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Quizzes > High School Quizzes > Mathematics

Mathematical Representations Practice Quiz

Test your skills with quick check problems

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Math Reps Quick Check, a fast-paced trivia quiz for students.

Which expression correctly represents the sum of a number and five?
5n
n + 5
n - 5
5 - n
The expression 'n + 5' adds five to the variable n, correctly representing the sum of a number and five. The other options do not represent this operation accurately.
Solve the equation: x + 4 = 9.
9
4
13
5
By subtracting 4 from both sides, we find x = 5. This is the unique solution to the equation.
Which expression correctly expands 3(x + 2)?
3x - 2
3x + 5
3x + 2
3x + 6
Multiplying 3 by each term inside the parentheses results in 3x + 6. This shows the correct use of the distributive property.
Which of the following equations shows that y is directly proportional to x?
y = x + 5
y = 5 - x
y = 5/x
y = 5x
Direct proportionality is expressed by y = kx, where k is a constant. Here, k is 5, making y = 5x the correct representation.
Which ordered pair represents a point 3 units to the right and 2 units upward from the origin?
(2, 3)
(3, -2)
(3, 2)
(-3, 2)
The ordered pair (3, 2) indicates a movement of 3 units on the x-axis and 2 units on the y-axis from the origin. The other options either swap the coordinates or include negative values, which do not match the description.
Which expression correctly represents the area of a triangle with base b and height h?
2(b + h)
(b * h) / 2
b * h
b + h
The area of a triangle is calculated as one-half the product of its base and height. The expression (b * h) / 2 reflects this formula accurately.
Which linear equation represents a line passing through the point (0, 3) with a slope of 2?
y = 3x + 2
y = x + 3
y = 2x - 3
y = 2x + 3
A line with a slope of 2 and a y-intercept of 3 is expressed as y = 2x + 3. This satisfies the condition of passing through (0, 3).
Rewrite the equation 4x - 2y - 6 = 0 in slope-intercept form (y = mx + b).
y = -2x - 3
y = 2x + 3
y = 2x - 3
y = -2x + 3
Isolating y in the equation gives -2y = -4x + 6 and dividing by -2 results in y = 2x - 3. This is the correct slope-intercept form.
If f(x) = 3x - 2, what is the value of f(4)?
8
14
10
12
Substituting x = 4 into the function f(x) gives f(4) = 3(4) - 2, which simplifies to 10. This is the correct output for the function at x = 4.
Simplify the expression: 2(3x + 4) - 5.
6x - 9
6x + 3
6x - 3
6x + 9
Distribute the 2 to obtain 6x + 8, and then subtract 5 to get 6x + 3. This is the simplest form of the given expression.
Which expression represents the perimeter of a rectangle with length l and width w?
l + w
l * w
2l + w
2(l + w)
The perimeter of a rectangle is calculated by summing twice the length and twice the width, which can be written as 2(l + w). This formula accurately reflects the total distance around the rectangle.
What is the slope of a line perpendicular to a line with a slope of 4?
1/4
-4
-1/4
4
Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of the line perpendicular to one with slope 4 is -1/4.
Given the function f(x) = x^2, what is the value of f(3)?
6
3
9
12
Substituting x = 3 into the function f(x) = x^2 yields 3^2 = 9. This is the correct value of f(3).
How can you express the statement 'y is directly proportional to x^2' in equation form?
y = kx^2
y = x^2
y = k + x^2
y = k/x^2
Direct proportionality between y and x^2 means that y equals a constant k multiplied by x^2. The correct representation is y = kx^2, where k is the constant of proportionality.
Solve for x in the equation: 2x - 7 = 3.
10
5
-5
4
Adding 7 to both sides of the equation gives 2x = 10, and dividing by 2 yields x = 5. This is the unique solution to the equation.
Solve the system of equations: 2x + y = 7 and x - y = 1.
(8/3, 5/3)
(3, 1)
(1, 2)
(2, 3)
Substitute y from the second equation (y = x - 1) into the first equation to solve for x, yielding x = 8/3. Then, substituting back gives y = 5/3. This ordered pair is the solution to the system.
Find the solutions for x in the quadratic equation x^2 - 5x + 6 = 0.
x = 2 and x = 3
x = 1 and x = 6
x = 3 only
x = -2 and x = -3
The quadratic factors as (x - 2)(x - 3) = 0, which gives the solutions x = 2 and x = 3. Both values satisfy the original equation.
For the function f(x) = 1/(x - 2), for which value of x is the function undefined?
x = 1
x = -2
x = 0
x = 2
The function is undefined when its denominator equals zero. Since x - 2 = 0 when x = 2, the function cannot be evaluated at that point.
What is the slope of the line that passes through the points (2, -3) and (-4, 3)?
-2
-1
2
1
Using the slope formula, the slope is calculated as (3 - (-3))/(-4 - 2) = 6/(-6) = -1. This indicates that the line falls one unit vertically for every unit it moves horizontally.
If g(x) = (x^2 - 4)/(x - 2), simplify g(x) and then find the value of g(5).
3
9
5
7
The numerator factors as (x - 2)(x + 2), which cancels with the denominator for x ≠ 2, simplifying g(x) to x + 2. Substituting x = 5 yields 5 + 2 = 7.
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Study Outcomes

  1. Understand key mathematical representations and their applications in solving problems.
  2. Apply graphical methods to interpret and analyze data effectively.
  3. Analyze numerical patterns to derive relationships and make predictions.
  4. Synthesize algebraic techniques to solve real-world problems.
  5. Evaluate problem-solving strategies to boost confidence before tests and exams.

Math Representations Quick Check Cheat Sheet

  1. Master the laws of exponents - Ready to make exponent rules your best friend? When you multiply like bases, just add the exponents to simplify expressions like am × an. These shortcuts will save you tons of time on quizzes and real‑world problems. thecorestandards.org
  2. Understand the Pythagorean Theorem - In any right triangle, the squares of the legs add up to the square of the hypotenuse: a2 + b2 = c2. This formula helps you find missing side lengths, design ramps, or even check plotting grids in video games. It's a geometry classic you'll revisit again and again. mathsisfun.com
  3. Solve linear equations in one variable - Equations like 2x + 3 = 7 are puzzles you can crack by isolating x on one side. Subtract, divide, and check your work to ensure you haven't slipped up. Mastering this makes algebra a lot less scary (and a lot more fun!). thecorestandards.org
  4. Learn volume formulas for cones, cylinders & spheres - Whether it's calculating how much paint fits in a bucket or the capacity of a silo, knowing V = (1/3)πr²h, V = πr²h, and V = (4/3)πr³ is key. Visualising these 3D shapes turns abstract numbers into real‑life solutions. Soon you'll be the go‑to geometry guru in your study group! mathsisfun.com
  5. Practice square and cube roots - Inverse operations are your secret weapon: x² = 16 gives x = ±4, and x³ = 27 gives x = 3. Root rules help reverse exponent problems and unlock deeper algebra topics. With steady practice, taking roots will feel as natural as breathing. thecorestandards.org
  6. Explore rational numbers - Fractions, decimals, and ratios all fall under rational numbers, and they love neat, repeating patterns. Plot them on a number line, add, subtract, multiply, and divide to see how they interact. Master these and you'll ace finance topics, measurement conversions, and more. geeksforgeeks.org
  7. Discover irrational numbers - Numbers like π and √2 never repeat or terminate as decimals, which makes them fascinating outliers on the number line. Understanding their unique properties will give you insights into circles, trigonometry, and the mysterious side of math. Embrace the irrational - there's beauty in unpredictability! geeksforgeeks.org
  8. Study angles with parallel lines & a transversal - When a line crosses two parallel lines, you get corresponding, alternate interior, and alternate exterior angles. Spotting these angle pairs will help you solve geometry proofs in no time. It's like solving a visual puzzle every time you see a set of parallel lines! mathsisfun.com
  9. Explore functions and their graphs - Think of a function as a machine: you feed in x, and out pops f(x). Plotting linear functions shows straight‑line relationships - vital for economics, physics, and everyday data analysis. Graphing helps you "see" the math story behind the numbers. mathsisfun.com
  10. Solve systems of linear equations - Two equations, two variables, one intersection point - that's your solution! Use substitution or elimination to decode these algebraic duos. Mastering this lets you tackle real‑life scenarios like budgeting and rate problems with confidence. thecorestandards.org
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