Algebra Practice

Evaluating Algebraic Expressions Practice Test

Substitute values accurately and apply order of operations to numerical, functional, and formula-based expressions.

Evaluating Algebraic Expressions Practice Test

20 expression-evaluation questions with worked calculations.

Instant feedback · Worked explanations
After the test · evaluation console

Evaluating an expression is a controlled input-output process

The algebraic expression is the rule. The assigned variable values are the inputs. Your job is to replace every variable consistently and then perform the resulting numerical calculation without changing the original structure.

Signed valuesSeveral variablesExponentsFractions FunctionsAbsolute valueFormulasUnits
Substitution bench

Replace every occurrence of every variable before doing arithmetic

With several variables, substitute them all first. This keeps the algebraic structure visible and reduces the chance that one occurrence is forgotten.

Rule + inputs 3x² − 2y
x = −2y = 5
→
Fully substituted 3(−2)² − 2(5)
= 12 − 10= 2
Sign microscope

A negative input needs parentheses

(−3)²

Parentheses preserve the fact that the negative sign belongs to the substituted value. This matters especially with exponents.

(−3)² = 9
−3² = −9
The two expressions are not equivalent.
Computation runway

After substitution, the problem becomes a numerical order-of-operations problem

Once variables are gone, stop thinking symbolically and evaluate the resulting number expression in a controlled sequence.

1GroupingWork inside parentheses first.
2PowersEvaluate exponents before multiplication.
3× and ÷Work from left to right.
4+ and −Finish the calculation.
Function notation machine

f(x) names an output rule — it does not mean f multiplied by x

If f(x) = 2x² − 3x + 1, then f(−2) means evaluate the rule at x = −2.

Input x = −2
f(x) = 2x² − 3x + 1
↓
2(−2)² − 3(−2) + 1
Output f(−2) = 15
Denominator checkpoint

Rational expressions require one safety check before evaluation

A substitution that makes the denominator zero is not allowed. Check the denominator before completing the arithmetic.

Allowed input

(x + 4)/(x − 2), x = 5
→ 9/3 = 3

Restricted input

(x + 4)/(x − 2), x = 2
Denominator = 0 → the expression is undefined.
Absolute-value stage

Evaluate what is inside the bars before taking absolute value

Absolute value reports distance from zero, so the final value cannot be negative.

For a = 5:

|2a − 7|
= |2(5) − 7|
= |3|
= 3
Formula passport

Applied formulas are still algebraic expressions — but the units travel with the values

Geometry, temperature, distance, and other applied formulas use the same substitution process. The difference is that each variable represents a measured quantity, so the final unit is part of the answer.

Keep with the calculation value + meaning + unit
Geometry A = ½h(b₁ + b₂)
Temperature F = 9/5C + 32
Rate d = rt
If r is measured in miles per hour and t in hours, d is measured in miles. If an area formula uses centimeters, the result is in square centimeters.
Evaluation audit

When an answer is wrong, locate the stage where the value changed incorrectly

Input audit Were all assigned values copied correctly, including signs, decimals, and fractions?
Substitution audit Was every occurrence of every variable replaced? Were negative values placed in parentheses?
Operation audit Were powers evaluated before multiplication and division? Was absolute value applied after its interior was computed?
Restriction audit Did any denominator become zero, or did an applied formula require a value outside its allowed context?
Interpretation audit If the expression represents length, area, temperature, cost, or rate, does the final unit and magnitude make sense?
Use your test result diagnostically

Group missed questions by evaluation skill, not by the exact expression

That reveals whether the problem is substitution, signs, order of operations, function notation, rational expressions, or applied formulas.

Signed substitutionNegative inputs, powers, parentheses.
Several variablesReplace every occurrence consistently.
Functions & fractionsInput notation and denominator restrictions.
Applied formulasUnits, geometry, temperature, rates.