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Praxis Algebra I study materials
Praxis Algebra I study resources

Praxis Algebra I practice questions

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Question 1Algebra I content domains (not enumerated in source)

The function f is defined by f(x) = 3x − 5. What is the value of f(4)?

  1. 17
  2. 12
  3. 7 Correct answer.
  4. 2

Explanation

Substitute x = 4 into the rule: 3(4) − 5 = 12 − 5 = 7. Function notation f(4) means the output when the input is 4, so the multiplication by 3 must be done before subtracting 5.

Question 2Algebra I content domains (not enumerated in source)

A line passes through the points (0, 3) and (4, 11). What is the slope of this line?

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

Explanation

Slope equals the change in y divided by the change in x: (11 − 3)/(4 − 0) = 8/4 = 2. The slope measures vertical change per one unit of horizontal change, so the ratio must be simplified.

Question 3Algebra I content domains (not enumerated in source)

Which expression is equivalent to (2x^3)(5x^4)?

  1. 7x^12
  2. 7x^7
  3. 10x^7 Correct answer.
  4. 10x^12

Explanation

Multiply the coefficients (2 · 5 = 10) and add the exponents of like bases (x^3 · x^4 = x^7). The product rule for exponents applies because the bases are identical, giving 10x^7.

Question 4Algebra I content domains (not enumerated in source)

What is the solution set of the inequality 4x − 7 < 9?

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

Explanation

Add 7 to both sides to get 4x < 16, then divide by 4 to get x < 4. Because 4 is positive, the direction of the inequality sign is unchanged, so the solution is all numbers less than 4.

Question 5Algebra I content domains (not enumerated in source)

The graph of y = x^2 − 6x + 5 crosses the x-axis at which pair of values?

  1. x = 1 and x = 5 Correct answer.
  2. x = −1 and x = −5
  3. x = 0 and x = 6
  4. x = 2 and x = 3

Explanation

Factor x^2 − 6x + 5 as (x − 1)(x − 5), whose zeros are x = 1 and x = 5. These are the x-intercepts because y = 0 exactly where a factor equals zero.

Question 6Algebra I content domains (not enumerated in source)

A system of two linear equations has no solution. Which description must be true of its graphs?

  1. The lines intersect at exactly one point.
  2. The lines are the same line.
  3. The lines are perpendicular.
  4. The lines are parallel and distinct. Correct answer.

Explanation

No solution means the two equations are never satisfied by the same point, which occurs when the lines are parallel and never meet. Parallel distinct lines have equal slopes and different y-intercepts.

Question 7Algebra I content domains (not enumerated in source)

Simplify (6x^5 y^2)/(3x^2 y^6), assuming x and y are nonzero.

  1. 2x^7/y^4
  2. 18x^3/y^4
  3. 2x^3 y^4
  4. 2x^3/y^4 Correct answer.

Explanation

Divide coefficients to get 2, subtract exponents on x to get x^3, and subtract exponents on y to get y^(2−6) = y^−4, which is written as 1/y^4. Combining gives 2x^3/y^4.

Question 8Algebra I content domains (not enumerated in source)

The equation 5x + 2y = 20 is graphed in the coordinate plane. What is the y-intercept of the graph?

  1. (4, 0)
  2. (0, 10) Correct answer.
  3. (0, 5)
  4. (0, 2)

Explanation

A y-intercept occurs where x = 0, so substitute to get 2y = 20 and y = 10, giving the point (0, 10). Solving for y first gives y = −(5/2)x + 10, confirming the intercept.

Question 9Algebra I content domains (not enumerated in source)

A sequence is defined by a_1 = 4 and a_n = a_(n−1) + 7 for n ≥ 2. What is a_5?

  1. 25
  2. 39
  3. 32 Correct answer.
  4. 11

Explanation

Each term adds 7 to the previous term, so the terms are 4, 11, 18, 25, 32. Equivalently, a_5 = 4 + 4(7) = 32 using the arithmetic sequence pattern.

Question 10Algebra I content domains (not enumerated in source)

Which expression represents the complete factorization of x^2 − 9 over the integers?

  1. (x − 3)(x + 3) Correct answer.
  2. (x − 9)(x + 1)
  3. (x − 3)^2
  4. (x + 3)^2

Explanation

The expression is a difference of squares, a^2 − b^2 = (a − b)(a + b), with a = x and b = 3. Expanding (x − 3)(x + 3) returns x^2 − 9, confirming the factorization.

Question 11Algebra I content domains (not enumerated in source)

The function g(x) = −2x + 6 is graphed. Compared with the graph of y = x, how does the graph of g behave?

  1. It falls from left to right and is steeper. Correct answer.
  2. It rises from left to right and is less steep.
  3. It is horizontal.
  4. It rises from left to right and is steeper.

Explanation

The slope of g is −2: the negative sign makes the line fall from left to right, and |−2| > 1 makes it steeper than y = x. The +6 only shifts the line vertically and does not affect steepness.

Question 12Algebra I content domains (not enumerated in source)

A taxi charges a flat fee of $3 plus $2 per mile. Which equation gives the total cost C in dollars for m miles?

  1. C = 2m + 3 Correct answer.
  2. C = 3m − 2
  3. C = 3m + 2
  4. C = 2m − 3

Explanation

The per-mile charge is the rate that multiplies m, and the flat fee is the constant added once. This gives C = 2m + 3, a linear model with slope 2 and y-intercept 3.

Question 13Algebra I content domains (not enumerated in source)

What is the value of (2^3)^2 · 2^−1?

  1. 16
  2. 64
  3. 32 Correct answer.
  4. 8

Explanation

Power of a power multiplies exponents: (2^3)^2 = 2^6 = 64. Multiplying by 2^−1 adds exponents to give 2^5 = 32.

Question 14Algebra I content domains (not enumerated in source)

The quadratic function h(x) = x^2 + 4x + 1 is written in vertex form. What is the vertex of its graph?

  1. (2, 13)
  2. (−2, −3) Correct answer.
  3. (−2, 5)
  4. (2, −3)

Explanation

Complete the square: x^2 + 4x + 1 = (x + 2)^2 − 4 + 1 = (x + 2)^2 − 3. Vertex form (x − h)^2 + k gives vertex (−2, −3), matching x = −b/(2a) = −2.

Question 15Algebra I content domains (not enumerated in source)

The expression (x^2 − 4)/(x^2 − x − 2) is simplified for x ≠ 2 and x ≠ −1. Which expression is equivalent?

  1. (x − 2)/(x + 1)
  2. (x + 2)/(x − 1)
  3. (x + 2)/(x + 1) Correct answer.
  4. (x − 2)/(x − 1)

Explanation

Factor the numerator as (x − 2)(x + 2) and the denominator as (x − 2)(x + 1). Canceling the common factor (x − 2) leaves (x + 2)/(x + 1).

Question 16Algebra I content domains (not enumerated in source)

A data set of 12 values has a mean of 15. When one additional value is included, the mean of the 13 values is 16. What is the added value?

  1. 16
  2. 28 Correct answer.
  3. 31
  4. 1

Explanation

The original total is 12 · 15 = 180, and the new total is 13 · 16 = 208. The added value is the difference, 208 − 180 = 28.

Question 17Algebra I content domains (not enumerated in source)

Which equation describes a line perpendicular to y = (2/3)x + 1 and passing through the point (4, 1)?

  1. y = −(3/2)x + 7 Correct answer.
  2. y = −(2/3)x + 11/3
  3. y = (3/2)x − 5
  4. y = (2/3)x − 5/3

Explanation

Perpendicular slopes are negative reciprocals, so the new slope is −3/2. Using point-slope form, y − 1 = −(3/2)(x − 4) simplifies to y = −(3/2)x + 7.

Question 18Algebra I content domains (not enumerated in source)

The function f(x) = 2x + 3 has an inverse. What is f^−1(x)?

  1. (x − 3)/2 Correct answer.
  2. (x + 3)/2
  3. 2x − 3
  4. 1/(2x + 3)

Explanation

Swap x and y in y = 2x + 3 to get x = 2y + 3, then solve for y: y = (x − 3)/2. The inverse undoes the operations in reverse order, subtracting 3 first and then dividing by 2.

Question 19Algebra I content domains (not enumerated in source)

The graph of y = f(x) is shifted 3 units to the right and 2 units down. Which equation represents the new graph?

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

Explanation

A horizontal shift right by 3 replaces x with x − 3, and a vertical shift down by 2 subtracts 2 from the output. Combining gives y = f(x − 3) − 2.

Question 20Algebra I content domains (not enumerated in source)

The system 3x + y = 10 and x − y = 2 is solved. What is the value of x?

  1. 2
  2. 3 Correct answer.
  3. 1
  4. 4

Explanation

Adding the equations eliminates y: 4x = 12, so x = 3. Substituting back gives y = 1, and both equations check with (3, 1).

Question 21Algebra I content domains (not enumerated in source)

A geometric sequence begins 3, 12, 48, 192. Which formula gives the nth term?

  1. a_n = 4 · 3^(n − 1)
  2. a_n = 3 · 4^(n − 1) Correct answer.
  3. a_n = 3 + 4(n − 1)
  4. a_n = 3 · 4^n

Explanation

Each term is 4 times the previous term, so the common ratio is 4 and the first term is 3. The explicit formula for a geometric sequence is a_n = a_1 · r^(n − 1), giving 3 · 4^(n − 1).

Question 22Algebra I content domains (not enumerated in source)

What is the solution set of x^2 − 5x − 6 ≤ 0?

  1. −1 ≤ x ≤ 6 Correct answer.
  2. −6 ≤ x ≤ 1
  3. x ≤ −1 or x ≥ 6
  4. x ≤ −6 or x ≥ 1

Explanation

Factor as (x − 6)(x + 1) ≤ 0, with zeros at x = 6 and x = −1. Because the parabola opens upward, it is at or below zero between its roots, so the solution is −1 ≤ x ≤ 6.

Question 23Algebra I content domains (not enumerated in source)

If y varies directly with x and y = 18 when x = 6, what is y when x = 10?

  1. 30 Correct answer.
  2. 108
  3. 3
  4. 18

Explanation

Direct variation has the form y = kx, so k = 18/6 = 3. Then y = 3 · 10 = 30 when x = 10.

Question 24Algebra I content domains (not enumerated in source)

The expression (x + 4)(2x − 3) is expanded. What is the coefficient of x in the result?

  1. −12
  2. 5 Correct answer.
  3. 8
  4. 2

Explanation

Using FOIL, the outer and inner products give 8x and −3x, which combine to 5x. The coefficient of x is therefore 5, while the constant term is −12.

Question 25Algebra I content domains (not enumerated in source)

A scatterplot shows a strong negative linear association between hours of exercise and resting heart rate. Which statement best describes the line of best fit?

  1. It has a negative slope, so resting heart rate causes exercise hours.
  2. It has a slope of zero because the association is linear.
  3. It has a positive slope, so higher exercise hours predict higher resting heart rate.
  4. It has a negative slope, so higher exercise hours predict lower resting heart rate. Correct answer.

Explanation

A negative association means the line of best fit slopes downward, so increases in the explanatory variable pair with decreases in the response. Slope describes the direction and strength of the linear trend, not causation.

Question 26Algebra I content domains (not enumerated in source)

A line passes through the points (2, 5) and (6, 13). What is the slope of the line?

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

Explanation

Slope equals the change in y divided by the change in x: (13 − 5)/(6 − 2) = 8/4 = 2. So the line rises 2 units for every 1 unit it moves right.

Question 27Algebra I content domains (not enumerated in source)

Which expression is equivalent to 4x + 7 − 2x + 3?

  1. 6x + 4
  2. 2x + 4
  3. 2x + 10 Correct answer.
  4. 6x + 10

Explanation

Combine like terms: 4x − 2x = 2x and 7 + 3 = 10. The simplified expression is 2x + 10.

Question 28Algebra I content domains (not enumerated in source)

What is the value of 3^4?

  1. 81 Correct answer.
  2. 12
  3. 64
  4. 27

Explanation

The exponent 4 means multiply 3 by itself four times: 3 · 3 · 3 · 3 = 81. Multiplying the base by the exponent (3 · 4 = 12) is not exponentiation.

Question 29Algebra I content domains (not enumerated in source)

The equation y = 3x − 4 is graphed in the coordinate plane. What is the y-intercept of the graph?

  1. (3, 0)
  2. (0, 3)
  3. (0, −4) Correct answer.
  4. (−4, 0)

Explanation

In slope-intercept form y = mx + b, the value b is the y-intercept. Here b = −4, so the graph crosses the y-axis at the point (0, −4).

Question 30Algebra I content domains (not enumerated in source)

A function is defined by f(x) = 5x + 2. What is f(−3)?

  1. −13 Correct answer.
  2. −1
  3. 17
  4. −17

Explanation

Substitute x = −3: 5(−3) + 2 = −15 + 2 = −13. Function notation tells you to evaluate the expression at the given input.

Question 31Algebra I content domains (not enumerated in source)

Which value of x makes the equation 2(x − 3) = 10 true?

  1. 8 Correct answer.
  2. 2
  3. 11
  4. 5

Explanation

Distribute or divide both sides by 2 to get x − 3 = 5, then add 3 to both sides: x = 8. Checking gives 2(8 − 3) = 2(5) = 10.

Question 32Algebra I content domains (not enumerated in source)

The inequality −2x < 6 is solved for x. Which inequality gives the solution set?

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

Explanation

Divide both sides by −2, and because you divide by a negative number, reverse the inequality symbol. This gives x > −3.

Question 33Algebra I content domains (not enumerated in source)

A relation consists of the ordered pairs (1, 2), (2, 4), (3, 6), and (4, 8). Why is this relation a function?

  1. The inputs and outputs are all positive numbers
  2. The ordered pairs form a straight line when graphed
  3. Each output value appears only once in the relation
  4. Each input value is paired with exactly one output value Correct answer.

Explanation

A relation is a function when no input is paired with two different outputs. Here the inputs 1, 2, 3, and 4 each appear once, so each has exactly one output.

Question 34Algebra I content domains (not enumerated in source)

Which expression represents the complete factorization of x^2 + 7x + 12 over the integers?

  1. (x + 2)(x + 6)
  2. (x + 3)(x + 4) Correct answer.
  3. (x + 1)(x + 12)
  4. (x − 3)(x − 4)

Explanation

You need two integers whose product is 12 and whose sum is 7. The numbers 3 and 4 satisfy both conditions, so the factorization is (x + 3)(x + 4).

Question 35Algebra I content domains (not enumerated in source)

The quadratic equation x^2 − 6x + 5 = 0 is solved. What are its solutions?

  1. x = 1 and x = 5 Correct answer.
  2. x = −1 and x = −5
  3. x = 1 and x = −5
  4. x = 2 and x = 3

Explanation

Factor the quadratic as (x − 1)(x − 5) = 0. Setting each factor equal to zero gives x = 1 and x = 5, and both check in the original equation.

Question 36Algebra I content domains (not enumerated in source)

The expression (2x^3)(5x^4) is simplified. Which expression is equivalent?

  1. 10x^7 Correct answer.
  2. 7x^7
  3. 7x^12
  4. 10x^12

Explanation

Multiply the coefficients: 2 · 5 = 10. When multiplying powers with the same base, add the exponents: x^3 · x^4 = x^7. The result is 10x^7.

Question 37Algebra I content domains (not enumerated in source)

A line is parallel to the line y = −3x + 2 and passes through the point (1, 4). Which equation represents this line?

  1. y = −3x + 7 Correct answer.
  2. y = (1/3)x + 7
  3. y = 3x + 1
  4. y = −3x + 4

Explanation

Parallel lines have equal slopes, so the new line has slope −3. Using point-slope form, y − 4 = −3(x − 1), which simplifies to y = −3x + 7.

Question 38Algebra I content domains (not enumerated in source)

The system of equations y = 2x + 1 and y = −x + 10 is solved. What is the value of y in the solution?

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

Explanation

Set the expressions equal: 2x + 1 = −x + 10, so 3x = 9 and x = 3. Substituting gives y = 2(3) + 1 = 7, which checks in the second equation as well.

Question 39Algebra I content domains (not enumerated in source)

A line passes through the point (−2, 3) and has a slope of −1/2. Which equation represents the line in point-slope form?

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

Explanation

Point-slope form is y − y₁ = m(x − x₁). With m = −1/2 and (x₁, y₁) = (−2, 3), this becomes y − 3 = −(1/2)(x − (−2)), which simplifies to y − 3 = −(1/2)(x + 2).

Question 40Algebra I content domains (not enumerated in source)

The function f(x) = x^2 − 4x + 7 is graphed. What is the minimum value of f(x)?

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

Explanation

Complete the square: x^2 − 4x + 7 = (x − 2)^2 + 3. The squared term is never negative, so the minimum occurs at x = 2 and equals 3.

Question 41Algebra I content domains (not enumerated in source)

The expression (x^2 − 25)/(x + 5) is simplified for x ≠ −5. Which expression is equivalent?

  1. x + 5
  2. (x − 5)/(x + 5)
  3. x^2 − 5
  4. x − 5 Correct answer.

Explanation

The numerator is a difference of squares: x^2 − 25 = (x − 5)(x + 5). Canceling the common factor (x + 5) leaves x − 5, valid where x ≠ −5.

Question 42Algebra I content domains (not enumerated in source)

A sequence is defined by a_n = 3n − 2. What is the 10th term of the sequence?

  1. 32
  2. 25
  3. 30
  4. 28 Correct answer.

Explanation

Substitute n = 10 into the explicit formula: a_10 = 3(10) − 2 = 28. The formula gives each term directly from its position.

Question 43Algebra I content domains (not enumerated in source)

The expression (3x^2 − 2x + 5) − (x^2 + 4x − 1) is simplified. Which expression is equivalent?

  1. 4x^2 + 2x + 4
  2. 2x^2 − 6x + 4
  3. 2x^2 + 2x + 4
  4. 2x^2 − 6x + 6 Correct answer.

Explanation

Distribute the subtraction to every term in the second polynomial: 3x^2 − 2x + 5 − x^2 − 4x + 1. Combining like terms gives 2x^2 − 6x + 6.

Question 44Algebra I content domains (not enumerated in source)

The equation of a line is 6x + 3y = 12. What is the slope of the line?

  1. 6
  2. −6
  3. 2
  4. −2 Correct answer.

Explanation

Solve for y: 3y = −6x + 12, so y = −2x + 4. The coefficient of x in slope-intercept form is the slope, which is −2.

Question 45Algebra I content domains (not enumerated in source)

The function f(x) = |x − 3| + 2 is graphed. What is the vertex of the graph?

  1. (3, −2)
  2. (3, 2) Correct answer.
  3. (2, 3)
  4. (−3, 2)

Explanation

An absolute value function of the form y = |x − h| + k has its vertex at (h, k). Here h = 3 and k = 2, so the vertex is (3, 2).

Question 46Algebra I content domains (not enumerated in source)

A quadratic function has roots at x = −1 and x = 5 and opens downward. Which equation could represent the function?

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

Explanation

Roots at x = −1 and x = 5 require factors (x + 1) and (x − 5). A negative leading coefficient makes the parabola open downward, so y = −(x + 1)(x − 5) fits all conditions.

Question 47Algebra I content domains (not enumerated in source)

The expression (x + 2)/(x^2 − 4) is simplified for x ≠ 2 and x ≠ −2. Which expression is equivalent?

  1. x − 2
  2. 1/(x − 2) Correct answer.
  3. 1/(x + 2)
  4. (x + 2)/(x − 2)

Explanation

Factor the denominator as (x − 2)(x + 2). Canceling the common factor (x + 2) from numerator and denominator leaves 1/(x − 2).

Question 48Algebra I content domains (not enumerated in source)

A system consists of y = x^2 − 2x + 3 and y = x + 3. How many real solutions does the system have?

  1. Two Correct answer.
  2. Zero
  3. One
  4. Infinitely many

Explanation

Set the expressions equal: x^2 − 2x + 3 = x + 3, which simplifies to x^2 − 3x = 0, or x(x − 3) = 0. The solutions x = 0 and x = 3 give two distinct intersection points.

Question 49Algebra I content domains (not enumerated in source)

The function f(x) = 2x^2 − 8x + 5 is rewritten in vertex form. Which equation is equivalent?

  1. f(x) = 2(x + 2)^2 − 3
  2. f(x) = 2(x − 2)^2 − 3 Correct answer.
  3. f(x) = 2(x − 2)^2 + 5
  4. f(x) = 2(x − 4)^2 − 3

Explanation

Factor 2 from the first two terms: 2(x^2 − 4x) + 5. Completing the square inside gives 2((x − 2)^2 − 4) + 5 = 2(x − 2)^2 − 3.

Question 50Algebra I content domains (not enumerated in source)

The expression (x^2 + 5x + 6)/(x^2 − 9) is divided by (x + 2)/(x − 3), for values where both expressions are defined. Which expression is equivalent?

  1. (x + 2)^2/((x − 3)^2)
  2. (x + 2)/(x − 3)
  3. 1 Correct answer.
  4. (x + 3)/(x − 3)

Explanation

Factor to get ((x + 2)(x + 3))/((x − 3)(x + 3)) divided by (x + 2)/(x − 3). Multiplying by the reciprocal and canceling (x + 2), (x + 3), and (x − 3) leaves 1.