividing the difference in y-values by the difference in x-values.
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Given the sequence: 2, 5, 8, .... a) Find the NEXT THREE terms: ____, ____, ____, b) Use the formula: an = a1 + d(n – 1) to find a121.
Given the sequence: 2, 5, 8, .... a) Find the NEXT THREE terms: ____, ____, ____, b) Use the formula: an = a1 + d(n – 1) to find a121.
An arithmetic sequence is a sequence where the difference between consecutive terms is constant.
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Suppose y varies directly as x. If y = 3 when x = 6. Find y when x = 10.
Suppose y varies directly as x. If y = 3 when x = 6. Find y when x = 10.
Direct variation means that one variable is a constant multiple of the other. Set up a proportion and solve for y.
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Write an equation of a line with m = -3 that passes through the point (-2, 6).
Write an equation of a line with m = -3 that passes through the point (-2, 6).
The equation of a line can be written in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Use the given slope and point to solve for b.
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Write an equation of a line that passes through (-2, 2) and (4, 8)
Write an equation of a line that passes through (-2, 2) and (4, 8)
The slope-intercept form of a line allows you to write an equation using the slope (m) and y-intercept (b).
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From 2005 to 2017, the number of airports in the United States increased at a constant rate of 150 airports per year. In 2010 there were 20,245 airports in the United States. Write an equation of the line that gives the number of airports as a function of time since 2005 (Hint: let x = 0 be 2005).
From 2005 to 2017, the number of airports in the United States increased at a constant rate of 150 airports per year. In 2010 there were 20,245 airports in the United States. Write an equation of the line that gives the number of airports as a function of time since 2005 (Hint: let x = 0 be 2005).
The equation of a line can be written in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Use the given information to find the slope and y-intercept.
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Write an equation of a line that is parallel to 3x + 4y = -8 and passes through the point (-4, 6)
Write an equation of a line that is parallel to 3x + 4y = -8 and passes through the point (-4, 6)
Parallel lines have the same slope. Find the slope of the given line, then use the point-slope form to write an equation of a parallel line passing through the given point.
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Find the inverse of f(x) = -2x + 8
Find the inverse of f(x) = -2x + 8
To find the inverse of a function, switch x and y and solve for y.
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Solve if possible: -2x + 4 < 8
Solve if possible: -2x + 4 < 8
Solve for x by isolating the variable using inverse operations, remembering to flip the inequality sign when multiplying or dividing by a negative number.
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Solve if possible: 4x + 15 < 3 and x – 5 > -3
Solve if possible: 4x + 15 < 3 and x – 5 > -3
Solve for x by isolating the variable using inverse operations, remembering to flip the inequality sign when multiplying or dividing by a negative number.
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Solve if possible: |4x – 2| < 4
Solve if possible: |4x – 2| < 4
Solve for x by considering both positive and negative cases of the absolute value.
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Use desmos to graph the following system and identify their point of intersection: -3x + 2y = -2 3x + 3y = 12
Use desmos to graph the following system and identify their point of intersection: -3x + 2y = -2 3x + 3y = 12
Graph the system of equations using graphing technology (Desmos) to identify the point where the two lines intersect.
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Algebra 1 - Midterm Exam Review
- Algebraic Expressions: Find the product of five and a number less than two. This is written as 5(x-2), where 'x' represents the unknown number.
- Simplifying Expressions: 24 ÷ 2 * 4 + 3 = 12 * 4 + 3 = 48 + 3 = 51. 11 – 2(-3x + 4) + 2(-4x - 5) = 11 + 6x - 8 - 8x - 10 = -6x - 7
- Simplifying Expressions: If a = 2, b = -4, c = 3, b² - 4ac equals (-4)² - 4 * 2 * 3 = 16 - 24 = -8
- Evaluating Functions:
- Given f(x) = 3x + 5 and g(x) = x² - 5, f(3) = 3(3) + 5 = 14, and g(-2) = (-2)² - 5 = 4 - 5 = -1
- Relations and Functions:
- Determine if the set {(-2,7), (6,7), (0,9), (5, -2)} is a function. Yes, it's a function as each input has only one output
- Linear Equations:
- Solve for x: 2x + 3 = 27... x=12
- Solve for x: 10. Solve: 6(3x + 1) – 30 = 3(2x - 4)... x=4
- Solve for x: |2x - 4| = 8... x=6 or x=-2
- Graphing: Sketch a graph of your hair length during a year. (Note: This is an open-ended question.)
- Absolute Value Equations: Write an absolute value equation based on a provided graph, shown.
- Perimeter Problems: Find the perimeter of a square, with side lengths given as (x + 6) & (2x + 2).
- Discounts and Taxes: Determine the total cost of an item including a discount (30%) and 6% tax. Example for a $36.99 item: Calculate the 30% discount: $36.99 * 0.30 = $11.097 Subtracted from the original total $36.99 - $11.097 = $25.893. Calculating the 6% tax on this new total: 25.893 * 0.06 = $1.55358 Add this to the discounted price $25.893 + 1.554 = $27.447
- Percent Change: Calculate the percent change of a game from $75 to $60
- Consecutive Integers: Find three consecutive odd integers whose sum is 111: 35, 37, 39
- Direct Variation: If y varies directly as x, and y = 3 when x = 6, find y when x = 10.
- Linear Equations: Find the equation of a line with slope (-3) that passes through point (-2, 6).
- Linear Equations: Find the equation (of a line) passing through (-2, 2) and (4, 8).
- Inverse functions: Find the inverse function of f(x) = -2x + 8. f⁻¹(x) = (x - 8)/-2
- Linear Inequalities: Solve -2x + 4 < 8 if possible
- Absolute Value Inequalities: Solve |4x - 2| < 4 if possible;
Additional Topics
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Linear System Intersection: Use desmos or other graphing tool to find the x, y point that intersects the system of equations (given -3x + 2y = -2, 3x + 3y = 12).
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Parallel Lines: Find the equation of a line that is parallel to 3x + 4y = -8 and that goes through (-4, 6).
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Ordering Slopes: Order the slopes of lines A, B, C, and D from least to greatest using the graph provided.
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Linear Inequalities: Solve 4x + 15 < 3 and x - 5 > -3.
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(Sequence Problems) Identify the next three terms of a sequence, like 2, 5, 8,... and find the 12th term.
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(Water Leak) Calculate how much water was wasted from a faucet if it leaked 1.5 gallons every 5 minutes, and the leak lasted 22 minutes.
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