2026 Algebra Final Exam Review

Compendium of practice questions and answers for the 2026 Algebra Final Exam, covering topics including quadratic equations, factoring, linear functions, and systems of equations.

Solve for $D$ in terms of $C$ and $\pi$ for the equation $C = \pi D$.

$$D = \frac{C}{\pi}$$

What is the equation of the line that passes through the point $(5, -2)$ and has a slope of $-3$?

$$y = -3x + 13$$

What is the solution to the quadratic equation $2x^2 + 5x - 1 = 0$?

$$\frac{-5 \pm \sqrt{33}}{4}$$

The expression $\frac{6\sqrt{20}}{3\sqrt{5}}$ is equivalent to what integer?

$$4$$

Solve the equation $4(3x - 5) = 5(2x + 4)$ for $x$.

$$20$$

Factor the binomial expression $x^2 - 16$.

$$(x + 4)(x - 4)$$

Ramon used two pieces of equipment for 6 hours each at a total cost of $90. On a second job, he used the first for 4 hours and the second for 8 hours for $100. What is the hourly cost for each?

$5$ for the sprayer and $10$ for the generator

Which number is irrational: $2.6$, $\sqrt{100}$, $\frac{3}{4}$, or $\sqrt{14}$?

$$\sqrt{14}$$

What is the solution set of the equation $x^2 - 3x - 10 = 0$?

$$\{5, -2\}$$

Simplify the radical expression $\sqrt{90} - \sqrt{40} - \sqrt{8} - \sqrt{18}$.

$$48$$

The expression $(x - 4)^2$ is equivalent to which trinomial?

$$x^2 - 8x + 16$$

Solve the inequality $2x > x + 7$.

$$x > 7$$

Which algebraic property is illustrated by the equation $a \cdot (b \cdot c) = (a \cdot b) \cdot c$?

Associative property

Solve the inequality $3x + 2 > x + 8$ for $x$.

$$x > 3$$

Express the product $(2x - 3)(x + 5)$ as a trinomial.

$$2x^2 + 7x - 15$$

What is the multiplicative inverse of $-\frac{5}{6}$?

$$-\frac{6}{5}$$

What is the positive value of $x$ in the equation $x^2 - 64 = 0$?

$$8$$

The expression $3^2 \cdot 3^3 \cdot 3^4$ is equivalent to what power of $3$?

$$3^9$$

What is the slope of a line parallel to the line whose equation is $y = \frac{2}{5}x - 3$?

$$\frac{2}{5}$$

Solve the inequality $4p + 2 < 2(p + 5)$.

$$p < 4$$

Represent the expression $x^{-1}y^2$ using only positive exponents.

$$\frac{y^2}{x}$$

What is the value of $5^{-2}$?

$$\frac{1}{25}$$

If point $(-1, 0)$ is on the line $y = 2x + b$, what is the value of $b$?

$$2$$

Factor the trinomial $x^2 + 6x + 8$.

$$(x + 4)(x + 2)$$

What is the greatest whole number that satisfies the inequality $3x - 1 < 8$?

$$2$$

Express the quadratic $2x^2 - 3x - 5$ as the product of two binomial factors.

$$(2x - 5)(x + 1)$$

What is the sum of $\sqrt{18}$ and $6\sqrt{2}$ simplified?

$$9\sqrt{2}$$

What is the slope of the line that passes through the points $(4, 5)$ and $(7, 3)$?

$$-\frac{2}{3}$$

Solve for $x$ in terms of $b$ and $c$: $2x - b = c$.

$$x = \frac{b + c}{2}$$

What are the coordinates of the turning point of the parabola $y = x^2 - 6x + 5$?

$$(3, -4)$$

What is the quotient when $15x^6y$ is divided by $-3x^3$?

$$-5x^3y$$

Three bags of potatoes and four cases of corn cost $40, while five bags of potatoes and two cases of corn cost $34. What is the cost per bag and per case?

$4$ per bag of potatoes and $7$ per case of corn

Write the number $198,000,000$ in scientific notation as $1.98 \times 10^{n}$. What is the value of $n$?

$$8$$

The sentence $3 + (5 + 2) = (5 + 2) + 3$ illustrates which property?

Commutative property of addition

Cedric bought 2 rolls of foil and 3 battery packs for $21. Zelda bought 5 rolls and 2 battery packs for $25. What is the individual cost of a roll and a battery pack?

$3$ for one jumbo roll of foil and $5$ for one package of batteries

What is the slope of the line whose equation is $y = -3x + 6$?

$$-3$$

What is the result of half of $2^6$?

$$2^5$$

Which expression represents the number $0.00017$ written in scientific notation?

$$1.7 \times 10^{-4}$$

Factor the difference of squares expression $25x^2 - 9$.

$$(5x - 3)(5x + 3)$$

What is the slope of the line whose equation is $5y = 2x + 10$?

$$\frac{2}{5}$$

In the expression $3 - 4^2 + \frac{6}{2}$, which operation would be performed last according to the order of operations?

Adding

What is the turning point of the parabola whose equation is $y = 2x^2 + 4x - 3$?

$$(-1, -5)$$

What is the slope of a line perpendicular to the graph of the equation $5x - 3y = 2$?

$$-\frac{3}{5}$$

Which polynomial is twice the sum of $4x^2 - x + 1$ and $-6x^2 + x - 4$?

$$-4x^2 - 6$$