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Quizzes > High School Quizzes > Mathematics

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Difficulty: Moderate
Grade: Other
Study OutcomesCheat Sheet
Paper art promoting QuizBee Brain Busters, a challenging math trivia for middle school students.

Solve the equation: x + 5 = 12.
5
7
6
8
To solve x + 5 = 12, subtract 5 from both sides to get x = 7. This demonstrates basic algebraic manipulation and reinforces solving simple linear equations.
What is the area of a rectangle with length 8 units and width 3 units?
32
30
24
11
The area of a rectangle is calculated by multiplying its length by its width. Multiplying 8 by 3 gives 24, which is the correct answer.
Convert the fraction 1/2 to a decimal.
0.75
0.25
0.5
2
Dividing 1 by 2 results in 0.5. This conversion illustrates a fundamental skill in understanding fractional and decimal representations.
What is the probability of getting a head when tossing a fair coin?
2
1/2
1
0
A fair coin has two equally likely outcomes, so the probability of landing on heads is 1/2. This basic probability concept is key to understanding random events.
What is the average of the numbers 2, 5, and 11?
7
5
8
6
The average (mean) is found by summing the numbers (2 + 5 + 11 = 18) and dividing by the number of values (3). This gives a result of 6, demonstrating the calculation of a simple average.
What is the sum of the solutions of the quadratic equation x^2 - 5x + 6 = 0?
2
6
3
5
Using Vieta's formulas, the sum of the roots of the quadratic equation ax^2 + bx + c = 0 is -b/a. For this equation, that sum is 5, which is confirmed by factoring the equation into (x - 2)(x - 3).
Simplify the expression: 3(2x - 4) + 4(1 - x).
2x - 8
6x - 8
2x + 8
6x - 16
First, distribute the multiplication to get 6x - 12 + 4 - 4x. Then combine like terms to simplify the expression to 2x - 8. This tests your ability to expand and simplify algebraic expressions.
In a triangle, if two angles measure 45° and 55°, what is the measure of the third angle?
90°
85°
80°
70°
The sum of the interior angles in any triangle is 180°. Subtracting the sum of the given angles (45° + 55° = 100°) from 180° gives 80° for the third angle.
What is the value of 2^3 * 3^2?
64
96
72
54
Evaluate each exponent separately: 2^3 is 8 and 3^2 is 9. Multiplying these results in 8 * 9 = 72, showing the use of exponent rules in multiplication.
A bag contains 3 red, 2 blue, and 5 green marbles. What is the probability of selecting a blue marble?
1/10
2/5
1/2
1/5
There are 2 blue marbles out of a total of 10 marbles. Dividing 2 by 10 gives 1/5, which is the probability of selecting a blue marble.
Solve for x in the equation 3x - 7 = 2x + 5.
11
12
13
10
By subtracting 2x from both sides and then adding 7, the equation simplifies to x = 12. This illustrates the process of isolating the variable in a linear equation.
If the price of a shirt increases from $20 to $25, what is the percent increase?
20%
30%
25%
35%
The increase in price is $5 and the original price is $20, so the percent increase is (5/20)*100 = 25%. This tests your ability to calculate percentage changes.
What is the slope of the line passing through the points (2, 3) and (6, 11)?
8
-2
4
2
The slope is given by the formula (y2 - y1) / (x2 - x1). Substituting the points (2, 3) and (6, 11) gives (11 - 3) / (6 - 2) = 8/4 = 2.
Solve the proportion: 3/4 = x/8.
5
6
4
7
Cross-multiplying the proportion gives 3Ã - 8 = 4Ã - x, leading to 24 = 4x. Dividing both sides by 4, we find x = 6.
What is the value of 5! ?
24
720
120
60
The factorial 5! is the product of all positive integers up to 5: 5Ã - 4Ã - 3Ã - 2Ã - 1, which equals 120. This tests understanding of factorial notation.
Solve the system of equations: x + y = 7 and x - y = 3. What is the ordered pair (x, y)?
(3, 4)
(6, 1)
(5, 2)
(4, 3)
Adding the two equations eliminates y, resulting in 2x = 10, which gives x = 5. Substituting x back into one of the equations determines y = 2, so the solution is (5, 2).
Factor the expression completely: x^3 - 3x^2 - 4x + 12.
(x - 3)(x - 2)^2
(x - 2)^2(x + 3)
(x - 3)(x^2 - 4)
(x - 3)(x - 2)(x + 2)
Grouping the terms yields (x - 3)(x^2 - 4), and recognizing that x^2 - 4 is a difference of squares, it factors into (x - 2)(x + 2). This results in the complete factorization (x - 3)(x - 2)(x + 2).
Determine the value of x that satisfies the equation: logâ‚‚(x) + logâ‚‚(x - 6) = 3.
4
3 - √17
3 + √17
8
By using the property of logarithms that allows the sum of two logs to be written as the log of the product, we combine the terms to get log₂[x(x-6)] = 3. This implies x(x-6) = 8, and after solving the quadratic while considering domain restrictions, the valid solution is x = 3 + √17.
A circle has a radius of 5 units. What is the length of the arc intercepted by a central angle of 60°?
(5Ï€)/6
(10Ï€)/3
(Ï€)/3
(5Ï€)/3
The arc length is calculated using the formula (θ/360) à - 2πr. With a central angle of 60° and a radius of 5, the arc length becomes (60/360) à - 10π = (5π)/3.
How many distinct 3-digit numbers can be formed using the digits 1, 2, 3, 4 without repetition?
20
24
12
18
The number of 3-digit numbers from 4 distinct digits without repetition is calculated using the permutation formula: 4P3 = 4 Ã - 3 Ã - 2 = 24. This applies combinatorial reasoning to count arrangements.
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Study Outcomes

  1. Analyze complex problems using mathematical reasoning.
  2. Apply problem-solving strategies to tackle brain-teasing challenges.
  3. Identify and address knowledge gaps in key mathematical concepts.
  4. Evaluate and improve exam readiness through practice and self-assessment.

QuizBee Practice Test Cheat Sheet

  1. Master the Pythagorean Theorem - In any right triangle, the squares of the two legs add up to the square of the hypotenuse, so \(a^2 + b^2 = c^2\). Practicing with different side lengths will make this formula second nature and help you solve all sorts of geometry and physics problems. Embrace this theorem as your secret weapon for finding missing sides quickly. OpenStax: Intermediate Algebra Key Concepts
  2. Understand the properties of triangles - The three interior angles of any triangle always sum to 180°, making it easy to find unknown angles once you know the other two. This rule also helps you recognize special triangles and solve angle-chasing puzzles. Keep this fact in your back pocket whenever angles appear in a geometry problem. OpenStax Prealgebra: Triangle Properties
  3. Learn the area formula for triangles - The area of a triangle is half the product of its base and height: \(\tfrac \times \text \times \text\). Visualizing a triangle as half a rectangle can make this formula feel more intuitive. Use this whenever you need to calculate land plots, architectural designs, or any triangular shape in real life. OpenStax Prealgebra: Triangle Area
  4. Familiarize yourself with rectangle properties - Opposite sides of a rectangle are equal in length, and all four angles are right angles (90°), making calculations straightforward. Knowing these traits helps you spot rectangles and apply the right formulas without a second thought. This knowledge also lays the groundwork for understanding parallelograms and other quadrilaterals. OpenStax Prealgebra: Rectangle Properties
  5. Calculate the area of a rectangle - Simply multiply length by width: \(\text = \text \times \text\). This direct formula is one of the easiest area calculations you'll encounter. Use it to solve everything from floor plans to screen resolutions in a flash. OpenStax Prealgebra: Rectangle Area
  6. Understand circle properties - A circle's circumference is \(2\pi r\) and its area is \(\pi r^2\), where \(r\) is the radius. These formulas let you measure everything from round ponds to pizza sizes. Memorize them and picture cutting a circle into tiny pie slices to see why the area formula makes sense. OpenStax Prealgebra: Circle Formulas
  7. Learn the distance formula - To find the straight-line distance between \((x_1,y_1)\) and \((x_2,y_2)\), use \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). It's like applying the Pythagorean Theorem on the coordinate plane, perfect for mapping and physics problems. Keep this at hand for any time you need to measure gaps between points. EffortlessMath: Distance Formula
  8. Understand the slope formula - The slope between two points is \(\frac{y_2 - y_1}{x_2 - x_1}\), showing you how steep a line is. Positive slopes rise to the right, negative slopes fall, and zero slope means a flat line. Use this to analyze trends in data or sketch precise graphs. EffortlessMath: Slope Formula
  9. Learn the midpoint formula - The midpoint between \((x_1,y_1)\) and \((x_2,y_2)\) is \(\bigl(\tfrac{x_1 + x_2},\,\tfrac{y_1 + y_2}\bigr)\), giving you the exact center point. It's like finding the halfway spot on a line segment - super handy in coordinate geometry. Perfect for splitting distances or placing labels on graphs. EffortlessMath: Midpoint Formula
  10. Understand parallel vs. perpendicular lines - Parallel lines have equal slopes, while perpendicular lines have slopes that are negative reciprocals of each other. This key idea helps you prove angles are right angles and solve intersection problems. Armed with this, you'll ace coordinate proofs and geometry challenges. EffortlessMath: Parallel & Perpendicular Lines
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