Your FREE Praxis Algebra I (5162) Practice Test 2026 – 120+ Q&A

Correct answer: 6

Add 7 to both sides: $3x = 18$. Divide by 3: $x = 6$.

Correct answer: 7

Distribute: $5x - 10 = 3x + 4$. Subtract $3x$: $2x - 10 = 4$. Add 10: $2x = 14$, so $x = 7$.

Correct answer: $x > 0$

Expand: $2x - 6 < 4x - 6$. Subtract $2x$ and add 6: $0 < 2x$, so $x > 0$.

Correct answer: 24

Subtract 3: $\frac{x}{4} = 6$. Multiply by 4: $x = 24$.

Correct answer: $t = \frac{d}{r}$

Divide both sides of $d = rt$ by $r$: $t = \frac{d}{r}$.

Correct answer: 1

Inverse variation means $xy = k$. Here $k = 4 \times 3 = 12$. When $x = 12$, $y = \frac{12}{12} = 1$.

Correct answer: 6

Substitute $x = 10$: $\frac{10}{5} = \frac{y}{3}$, so $2 = \frac{y}{3}$ and $y = 6$.

Correct answer: $x = \frac{3}{2}$

Since $81 = 3^{4}$, set $2x + 1 = 4$. Then $2x = 3$, so $x = \frac{3}{2}$.

Correct answer: $4x^{10}$

$\left(2x^{3}\right)^{2} = 4x^{6}$. Multiply by $x^{4}$: $4x^{6+4} = 4x^{10}$.

Correct answer: -31

$2(-8) - (4) + (-8) - 7 = -16 - 4 - 8 - 7 = -31$.

Correct answer: 21

$2(4) - 5(-2) + 3 = 8 + 10 + 3 = 21$.

Correct answer: $x^{2} - 2x - 15$

FOIL: $x^{2} - 5x + 3x - 15 = x^{2} - 2x - 15$.

Correct answer: $(x - 3)(x + 3)$

This is a difference of squares: $x^{2} - 9 = (x - 3)(x + 3)$.

Correct answer: $(2x + 1)(x + 3)$

$(2x + 1)(x + 3) = 2x^{2} + 6x + x + 3 = 2x^{2} + 7x + 3$.

Correct answer: $x = 2$ and $x = 3$

Factor: $(x - 2)(x - 3) = 0$, so $x = 2$ or $x = 3$.

Correct answer: $x = 3$ only

$x^{2} - 6x + 9 = (x - 3)^{2} = 0$, a perfect square with the single repeated root $x = 3$.

Correct answer: 6

One real solution means the discriminant is zero: $k^{2} - 4(1)(9) = 0$, so $k^{2} = 36$ and $k = 6$ (taking $k > 0$).

Correct answer: $y = (x - 2)^{2} - 3$

Complete the square: $x^{2} - 4x = (x - 2)^{2} - 4$. So $y = (x - 2)^{2} - 4 + 1 = (x - 2)^{2} - 3$.

Correct answer: 12

For $ax^{2} + bx + c = 0$, the product of the roots is $\frac{c}{a} = \frac{12}{1} = 12$ (the roots are 3 and 4).

Correct answer: 4

The sum of the roots is $-\frac{b}{a} = -\frac{-8}{2} = 4$.

Correct answer: $\frac{2}{3}$

Solve for $y$: $-3y = -2x + 6$, so $y = \frac{2}{3}x - 2$. The slope is $\frac{2}{3}$.

Correct answer: $y = -2x + 7$

Slope $= \frac{-1 - 3}{4 - 2} = -2$. Using $(2, 3)$: $3 = -2(2) + b$ gives $b = 7$, so $y = -2x + 7$.

Correct answer: 8

The line is $y = -\frac{1}{2}x + 4$. Set $y = 0$: $0 = -\frac{1}{2}x + 4$, so $x = 8$.

Correct answer: 3

Add the equations: $3x = 9$, so $x = 3$ (and $y = 1$).

Correct answer: $-\frac{10}{3}$

A system has no solution when the lines are parallel (equal slopes, different intercepts). Slopes are $-\frac{2}{3}$ and $\frac{k}{5}$. Setting $\frac{k}{5} = -\frac{2}{3}$ gives $k = -\frac{10}{3}$.

Correct answer: $\frac{x + 4}{x - 1}$

Factor: $\frac{(x - 4)(x + 4)}{(x - 1)(x - 4)}$. Cancel $(x - 4)$: $\frac{x + 4}{x - 1}$.

Correct answer: $x = 1$

A rational function is undefined where its denominator is zero: $x - 1 = 0$, so $x = 1$.

Correct answer: $\frac{x + 2}{x^{2}}$

Common denominator $x^{2}$: $\frac{x}{x^{2}} + \frac{2}{x^{2}} = \frac{x + 2}{x^{2}}$.

Correct answer: $x = 4$ or $x = -3$

Either $2x - 1 = 7$ (so $x = 4$) or $2x - 1 = -7$ (so $x = -3$).

Correct answer: $-7 < x < 3$

$|x + 2| < 5$ means $-5 < x + 2 < 5$. Subtract 2: $-7 < x < 3$.

Correct answer: $(x - 3)^{2}$

It is a perfect-square trinomial: $x^{2} - 6x + 9 = (x - 3)^{2}$.

Correct answer: $4x(x - 3)$

The GCF is $4x$: $4x^{2} - 12x = 4x(x - 3)$. The other forms are not fully factored or are incorrect.

Correct answer: 13

$a + b = 5$ and $ab = 6$. Then $a^{2} + b^{2} = (a + b)^{2} - 2ab = 25 - 12 = 13$.

Correct answer: $(x - 3)^{2} + (y + 4)^{2} = 25$

Standard form is $(x - h)^{2} + (y - k)^{2} = r^{2}$ with center $(h, k) = (3, -4)$ and $r^{2} = 25$.

Correct answer: 8

Multiply by 3: $2x - 1 = 15$. Add 1: $2x = 16$, so $x = 8$.

Correct answer: $6w + 6$

Length $= 2w + 3$. Perimeter $= 2(\text{length} + \text{width}) = 2(2w + 3 + w) = 2(3w + 3) = 6w + 6$.

Correct answer: -10

Set $x = 0$: $-2y = 20$, so $y = -10$. The $y$-intercept is $-10$.

Correct answer: $-1 \leq x \leq 3$

Add 1 throughout: $-2 \leq 2x \leq 6$. Divide by 2: $-1 \leq x \leq 3$.

Correct answer: $x = 0$ or $x = 5$

Rewrite as $x^{2} - 5x = 0$, factor $x(x - 5) = 0$: $x = 0$ or $x = 5$. Dividing by $x$ would lose the $x = 0$ solution.

Correct answer: $x = -1 \pm \sqrt{2}$

$x = \frac{-2 \pm \sqrt{4 + 4}}{2} = \frac{-2 \pm 2\sqrt{2}}{2} = -1 \pm \sqrt{2}$.

Correct answer: $-8$; two complex (no real) solutions

Discriminant $= b^{2} - 4ac = (-4)^{2} - 4(3)(2) = 16 - 24 = -8$. A negative discriminant means no real solutions (two complex roots).

Correct answer: $\frac{3x^{2}}{y^{3}}$

Divide coefficients $\frac{6}{2} = 3$, subtract exponents: $x^{3-1} = x^{2}$ and $y^{2-5} = y^{-3}$. Result: $\frac{3x^{2}}{y^{3}}$.

Correct answer: 10

Try factor pairs with $a > b$: $a = 8, b = -3$ gives $ab = -24$ and $a - b = 11$; $a = 12, b = -2$ gives $a - b = 14$; $a = 2, b = -12$ gives $a - b = 14$; $a = 4, b = -6$ gives $a - b = 10$. Only 10 is attainable among the choices.

Correct answer: 13

Square both sides: $x + 3 = 16$, so $x = 13$. Check: $\sqrt{16} = 4$.

Correct answer: $x < -3$

Subtract 5: $-2x > 6$. Divide by $-2$ and flip the inequality: $x < -3$.

Correct answer: -7

Subtract $2x$: $2x + 9 = -5$. Subtract 9: $2x = -14$, so $x = -7$.

Correct answer: $(x + 7)(x - 2)$

Find two numbers with product $-14$ and sum $5$: $7$ and $-2$. So $x^{2} + 5x - 14 = (x + 7)(x - 2)$.

Correct answer: $2x - 4$

Factor the numerator: $2x^{2} - 8 = 2(x^{2} - 4) = 2(x - 2)(x + 2)$. Cancel $(x + 2)$: $2(x - 2) = 2x - 4$.

Correct answer: 6

$3(1) - 2(-1) + 1 = 3 + 2 + 1 = 6$.

Correct answer: 4

$2(9) + 3(-3) - 5 = 18 - 9 - 5 = 4$.

Correct answer: $f^{-1}(x) = \frac{x + 4}{3}$

Set $y = 3x - 4$, swap and solve: $x = 3y - 4 \Rightarrow y = \frac{x + 4}{3}$.

Correct answer: $x > -2$

A logarithm requires a positive argument: $x + 2 > 0$, so $x > -2$.

Correct answer: $y \geq 0$

The principal square root is never negative, so outputs satisfy $y \geq 0$. (The domain is $x \geq 2$, but the range is $y \geq 0$.)

Correct answer: $-3 \leq x \leq 3$

Require $9 - x^{2} \geq 0$, i.e. $x^{2} \leq 9$, which gives $-3 \leq x \leq 3$.

Correct answer: $y = x^{2} - 4$

Symmetry about the $y$-axis means an even function, $f(-x) = f(x)$. Only $y = x^{2} - 4$ satisfies this.

Correct answer: 0

An absolute value is never negative and reaches 0 when $x = 3$, so the minimum value is 0.

Correct answer: $(1, 3)$

In vertex form $a(x - h)^{2} + k$, the vertex is $(h, k) = (1, 3)$.

Correct answer: $x = 2$ and $x = -2$

Vertical asymptotes occur where the denominator is zero: $x^{2} - 4 = 0$, so $x = \pm 2$.

Correct answer: 2

Solve $3^{x+1} = 27 = 3^{3}$: $x + 1 = 3$, so $x = 2$. Thus $h^{-1}(27) = 2$.

Correct answer: As $x \rightarrow \infty,\ f(x) \rightarrow \infty$; as $x \rightarrow -\infty,\ f(x) \rightarrow -\infty$

The leading term $x^{3}$ has odd degree and positive coefficient, so the graph rises to the right and falls to the left.

Correct answer: $f(x) = \frac{x + 1}{x}$

$\frac{x + 1}{x} = 1 + \frac{1}{x} \rightarrow 1$ as $x \rightarrow \pm\infty$. Its horizontal asymptote is $y = 1$.

Correct answer: shifted up 3 units

Adding a constant to the output value translates the graph vertically: $+3$ shifts it up 3 units.

Correct answer: shifted right 4 units

Replacing $x$ with $x - 4$ shifts the graph horizontally to the right by 4 units.

Correct answer: exponential

Growing by equal factors (a common ratio) over equal intervals is the defining property of an exponential function; linear functions grow by equal differences.

Correct answer: multiplies by 2

$f(x + 1) = 2^{x+1} = 2 \cdot 2^{x} = 2 f(x)$, so each unit increase in $x$ multiplies the output by 2.

Correct answer: 9

$(f \circ g)(2) = f(g(2)) = f(3) = 3^{2} = 9$.

Correct answer: 49

$f(3) = 7$, then $g(7) = 7^{2} = 49$.

Correct answer: 5

Average rate of change $= \frac{f(4) - f(1)}{4 - 1} = \frac{16 - 1}{3} = \frac{15}{3} = 5$.

Correct answer: 3

For a linear function the average rate of change equals the slope, which is 3 on every interval.