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Quizzes > High School Quizzes > Mathematics

Pre Algebra Practice Quiz

Boost Your Skills with Pre-Calc Practice

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Colorful paper art promoting a Pre-Algebra and Pre-Calc Power quiz for middle and high school students.

What is the value of 3 + 5 * 2?
13
16
10
18
According to the order of operations, you first multiply 5 by 2 to get 10, then add 3, which results in 13.
Solve for x: x - 4 = 6.
10
2
6
4
By adding 4 to both sides of the equation, you determine that x equals 10.
What is the simplified form of 2/4?
1/2
2/3
3/4
1/4
Dividing both the numerator and the denominator by their greatest common factor, 2, simplifies 2/4 to 1/2.
Which of the following represents the distributive property correctly?
a(b + c) = ab + ac
a(b + c) = ab + c
a(b + c) = a + bc
a(b + c) = a + b + c
The correct application of the distributive property is shown by a(b + c) = ab + ac, which multiplies the term a with each term inside the parentheses.
What is 15% of 200?
30
20
25
35
Calculating 15% of 200 involves multiplying 200 by 0.15, which results in 30.
Solve for x: 2x + 3 = 11.
4
5
3
8
Subtract 3 from both sides to get 2x = 8, then divide by 2 to find that x equals 4.
Simplify: 3/4 ÷ 1/8.
6
2
3
12
Dividing by a fraction means multiplying by its reciprocal. Thus, 3/4 multiplied by 8/1 equals 6.
If f(x) = 2x + 1, what is f(3)?
7
6
8
9
Substitute 3 for x in the function f(x) = 2x + 1 to obtain 2(3) + 1, which equals 7.
What is the slope of the line represented by y = 5x - 3?
5
-3
0
5x
In the slope-intercept form y = mx + b, the coefficient m represents the slope of the line. Here, m is 5.
Factor the expression: x^2 - 9.
(x - 3)(x + 3)
(x - 9)(x + 1)
x(x - 9)
(x - 3)^2
x^2 - 9 is a difference of squares and factors into (x - 3)(x + 3), which are the binomials representing its factors.
Solve for y: 2y + 4 = 0.
-2
2
-4
0
Subtract 4 from both sides to obtain 2y = -4, then divide both sides by 2 to find y = -2.
Simplify the expression: 4(2x - 3) + 6.
8x - 6
8x + 6
8x - 12
4x - 3
First distribute 4 to get 8x - 12, then add 6 to the constant term, resulting in 8x - 6.
Evaluate: 3^2 * 3^3.
243
81
54
729
When multiplying powers with the same base, add the exponents. Here, 3^2 * 3^3 equals 3^(2+3) or 3^5, which is 243.
Which equation represents a proportional relationship?
y = 4x
y = 4x + 5
y = x^2
y = 4(x + 2)
A proportional relationship is defined by a constant ratio and passes through the origin. The equation y = 4x meets these criteria.
Solve for x: 3x/4 = 6.
8
6
7
9
Multiply both sides by 4 to obtain 3x = 24, then divide by 3 to find that x equals 8.
What are the solutions of the equation x^2 - 5x + 6 = 0?
x = 2 and x = 3
x = -2 and x = -3
x = 1 and x = 6
x = -1 and x = -6
Factoring the quadratic gives (x - 2)(x - 3) = 0, which leads to the solutions x = 2 and x = 3.
Find the vertex of the quadratic function: f(x) = x^2 - 4x + 1.
(2, -3)
(-2, -3)
(2, 3)
(-2, 3)
The vertex of a quadratic function is found using the formula x = -b/(2a). Here, x = 2 and substituting back gives y = -3, so the vertex is (2, -3).
If f(x) = x^2 and g(x) = 2x + 3, what is (f o g)(x)?
(2x + 3)^2
2x^2 + 3
2x^2 + 6x + 3
x^2 + 2x + 3
Function composition (f o g)(x) means substituting g(x) into f, which results in (2x + 3)^2.
Solve the inequality: 2x - 5 > 3.
x > 4
x < 4
x ≥ 4
x ≤ 4
Add 5 to both sides to obtain 2x > 8, then divide by 2 to find that x must be greater than 4.
Simplify the expression: √50 + √8.
7√2
5√2
√58
√58 + √2
Simplify each radical by factoring: √50 becomes 5√2 and √8 becomes 2√2; adding these gives 7√2.
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0
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Study Outcomes

  1. Analyze algebraic expressions to identify key components and simplify them.
  2. Apply techniques to solve linear equations and inequalities confidently.
  3. Evaluate functions and interpret their properties accurately.
  4. Graph linear functions and determine critical features such as slope and intercepts.
  5. Simplify polynomial expressions and perform factorization effectively.
  6. Translate real-world problems into algebraic statements for problem-solving.

Pre-Algebra & Pre-Calc Cheat Sheet

  1. Order of Operations - Think of PEMDAS as your trusty math recipe: you always tackle Parentheses first, then Exponents, roll through Multiplication and Division left to right, and finish with Addition and Subtraction left to right. This sequence keeps your calculations neat and prevents number chaos from breaking out. OpenStax Prealgebra Key Concepts
  2. Laws of Exponents - Exponents can be your best friends once you know the rules: the Product Rule adds exponents when you multiply like bases, the Quotient Rule subtracts them when dividing, and the Power Rule multiplies exponents when you raise a power to another power. Mastering these shortcuts lets you simplify complex expressions in a snap and level up your algebra toolkit. Effortless Math Pre‑Algebra Formulas
  3. Quadratic Formula - The quadratic formula x = (-b ± √(b² - 4ac)) / (2a) is like a secret codebreaker for any ax² + bx + c = 0 equation. Plug in your a, b, and c, and voilà - you get the two possible x solutions faster than you can say "quadratic." It works every time, even for those trickiest curves. QuizGecko Key Precalculus Formulas
  4. Distance Formula - When you need to find the straight-line distance between two points (x₝, y₝) and (x₂, y₂), the formula d = √[(x₂ - x₝)² + (y₂ - y₝)²] has your back. It's basically the Pythagorean Theorem in disguise, measuring the hypotenuse of a right triangle on your coordinate grid. Crunch those squares and roots to figure out how far apart two points really are. QuizGecko Distance Formula Guide
  5. Midpoint Formula - Want the exact halfway point between (x₝, y₝) and (x₂, y₂)? Just average the x's and the y's: ((x₝ + x₂)/2, (y₝ + y₂)/2). In one formula, you get the perfect meetup spot between two coordinate pals. Use it to bisect line segments or find centers of shapes! QuizGecko Midpoint Formula Tips
  6. Slope‑Intercept Form - The classic y = mx + b makes graphing lines a breeze: m is your slope (steepness) and b is the y‑intercept (where the line touches the y‑axis). Just plug in m and b, draw your line, and watch linear equations unfold visually. It's the easiest way to turn algebraic data into a picture. CourseSideKick Linear Equations
  7. Point‑Slope Form - When you know a point (x₝, y₝) on the line and the slope m, point‑slope form y - y₝ = m(x - x₝) steps in like a precision tool. It's perfect for building an equation around specific info without hunting for the intercept. Great for modeling lines through known points or applying transformations. QuizGecko Point‑Slope Insights
  8. Absolute Value - Absolute value |x| measures the distance of x from zero on the number line, ignoring direction. So whether you have | - 5| or |5|, both equal 5, because distance never goes negative. It's super handy for solving equations and inequalities that involve magnitudes. Effortless Math Absolute Value Basics
  9. Functions - A function is like a vending machine: you insert an input, and it dispenses exactly one output every time. The domain is the set of all valid inputs, and the range is every snack (output) you can get. Understanding functions powers up your ability to map real‑world relations in algebra and beyond! CourseSideKick Function Fundamentals
  10. Law of Sines - In oblique triangles (no right angles here!), the Law of Sines sin A/a = sin B/b = sin C/c helps you solve for unknown sides or angles with ease. Match up your sines with their opposite sides, cross‑multiply, and solve - it's geometry made friendly. Ideal for surveying, navigation, and any adventurous triangle quests. OpenStax Precalculus Key Concepts
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