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Quizzes > High School Quizzes > Mathematics

Maths 8th Grade STAAR Practice Quiz

Boost Algebra & Exam Skills for Test Success

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Colorful paper art promoting STARRing Algebra Challenge, a high school algebra practice quiz.

Solve the equation 2x + 5 = 13.
x = 4
x = 6
x = 5
x = 3
Subtracting 5 from both sides yields 2x = 8 and dividing by 2 gives x = 4. This solution satisfies the original equation.
Simplify the expression: 3(x + 4) - 2x.
x + 7
3x + 4
5x + 4
x + 12
First, distribute 3 to get 3x + 12, then combine like terms with -2x to obtain x + 12. This is the simplified form.
Solve for y: 4y = 32.
y = 7
y = 4
y = 8
y = 16
Dividing both sides by 4 gives y = 8, which is the correct solution to the equation.
Evaluate the expression 2x^2 when x = 3.
12
18
15
21
Substituting x = 3 into 2x^2 gives 2(9) = 18. This calculation requires squaring 3 then multiplying by 2.
Find the slope of the line passing through the points (1, 2) and (3, 6).
1
3
4
2
The slope is calculated as (6 - 2) / (3 - 1) = 4/2 = 2. This shows the rise over run for the line.
Solve for x: 3x - 7 = 2x + 5.
x = 12
x = -12
x = 7
x = 5
Subtracting 2x from both sides gives x - 7 = 5, and adding 7 to both sides results in x = 12. This isolates the variable correctly.
Simplify the expression: 4(x - 2) + 3(2x + 1).
7x - 5
8x - 1
10x + 5
10x - 5
Distribute to get 4x - 8 + 6x + 3, then combine like terms to obtain 10x - 5. This is the correct simplified expression.
Solve for x: 2(x - 3) + 4 = x + 1.
x = 3
x = 2
x = -3
x = 1
Expanding gives 2x - 6 + 4 = 2x - 2; subtracting x from both sides leads to x - 2 = 1, hence x = 3. This method isolates the variable correctly.
Factor the quadratic expression: x^2 + 5x + 6.
(x + 2)(x + 4)
(x + 2)(x + 3)
(x + 3)^2
(x + 1)(x + 6)
The numbers 2 and 3 add to 5 and multiply to 6, allowing the expression to be factored as (x + 2)(x + 3). This is the standard factoring approach for quadratics.
Solve the equation: 5(x - 1) = 2x + 8.
x = 13/3
x = 15/3
x = 3
x = 13/2
Expanding the left side gives 5x - 5, so 5x - 5 = 2x + 8. Subtracting 2x and then adding 5 leads to 3x = 13, so x = 13/3.
Expand and simplify: (x + 3)(x - 2).
x^2 - x - 6
x^2 + x - 6
x^2 + x + 6
x^2 + 6x - 6
Using the FOIL method: x*x + x*(-2) + 3*x + 3*(-2) yields x^2 + x - 6 after combining like terms. This is the fully expanded form.
Solve for y in terms of x: 3y - 2x = 6.
y = 2x + 3
y = (2x - 6)/3
y = (3x + 6)/2
y = (2/3)x + 2
Add 2x to both sides to get 3y = 2x + 6, then divide by 3 yielding y = (2x + 6)/3, which simplifies to (2/3)x + 2.
Find the value of x: 2x/3 = 8.
x = 14
x = 8
x = 12
x = 10
Multiplying both sides by 3 gives 2x = 24, and dividing by 2 yields x = 12. This direct manipulation isolates x.
Solve the inequality: 2x - 4 < 10.
x ≤ 7
x < 7
x > 7
x < 6
Add 4 to get 2x < 14, then divide by 2 to obtain x < 7. The inequality remains strict throughout the process.
If f(x) = 2x + 3, what is f(4)?
11
8
7
10
Substitute 4 into the linear function: f(4) = 2(4) + 3 = 11. This follows directly from the function's definition.
Solve the quadratic equation: 2x^2 - 3x - 2 = 0.
x = 2 or x = -1/2
x = 1 or x = -2
x = 2 only
x = -1/2 only
The quadratic factors as (2x + 1)(x - 2) = 0, leading to the solutions x = -1/2 and x = 2. Both solutions satisfy the original equation.
Solve for x: (x + 1)/(x - 2) = 3.
x = 3
x = 7/2
x = -7/2
x = 2
Multiplying both sides by (x - 2) gives x + 1 = 3x - 6, and solving for x results in x = 7/2. It is important to note x ≠ 2.
If f(x) = x^2 - 4x + k has a repeated root, find the value of k.
k = 0
k = -4
k = 8
k = 4
A quadratic has a repeated root when its discriminant is zero. Here, 16 - 4k = 0 implies k = 4.
Solve for x: 1/(x + 1) + 1/(x - 1) = 1.
x = 2
x = √2
x = 1 + √2 or x = 1 - √2
x = 1 or x = -1
Combining the fractions over a common denominator yields (2x)/(x^2-1) = 1, which results in the quadratic equation x^2 - 2x - 1 = 0. Solving by the quadratic formula gives x = 1 ± √2, after ensuring the solutions do not violate the domain restrictions.
Solve for x: |2x - 5| = 3.
x = 3
x = 4 or x = 1
x = 4 only
x = -4 or x = -1
The absolute value equation gives two cases: 2x - 5 = 3 and 2x - 5 = -3. Solving these yields x = 4 and x = 1, respectively, which are the valid solutions.
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Study Outcomes

  1. Analyze exam-style algebra problems to identify underlying concepts.
  2. Apply techniques for solving linear equations and systems.
  3. Evaluate and simplify algebraic expressions with precision.
  4. Interpret variables and functions within problem contexts.
  5. Assess performance to determine strengths and identify improvement areas.

Maths 8th Grade & Algebra 2 STAAR Cheat Sheet

  1. Master the slope formula - Get comfortable with m = (y₂ − y₝)/(x₂ − x₝) by plugging in values and seeing how the steepness changes. Visualizing two points on a graph makes the concept stick and helps you tackle line problems with confidence. For instance, between (1, 2) and (3, 6), you get m = (6−2)/(3−1) = 2, so practice with different pairs to build intuition. High School Algebra I Study Guide for the STAAR test
  2. Understand the slope-intercept form - The equation y = mx + b lets you graph lines like a pro: m is your incline, and b is where the line hits the y-axis. Learning to identify m and b quickly saves tons of time on graphing questions. Experiment by changing m or b in y = mx + b and watching the line tilt or shift up and down. Formula Chart for STAAR® High School Algebra I Test
  3. Practice solving systems by graphing - When two lines cross, that intersection point is your solution. Sketch y = 2x − 4 and y = (x/2) + 2 on the same axes to see they meet at (4, 4). Graphing not only checks your algebra but also trains your eye to spot solutions faster. High School Algebra I Study Guide for the STAAR test
  4. Familiarize yourself with exponent rules - Rules like aᵝ·a❿ = aᵝ❺❿ and aᵝ/a❿ = aᵝ❻❿ turn monstrous expressions into neat answers. Mastering these shortcuts will speed up simplifying and solving. Try mixing positive, negative, and zero exponents to see how the rules always apply. Formula Chart for STAAR® High School Algebra I Test
  5. Learn to simplify square roots - Breaking numbers into perfect squares helps you extract factors: √252 = √(36×7) = 6√7. This trick makes radical work much smoother and prevents mistakes in complex problems. Practice with various radicands until factoring becomes second nature. High School Algebra I Study Guide for the STAAR test
  6. Understand function notation and evaluation - f(x) = 3x² − 4x + 1 means "plug in x and watch the magic." For x = −2, you get f(−2) = 3(4) − 4(−2) + 1 = 12 + 8 + 1 = 21. This process is key in applications and real-world modeling, so try different formulas to see how outputs change. High School Algebra I Study Guide for the STAAR test
  7. Recognize the standard form of a line - Ax + By = C keeps things neat when finding intercepts: set x=0 for the y-intercept and y=0 for the x-intercept. Converting between standard and slope-intercept form strengthens your algebra fluency. Work on transformations to see why both forms are useful. Formula Chart for STAAR® High School Algebra I Test
  8. Practice graphing linear inequalities - Solid lines for ≤ or ≥ and dashed lines for < or > keep your shading legit. Then decide which side of the line satisfies the inequality by testing a point. Visual practice with different slopes and intercepts makes this a breeze on exam day. High School Algebra I Study Guide for the STAAR test
  9. Understand transformations of the parent function - Starting with f(x)=x, try g(x)=−3(x+4)+2 to see four moves at once: reflect over the x-axis, stretch by 3, shift left 4, and up 2. Breaking complex transformations into steps helps you graph any function quickly. Jot down each tweak to avoid mix-ups. High School Algebra I Study Guide for the STAAR test
  10. Familiarize yourself with the quadratic formula - x = [−b ± √(b²−4ac)]/(2a) solves any quadratic, even when factoring fails. Always check the discriminant first (b²−4ac) to predict two, one, or no real roots. Plug it in, simplify step by step, and watch the solutions appear. Formula Chart for STAAR® High School Algebra I Test
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