Algebra Practice

Basic Algebra Practice Test

Review the essential skills needed before moving into full Algebra 1 coursework.

Basic Algebra Practice Test

20 foundational algebra questions with instant explanations.

Instant feedback · Worked explanations
Bauhaus Algebra Foundation Board

Basic algebra is about structure, balance, and meaning before speed.

This review combines the foundational ideas that support pre-algebra and early Algebra 1: evaluate expressions, simplify correctly, solve equations and inequalities, connect ordered pairs to rules, interpret slope, use exponent laws, work with fractions and proportions, factor simple quadratics, and translate short statements into equations. The goal is not mechanical repetition. Each skill should explain why the algebraic step is legal.

EvaluateSubstitute first, then follow the order of operations.
SimplifyCombine only like terms and distribute to every term.
SolveUndo operations while keeping both sides balanced.
CheckSubstitute the result back into the original rule or equation.
ExpressionsSubstitution, like terms, and distribution.
EquationsOne-step and multi-step solving.
InequalitiesSign changes when dividing by negatives.
CoordinatesOrdered pairs, slope, and linear rules.
Algebra toolsExponents, fractions, proportions, factoring, and translation.

1. Evaluate an expression by replacing the variable with its known value

Substitution changes an algebraic expression into a numerical one. Keep the structure intact until the replacement is complete.

Substitute first

3x−2
x=5
3·5−2=13

The variable is replaced by the stated number before arithmetic begins.

Watch negative signs

A negative sign attached to a term stays attached when a number is substituted. Treat parentheses carefully when the substituted value itself is negative.

2. Combine like terms, but keep unlike variable parts separate

Terms combine only when their variable parts match exactly.

Like terms

4x+7−2x+3
2x+10

Variable terms combine with variable terms; constants combine with constants.

Unlike terms do not combine

3x+2y

Different variable parts represent different quantities and must remain separate.

3. Distribution reaches every term inside the parentheses

The multiplier outside the parentheses must multiply each term inside.

Start
3(x−4)+2

Identify the multiplier attached to the grouped expression.

→
Distribute
3x−12+2

Multiply both terms inside the parentheses.

→
Combine
3x−10

Now combine the constant terms.

4. Solve equations by undoing operations in reverse order

Whatever operation is applied to one side must be balanced on the other side.

One-variable equation

4x−7=21
4x=28
x=7
4·7−7=21

Substitution verifies that the solution restores equality.

Multi-step equation

3(x+2)=2x+11
3x+6=2x+11
x=5

Distribute first, then collect variable terms and constants before isolating the variable.

5. Reverse an inequality only when multiplying or dividing by a negative number

The direction changes because multiplying by a negative reverses order on the number line.

Negative divisor

−3x>12
−3<0
x<−4

The symbol reverses because the division is by a negative coefficient.

Do not reverse automatically

Adding or subtracting the same quantity on both sides does not reverse the inequality. The reversal belongs specifically to multiplication or division by a negative number.

6. Ordered pairs, slope, and linear equations describe the same coordinate relationship

A point satisfies a linear rule when its coordinates make the equation true. Slope measures change in the vertical coordinate per change in the horizontal coordinate.

Test a point and calculate slope

(2,5)
y=2x+1
5=2·2+1
(1,2)
(4,8)
m=8−24−1
m=2

Slope is a ratio of two changes, not the vertical change alone.

Read slope-intercept form

y=2x−3
m=2
b=−3

The coefficient of the variable gives the slope; the constant is the vertical intercept.

Coordinate check

A point on a line must satisfy the rule numerically. This is often faster than trying to reason from the picture alone.

7. Exponent laws and fraction reduction both depend on structure

Exponent rules apply to matching bases; fraction reduction removes common factors rather than canceling unrelated terms.

Multiply matching bases

x3·x4
x7

Add exponents when multiplying powers with the same base.

Divide matching bases

a6a2
a4

Subtract exponents when dividing powers with the same base.

Reduce a fraction

12x18
2x3

Cancel a common numerical factor from numerator and denominator.

Add fractions with a common denominator

x4+x2
3x4

Rewrite equivalent fractions before adding numerators.

Do not cancel across addition

Cancellation works with factors in products, not arbitrary terms separated by addition or subtraction.

8. Proportions and simple factoring reverse familiar operations

Cross products solve a proportion; factoring reverses multiplication of binomials.

Proportion

x5=615
15x=30
x=2

Cross multiplication is shorthand for clearing the two denominators.

Factor a simple quadratic

x2+7x+12
(x+3)(x+4)
x=−3,x=−4

The two numbers must multiply to the constant term and add to the linear coefficient.

9. Translate words into algebra, and keep geometric formulas distinct

Many introductory errors come from choosing the wrong model before any algebra is done.

Statement to equation

3x+5=20
x=5

Identify the unknown, then translate each operation in the order described.

Rectangle area

x+2
x+5
(x+2)(x+5)

Area multiplies the two side lengths.

Rectangle perimeter

2(x+2)+2(x+5)

Perimeter adds the side lengths around the boundary instead of multiplying them.

10. A squared variable can produce two roots

When a square equals a positive number, both the positive and negative square roots satisfy the equation.

Do not keep only the positive root

x2=16
x=4 or x=−4

Both values square to the same positive number.

Check both

Substitution is the quickest way to verify that each root satisfies the original squared equation.

11. Error analysis: the most common mistakes are structural

A student can perform arithmetic correctly and still get the wrong answer if the algebraic structure is misread.

Negative sign dropped

Keep the sign attached to its term through substitution and simplification.

Unlike terms combined

Only terms with matching variable parts can be added or subtracted directly.

Distribution stopped after the first term

The outside factor multiplies every term inside the parentheses.

Inequality reversed at the wrong time

Reverse only when multiplying or dividing by a negative number.

Slope confused with rise alone

Slope is vertical change divided by horizontal change.

Only one root kept from a square

A positive squared value usually gives both positive and negative roots.

Final basic-algebra audit

Before accepting an answer, check the operation, sign, structure, units, and whether substitution confirms the result.

1
Did I substitute before calculating?Keep the original expression structure intact during replacement.
2
Am I combining only like terms?Variable parts must match exactly.
3
Did I distribute to every term?One missed term changes the whole expression.
4
Did I reverse an inequality only after multiplying or dividing by a negative?Do not reverse for ordinary addition or subtraction.
5
Does the coordinate or geometric interpretation match the algebra?Check slope, area, perimeter, and ordered-pair rules carefully.
6
Can I verify the answer by substitution?A quick check catches many sign and arithmetic errors.
This block supports the Basic Algebra Practice Test. Its examples are illustrative rather than copies of the test questions. The focus is numerical substitution, simplifying expressions, distributive property, one-step and multi-step equations, inequalities, ordered pairs, slope, linear equations, exponent laws, fractions, proportions, elementary factoring, translating statements into equations, distinguishing area from perimeter, and remembering both roots when a squared variable equals a positive number.