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Florida Algebra 1 EOC study materials
Florida Algebra 1 EOC study resources

Florida Algebra 1 EOC practice questions

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Question 1Algebra, functions, equations and data in explicit models

Simplify 3(2x - 5) + 4x.

  1. 6x - 15
  2. 10x - 15 Correct answer.
  3. 10x - 5
  4. 6x + 15

Explanation

Distribute 3 to get 6x - 15, then combine the x-terms: 6x + 4x = 10x. The simplified expression is 10x - 15.

Question 2Algebra, functions, equations and data in explicit models

Solve for x: 5x - 12 = 3x + 8.

  1. 4
  2. 8
  3. 10 Correct answer.
  4. 20

Explanation

Subtract 3x from both sides to get 2x - 12 = 8. Add 12 and divide by 2, so x = 10.

Question 3Algebra, functions, equations and data in explicit models

Which expression is equivalent to 2^3 * 2^5?

  1. 2^8 Correct answer.
  2. 2^15
  3. 4^8
  4. 2^2

Explanation

When powers with the same base are multiplied, the exponents are added. Since 3 + 5 = 8, the expression is 2^8.

Question 4Algebra, functions, equations and data in explicit models

What are the solutions of |x - 4| = 9?

  1. 5 or 13
  2. -13 or 5
  3. -5 or 13 Correct answer.
  4. -9 or 9

Explanation

An absolute value equation splits into x - 4 = 9 or x - 4 = -9. Solving gives x = 13 or x = -5.

Question 5Algebra, functions, equations and data in explicit models

Factor x^2 + 7x + 12.

  1. (x + 1)(x + 12)
  2. (x + 3)(x + 4) Correct answer.
  3. (x - 3)(x - 4)
  4. x(x + 7) + 12

Explanation

Find two numbers that multiply to 12 and add to 7. The numbers are 3 and 4, so the factorization is (x + 3)(x + 4).

Question 6Algebra, functions, equations and data in explicit models

Which expression is equivalent to (x - 5)(x + 2)?

  1. x^2 - 3x - 10 Correct answer.
  2. x^2 + 7x - 10
  3. x^2 - 7x - 10
  4. x^2 - 3x + 10

Explanation

Multiply each term: x*x = x^2, x*2 = 2x, -5*x = -5x, and -5*2 = -10. Combining 2x and -5x gives x^2 - 3x - 10.

Question 7Algebra, functions, equations and data in explicit models

What is the greatest common factor form of 4x^2 - 12x?

  1. 4x(x - 3) Correct answer.
  2. x(4x - 12x)
  3. 4(x - 3)
  4. 4x(x + 3)

Explanation

Both terms share a factor of 4x. Dividing 4x^2 and -12x by 4x leaves x and -3, so the expression factors as 4x(x - 3).

Question 8Algebra, functions, equations and data in explicit models

Solve for x: (2/3)x + 5 = 17.

  1. 8
  2. 12
  3. 18 Correct answer.
  4. 33

Explanation

Subtract 5 from both sides to get (2/3)x = 12. Multiplying by 3/2 gives x = 18.

Question 9Algebra, functions, equations and data in explicit models

Which expression represents 6 less than twice a number n?

  1. 6 - 2n
  2. 2n - 6 Correct answer.
  3. 6n - 2
  4. 2(n + 6)

Explanation

Twice a number n is 2n. Six less than that quantity means subtract 6, giving 2n - 6.

Question 10Algebra, functions, equations and data in explicit models

For nonzero x and y, simplify (8x^3y^2)/(2xy^4).

  1. 4x^2/y^2 Correct answer.
  2. 4x^3/y^3
  3. 6x^2/y^2
  4. 4x^2y^2

Explanation

Divide the coefficients to get 4. Subtract exponents on like bases: x^(3 - 1) = x^2 and y^(2 - 4) = y^-2, so the expression is 4x^2/y^2.

Question 11Algebra, functions, equations and data in explicit models

The simple interest formula is A = P(1 + rt). Which equation solves for t?

  1. t = (A - P)/(Pr) Correct answer.
  2. t = A - P/r
  3. t = A/(P + r)
  4. t = (A + P)/(Pr)

Explanation

Divide both sides by P to get A/P = 1 + rt. Subtract 1 and simplify: A/P - 1 = (A - P)/P, so t = (A - P)/(Pr).

Question 12Algebra, functions, equations and data in explicit models

If f(x) = x^2 - 4x, what is f(6)?

  1. 8
  2. 12 Correct answer.
  3. 20
  4. 28

Explanation

Substitute 6 for x: f(6) = 6^2 - 4(6) = 36 - 24. Therefore f(6) = 12.

Question 13Algebra, functions, equations and data in explicit models

What is the domain of g(x) = sqrt(x - 7) over the real numbers?

  1. x <= 7
  2. x >= 7 Correct answer.
  3. all real numbers
  4. x > -7

Explanation

The expression under a square root must be nonnegative. Set x - 7 >= 0 and solve to get x >= 7.

Question 14Algebra, functions, equations and data in explicit models

A table for a linear function contains the points (0, 5), (1, 9), and (2, 13). What is the rate of change?

  1. 2
  2. 4 Correct answer.
  3. 8
  4. 13

Explanation

For each increase of 1 in x, y increases by 4. The constant rate of change is therefore 4.

Question 15Algebra, functions, equations and data in explicit models

A function has outputs 4, 7, and 10 for inputs 1, 2, and 3. Which rule matches the function?

  1. f(x) = x + 3
  2. f(x) = 2x + 2
  3. f(x) = 3x + 1 Correct answer.
  4. f(x) = 4x

Explanation

The outputs increase by 3 when the inputs increase by 1, so the slope is 3. Using input 1 gives 4 = 3(1) + 1, so the rule is f(x) = 3x + 1.

Question 16Algebra, functions, equations and data in explicit models

If f(2) = 7 and f(6) = 23, what is the average rate of change from x = 2 to x = 6?

  1. 3
  2. 4 Correct answer.
  3. 5
  4. 16

Explanation

Average rate of change is change in output divided by change in input. The value is (23 - 7)/(6 - 2) = 16/4 = 4.

Question 17Algebra, functions, equations and data in explicit models

In the equation y = -2x + 7, what is the y-intercept?

  1. -2
  2. 2
  3. 7 Correct answer.
  4. -7

Explanation

Slope-intercept form is y = mx + b, where b is the y-intercept. In y = -2x + 7, the value of b is 7.

Question 18Algebra, functions, equations and data in explicit models

The sequence 4, 7, 10, 13, ... is arithmetic. Which explicit formula gives the nth term?

  1. a_n = n + 3
  2. a_n = 3n + 1 Correct answer.
  3. a_n = 4n - 1
  4. a_n = 3n + 4

Explanation

The common difference is 3. Since the first term is 4, a_n = 4 + (n - 1)3 = 3n + 1.

Question 19Algebra, functions, equations and data in explicit models

If f(x) = 3x - 2 and g(x) = x^2, what is f(g(4))?

  1. 14
  2. 30
  3. 46 Correct answer.
  4. 256

Explanation

First evaluate g(4) = 4^2 = 16. Then f(16) = 3(16) - 2 = 48 - 2 = 46.

Question 20Algebra, functions, equations and data in explicit models

Which equation represents the inverse of f(x) = 2x - 9?

  1. f^-1(x) = (x - 9)/2
  2. f^-1(x) = (x + 9)/2 Correct answer.
  3. f^-1(x) = 2x + 9
  4. f^-1(x) = 9 - 2x

Explanation

Let y = 2x - 9, then switch x and y: x = 2y - 9. Solving for y gives y = (x + 9)/2.

Question 21Algebra, functions, equations and data in explicit models

The function g(x) = (x - 3)^2 + 5 is a transformation of f(x) = x^2. Which describes the transformation?

  1. left 3 and up 5
  2. right 3 and up 5 Correct answer.
  3. right 5 and up 3
  4. left 3 and down 5

Explanation

Replacing x with x - 3 shifts the graph right 3 units. Adding 5 shifts the graph up 5 units.

Question 22Algebra, functions, equations and data in explicit models

A kayak rental costs C = 12 + 8t dollars for t hours. If rentals are available for up to 6 hours, which domain is reasonable for t?

  1. t >= 0
  2. 0 <= t <= 6 Correct answer.
  3. C >= 12
  4. 0 <= C <= 6

Explanation

Time cannot be negative, and the rental limit is 6 hours. Therefore the reasonable domain is 0 <= t <= 6.

Question 23Algebra, functions, equations and data in explicit models

A function p has zeros at -2 and 5. Which statement must be true?

  1. p(0) = 0
  2. p(2) = 5
  3. p(-2) = 0 and p(5) = 0 Correct answer.
  4. p(x) is linear

Explanation

A zero of a function is an input that makes the output equal to 0. Therefore p(-2) = 0 and p(5) = 0.

Question 24Algebra, functions, equations and data in explicit models

What is the median of the data set 3, 5, 7, 9, 10, 12?

  1. 7
  2. 8 Correct answer.
  3. 8.5
  4. 9

Explanation

There are six values, so the median is the average of the third and fourth values. The median is (7 + 9)/2 = 8.

Question 25Algebra, functions, equations and data in explicit models

For the data set 2, 4, 4, 7, 8, 10, 12, 15, what is the interquartile range?

  1. 4
  2. 7 Correct answer.
  3. 8
  4. 11

Explanation

The lower half has median 4, so Q1 = 4. The upper half has median 11, so the interquartile range is 11 - 4 = 7.

Question 26Algebra, functions, equations and data in explicit models

In a survey, 30 of 50 students who play a sport are on the honor roll, while 10 of 50 students who do not play a sport are on the honor roll. Which conclusion is best supported?

  1. Students who play a sport are more likely to be on the honor roll in this sample. Correct answer.
  2. Playing a sport causes every student to earn higher grades.
  3. Students who do not play a sport cannot be on the honor roll.
  4. The two variables have no possible association.

Explanation

In this sample, 30/50 = 60% of students who play a sport are on the honor roll, compared with 10/50 = 20% of those who do not. This supports an association, but it does not prove causation.

Question 27Algebra, functions, equations and data in explicit models

A scatter plot shows a strong positive association between weekly exercise time and water consumed. Which statement is most appropriate?

  1. More exercise always causes more water consumption.
  2. Water consumption always causes more exercise.
  3. There is no relationship between the variables.
  4. The data show association, but the graph alone does not prove causation. Correct answer.

Explanation

A scatter plot can show whether two variables are associated. It does not, by itself, prove that one variable causes the other.

Question 28Algebra, functions, equations and data in explicit models

A line of fit for a data set is y = 1.8x + 12. What is the predicted value of y when x = 10?

  1. 13.8
  2. 18
  3. 30 Correct answer.
  4. 120

Explanation

Substitute x = 10 into the model: y = 1.8(10) + 12 = 18 + 12. The predicted value is 30.

Question 29Algebra, functions, equations and data in explicit models

A survey estimates that 48% of students prefer online homework, with a margin of error of 4 percentage points. Which interval is reasonable?

  1. 4% to 48%
  2. 40% to 48%
  3. 44% to 52% Correct answer.
  4. 48% to 56%

Explanation

A margin of error of 4 percentage points means subtract and add 4 to the estimate. The interval is 44% to 52%.

Question 30Algebra, functions, equations and data in explicit models

A school records each student's grade level and number of absences. Which description fits these data?

  1. Univariate categorical data
  2. Bivariate data with one categorical variable and one numerical variable Correct answer.
  3. Bivariate data with two numerical variables
  4. Univariate numerical data only

Explanation

Grade level is categorical, while number of absences is numerical. Because two variables are recorded for each student, the data are bivariate.

Question 31Algebra, functions, equations and data in explicit models

Which method is most likely to produce a representative sample of all ninth-grade students at a school?

  1. Survey only students in the algebra club.
  2. Survey the first 100 students who arrive at a pep rally.
  3. Survey only students with last names beginning with A.
  4. Use a random number generator to select 100 students from the full ninth-grade roster. Correct answer.

Explanation

A random sample from the full roster gives every ninth-grade student a chance to be selected. The other methods are likely to overrepresent specific groups.

Question 32Algebra, functions, equations and data in explicit models

A savings balance is modeled by y = 2.5x + 10, where x is the number of weeks and y is dollars. What does the slope mean?

  1. The account started with $2.50.
  2. The balance increases by $2.50 each week. Correct answer.
  3. The balance increases by $10 each week.
  4. The account reaches $10 after 2.5 weeks.

Explanation

The slope is the coefficient of x, which is 2.5. In context, this means the balance increases by $2.50 for each additional week.

Question 33Algebra, functions, equations and data in explicit models

Solve 4(x - 2) = 20.

  1. 3
  2. 5
  3. 7 Correct answer.
  4. 12

Explanation

Divide both sides by 4 to get x - 2 = 5. Add 2 to both sides, so x = 7.

Question 34Algebra, functions, equations and data in explicit models

Which inequality is equivalent to -3x + 5 > 17?

  1. x > -4
  2. x < -4 Correct answer.
  3. x > 4
  4. x < 4

Explanation

Subtract 5 to get -3x > 12. Dividing by -3 reverses the inequality, giving x < -4.

Question 35Algebra, functions, equations and data in explicit models

What is the slope of the line through (-2, 3) and (4, 15)?

  1. 1/2
  2. 2 Correct answer.
  3. 6
  4. 12

Explanation

Slope is change in y divided by change in x. The slope is (15 - 3)/(4 - (-2)) = 12/6 = 2.

Question 36Algebra, functions, equations and data in explicit models

Which equation represents a line with slope 5 and y-intercept -1?

  1. y = 5x - 1 Correct answer.
  2. y = -x + 5
  3. y = x - 1
  4. y = 5x + 1

Explanation

Slope-intercept form is y = mx + b. With slope 5 and y-intercept -1, the equation is y = 5x - 1.

Question 37Algebra, functions, equations and data in explicit models

What is the x-intercept of 2x + 3y = 12?

  1. 4
  2. 6 Correct answer.
  3. 12
  4. -6

Explanation

At the x-intercept, y = 0. Substituting gives 2x = 12, so x = 6.

Question 38Algebra, functions, equations and data in explicit models

Which equation is the point-slope form of the line with slope -2 through (3, 5)?

  1. y - 5 = -2(x - 3) Correct answer.
  2. y + 5 = -2(x - 3)
  3. y - 3 = -2(x - 5)
  4. y - 5 = 2(x - 3)

Explanation

Point-slope form is y - y1 = m(x - x1). Using m = -2 and (x1, y1) = (3, 5) gives y - 5 = -2(x - 3).

Question 39Algebra, functions, equations and data in explicit models

Solve the system: x + y = 10 and x - y = 2.

  1. (4, 6)
  2. (5, 5)
  3. (6, 4) Correct answer.
  4. (8, 2)

Explanation

Add the equations to eliminate y: 2x = 12, so x = 6. Then 6 + y = 10, so y = 4.

Question 40Algebra, functions, equations and data in explicit models

Solve the system: 2x + y = 11 and x - y = 1.

  1. (3, 4)
  2. (4, 3) Correct answer.
  3. (5, 1)
  4. (2, 7)

Explanation

Add the equations to get 3x = 12, so x = 4. Substitute into x - y = 1 to get 4 - y = 1, so y = 3.

Question 41Algebra, functions, equations and data in explicit models

What is the solution to y = 3x + 2 and y = -x + 10?

  1. (1, 5)
  2. (2, 8) Correct answer.
  3. (3, 11)
  4. (8, 2)

Explanation

Set the expressions equal: 3x + 2 = -x + 10. Then 4x = 8, so x = 2, and y = 3(2) + 2 = 8.

Question 42Algebra, functions, equations and data in explicit models

Solve y = mx + b for m, assuming x is not 0.

  1. m = (y - b)/x Correct answer.
  2. m = y - bx
  3. m = x/(y - b)
  4. m = y/(x + b)

Explanation

Subtract b from both sides to get y - b = mx. Divide both sides by x to isolate m, giving m = (y - b)/x.

Question 43Algebra, functions, equations and data in explicit models

A club needs at least 20 volunteers. If x students and y adults volunteer, which inequality represents the situation?

  1. x + y <= 20
  2. x + y >= 20 Correct answer.
  3. x - y >= 20
  4. 20x + y >= 0

Explanation

At least 20 means the total number of volunteers must be 20 or greater. The total is x + y, so x + y >= 20.

Question 44Algebra, functions, equations and data in explicit models

A line is parallel to y = -3x + 4. What is the slope of the parallel line?

  1. 3
  2. -3 Correct answer.
  3. 1/3
  4. -1/3

Explanation

Parallel lines have the same slope. The slope of y = -3x + 4 is -3, so the parallel line also has slope -3.

Question 45Algebra, functions, equations and data in explicit models

A linear function has values (0, 5), (2, 11), (4, 17), and (6, 23). Which equation represents the function?

  1. y = 2x + 5
  2. y = 3x + 2
  3. y = 3x + 5 Correct answer.
  4. y = 6x + 5

Explanation

The y-values increase by 6 when x increases by 2, so the slope is 3. Since y = 5 when x = 0, the equation is y = 3x + 5.

Question 46Algebra, functions, equations and data in explicit models

A gym charges C = 25 + 4n dollars for n classes. What does 25 represent?

  1. The cost per class
  2. The number of classes
  3. The one-time starting fee Correct answer.
  4. The total cost after 25 classes

Explanation

In the model C = 25 + 4n, the constant term is the amount charged before any classes are added. It represents a one-time starting fee of $25.

Question 47Algebra, functions, equations and data in explicit models

Which description matches the graph of y < 2x + 1?

  1. Solid boundary line with shading above the line
  2. Dashed boundary line with shading below the line Correct answer.
  3. Solid boundary line with shading below the line
  4. Dashed vertical line with shading to the right

Explanation

The symbol < uses a dashed boundary line because points on the line are not included. The solution region is below the line y = 2x + 1.

Question 48Algebra, functions, equations and data in explicit models

Rewrite 2x - 3y = 12 in slope-intercept form.

  1. y = 2x - 12
  2. y = (-2/3)x + 4
  3. y = (2/3)x - 4 Correct answer.
  4. y = 3x - 12

Explanation

Subtract 2x from both sides to get -3y = -2x + 12. Dividing by -3 gives y = (2/3)x - 4.

Question 49Algebra, functions, equations and data in explicit models

What is the equation of the line through (1, 4) and (5, 12)?

  1. y = 2x + 2 Correct answer.
  2. y = 2x - 2
  3. y = 4x + 1
  4. y = 8x - 4

Explanation

The slope is (12 - 4)/(5 - 1) = 8/4 = 2. Using (1, 4), the equation 4 = 2(1) + b gives b = 2, so y = 2x + 2.

Question 50Algebra, functions, equations and data in explicit models

A line has slope -3 and passes through (2, -1). Which equation represents the line?

  1. y = -3x - 1
  2. y = -3x + 5 Correct answer.
  3. y = 3x - 7
  4. y = -x + 1

Explanation

Use y = mx + b with m = -3. Substituting (2, -1) gives -1 = -6 + b, so b = 5 and the equation is y = -3x + 5.