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Quizzes > High School Quizzes > Mathematics

Math 3 Review Practice Quiz

Sharpen your skills with math 2 and geometry review

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Colorful paper art representation of a Math 2 3 Blitz practice quiz for high school students.

Solve for x: 2x + 3 = 11.
x = 5
x = 4
x = 8
x = -4
Subtracting 3 from both sides gives 2x = 8. Dividing by 2 results in x = 4, demonstrating the basic method for solving linear equations.
Evaluate the function f(x) = 3x - 2 when x = 5.
13
10
8
15
Substituting x = 5 into the function results in 3×5 - 2 = 15 - 2 = 13. This confirms the correct evaluation of the function.
What is the slope of the line given by the equation y = 4x + 7?
7
4
-4
-7
In the slope-intercept form y = mx + b, the coefficient m represents the slope. Here, m = 4, so the slope is 4.
Calculate the value of 2^3.
7
8
9
6
2 raised to the power of 3 means 2 × 2 × 2, which equals 8. This question reinforces the concept of exponents.
If a fair coin is flipped, what is the probability of landing on heads?
0
1
1/4
1/2
A fair coin has two equally likely outcomes, so the probability of landing on heads is 1/2. This illustrates a basic idea in probability.
Solve for x: 3(x - 2) = 15.
x = 7
x = 6
x = 8
x = 5
Expanding the equation gives 3x - 6 = 15; adding 6 to both sides yields 3x = 21, and dividing by 3 results in x = 7. This question reinforces basic distribution and solving techniques.
Factor the expression x² - 9.
(x - 3)(x + 3)
(x - 3)²
(x - 9)(x + 1)
x(x - 9)
x² - 9 is recognized as a difference of two squares, which factors into (x - 3)(x + 3). This factorization is a key algebraic skill.
Simplify the expression: 2(3x + 4) - 5x.
6x + 4
x - 8
x + 8
8x + 8
Distributing 2 gives 6x + 8, and then subtracting 5x results in x + 8. This problem emphasizes the importance of the distributive property and combining like terms.
Solve for y: (2y)/3 = 10.
20
30
10
15
Multiplying both sides by 3 results in 2y = 30, and dividing by 2 gives y = 15. This illustrates solving equations that involve fractions.
What is the equation of the line that passes through (0, -2) with a slope of 3?
y = 3x - 2
y = -3x + 2
y = -3x - 2
y = 3x + 2
Using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we obtain y = 3x - 2. This aligns with the given point and slope.
If 1/5 of a number is 8, what is the number?
80
40
13
5
Multiplying 8 by 5 gives the original number, 40. This question tests understanding of fractions and inverse operations.
Which inequality represents the solution to x + 2 > 5?
x ≤ 3
x ≥ 3
x < 3
x > 3
Subtracting 2 from both sides results in x > 3. This reinforces the technique of isolating the variable in an inequality.
Simplify the expression: x³ * x².
x❹
x❵
x
x❶
When multiplying expressions with the same base, add the exponents: 3 + 2 = 5, so x³ * x² = x❵. This problem highlights exponent rules.
Solve for x: 4(x + 1) = 2x + 10.
3
2
4
6
Expanding the left side gives 4x + 4; setting the equation as 4x + 4 = 2x + 10, subtracting 2x and then 4 leads to 2x = 6, so x = 3. This steps through multiple algebraic manipulations.
Find the value of x that satisfies the proportion: 3/4 = x/12.
12
9
16
8
Cross-multiplying gives 4x = 36, so dividing both sides by 4 results in x = 9. This problem is a practical application of solving proportions.
What is the sum of the solutions of the quadratic equation x² - 6x + 8 = 0?
6
8
4
10
By Vieta's formulas, the sum of the roots of a quadratic equation ax² + bx + c = 0 is -b/a. For this equation, -(-6)/1 equals 6, making 6 the correct answer.
In the system of equations 2x + 3y = 12 and x - y = 1, what is the value of x?
5
3
2
4
Expressing x as y + 1 from the second equation and substituting into the first leads to solving for y, and eventually x = 3. This problem tests solving systems of linear equations.
If f(x) = 2x² - 3x + 1, what is the value of f(2)?
3
7
2
5
Substituting x = 2 into the function yields 2(4) - 3(2) + 1 = 8 - 6 + 1 = 3. This reinforces the evaluation of quadratic functions.
Simplify the radical expression: √50 - √8.
7√2
3√5
√2
3√2
Express √50 as 5√2 and √8 as 2√2; subtracting these gives 5√2 - 2√2 = 3√2. This problem requires simplifying radicals by factoring out perfect squares.
Determine the slope of a line perpendicular to the line with slope -2/3.
-2/3
2/3
-3/2
3/2
For two lines to be perpendicular, the product of their slopes must be -1. The negative reciprocal of -2/3 is 3/2, making it the correct answer.
0
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Study Outcomes

  1. Analyze math problems to identify key concepts and areas for improvement.
  2. Apply efficient problem-solving techniques to diverse review questions.
  3. Evaluate exam strategies to refine approaches for future tests.
  4. Synthesize multiple math concepts under time constraints.
  5. Reflect on quiz performance to strengthen overall exam preparedness.

Math 2 & 3 Review Cheat Sheet

  1. Master the Pythagorean Theorem - In a right-angled triangle, the square of the hypotenuse (the longest side) equals the sum of the squares of the other two sides: a² + b² = c². Use this superpower to tackle distance problems and uncover hidden lengths in any right triangle - your geometry homework won't know what hit it! The 10 Most Important Mathematical Formulas for High School Students
  2. Understand the Quadratic Formula - For any quadratic equation ax² + bx + c = 0, the solutions pop out as x = ( - b ± √(b² - 4ac)) / (2a). This trusty formula is your secret weapon for finding roots fast, whether you're graphing parabolas or solving real‑world problems. The 10 Most Important Mathematical Formulas for High School Students
  3. Learn the Slope Formula - The slope (m) between two points (x₝, y₝) and (x₂, y₂) is m = (y₂ - y₝) / (x₂ - x₝). Think of slope as your line's attitude - positive, negative, flat, or vertical - and use it to predict how it'll climb or dive through coordinate space. Ch. 3 Key Concepts - Intermediate Algebra 2e | OpenStax
  4. Apply the Distance Formula - To find the distance (d) between two points (x₝, y₝) and (x₂, y₂), use d = √[(x₂ - x₝)² + (y₂ - y₝)²]. This formula is just the Pythagorean Theorem in disguise, helping you measure straight-line distances on any coordinate grid. Ch. 2 Key Concepts - Algebra and Trigonometry 2e | OpenStax
  5. Calculate the Area of a Triangle - The area (A) of a triangle is given by A = ½ × base × height. Whether you're dealing with skinny triangles or super-wide ones, this simple formula unlocks all the "space inside" secrets in a jiffy. Basic Math Formulas | Algebra, Trigonometry, Geometry, Shapes Formulas
  6. Remember the Circumference and Area of a Circle - For a circle with radius r, the circumference (C) is C = 2πr, and the area (A) is A = πr². These round‑tastic formulas equip you for anything from wheel measurements to pizza‑slicing problems! Basic Math Formulas | Algebra, Trigonometry, Geometry, Shapes Formulas
  7. Understand the Law of Sines - In any triangle, a/sin(A) = b/sin(B) = c/sin(C). This rule is your go‑to for finding missing sides or angles when you're off the beaten path of right triangles. The 10 Most Important Mathematical Formulas for High School Students
  8. Apply the Law of Cosines - For any triangle, c² = a² + b² - 2ab × cos(C). It's the Pythagorean Theorem's cooler cousin - perfect for cases when you know two sides and the angle in between. The 10 Most Important Mathematical Formulas for High School Students
  9. Grasp Exponential Growth and Decay - The formula y = a × e^(kt) models how things explode or fizzle out over time, where a is the starting amount, k is the rate, and t is time. Use it to crunch populations, bank interest, or radioactive decay like a pro! The 10 Most Important Mathematical Formulas for High School Students
  10. Learn the Midpoint Formula - The midpoint (M) between two points (x₝, y₝) and (x₂, y₂) is M = ((x₝ + x₂)/2, (y₝ + y₂)/2). It's your quick‑draw tool for finding the exact center between two spots on the grid. Ch. 2 Key Concepts - Algebra and Trigonometry 2e | OpenStax
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