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Quizzes > High School Quizzes > Mathematics

After Twenty Years Practice Quiz

Explore comprehensive practice questions and answers

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Paper art promoting the 20 Years QA Challenge, a math trivia quiz for high school students.

Solve for x: 2x - 4 = 0.
x = 0
x = 2
x = -2
x = 4
To solve the equation, add 4 to both sides resulting in 2x = 4, then divide by 2 to get x = 2. This method ensures that x = 2 is the only solution.
What is the area of a rectangle with length 8 and width 5?
80
30
40
13
Multiply the length by the width to calculate the area: 8 x 5 equals 40. This straightforward calculation confirms the correct area of the rectangle.
Which of the following is an example of a linear equation?
y = 3/x + 4
y = √x + 1
y = 2x + 5
y = x^2 + 3
A linear equation is typically written in the form y = mx + b without any exponents on the variable x. The equation y = 2x + 5 fits this pattern, making it a linear equation.
Evaluate: 3².
9
8
3
6
3 squared means multiplying 3 by itself, which results in 9. This basic exponentiation is fundamental in mathematics.
What is the value of 0 factorial (0!)?
0
-1
1
2
By definition, 0! is equal to 1, which is a convention used in combinatorics to simplify formulas. This definition is essential for many counting problems.
What are the solutions of the quadratic equation x² - 5x + 6 = 0?
x = -2 and x = -3
x = 1 and x = 6
x = 2 and x = 3
x = -1 and x = -6
Factor the quadratic equation as (x - 2)(x - 3) = 0 to determine the roots. This method clearly shows that x = 2 and x = 3 are the solutions.
Simplify: 2(3x - 4) + 5x.
7x - 4
5x - 8
6x - 4
11x - 8
Distribute 2 to obtain 6x - 8 and then add the like term 5x to get 11x - 8. This simplification uses basic algebraic combining of like terms.
Find the slope of the line passing through the points (1, 3) and (4, 15).
5
4
6
3
The slope formula is (y₂ - y₝)/(x₂ - x₝). Calculating (15 - 3) divided by (4 - 1) gives 12/3, which simplifies to 4.
If f(x) = 2x + 3, what is f(4)?
12
8
7
11
Substitute x = 4 into the function f(x) = 2x + 3 to obtain 2(4) + 3, which equals 11. This process is a standard function evaluation.
Solve for x: (x/3) + 2 = 5.
15
3
6
9
Subtract 2 from both sides of the equation to get x/3 = 3, then multiply by 3 to find x = 9. This solution involves simple algebraic manipulation.
What is the value of the expression 4³ ÷ 2²?
32
20
16
8
Calculate 4³ to get 64 and 2² to get 4, then divide 64 by 4 which equals 16. This problem tests understanding of exponentiation and basic division.
Factor the expression: x² - 9.
(x - 9)(x + 1)
(x + 3)²
(x - 3)(x + 3)
(x - 3)²
Recognize that x² - 9 is a difference of squares, which factors into (x - 3)(x + 3). This technique is a standard method for factoring such expressions.
What is the median of the set {3, 7, 9, 15, 21}?
15
7
9
21
When the set is arranged in ascending order, the median is the middle number. In this case, 9 is the third value, making it the median.
If the probability of an event occurring is 1/4, what is the probability of it not occurring?
1/2
2/3
1/4
3/4
The probability of an event not occurring is the complement of the event, calculated as 1 minus the event's probability. Therefore, 1 - 1/4 equals 3/4.
Solve the inequality: 2x - 5 < 9.
x < 9
x < 14
x < 2
x < 7
Add 5 to both sides to get 2x < 14, then divide by 2 to obtain x < 7. This shows that all values of x less than 7 satisfy the inequality.
Find the solution of the system of equations: 2x + 3y = 12 and x - y = 1.
x = 2, y = 3
x = 1, y = 2
x = 3, y = 3
x = 3, y = 2
Solve the second equation for x to get x = y + 1 and substitute into the first equation. This substitution yields y = 2 and subsequently x = 3, which is the unique solution.
Solve for x: (x² - 16)/(x - 4) = 2x + 4.
x = 8
x = 4
x = -4
x = 0
Factor the numerator as (x - 4)(x + 4) and cancel the (x - 4) term (noting x ≠ 4) to obtain x + 4 = 2x + 4. Solving this equation leads to x = 0.
If f(x) = √(x + 3) and g(x) = x², what is f(g(1))?
4
2
3
1
First, compute g(1) which is 1² = 1. Then substitute this value into f(x) to get √(1 + 3) = √4, which equals 2.
A circle has an area of 50π. What is its radius?
5√2
5
25
10
The area of a circle is given by A = πr². Setting πr² = 50π and dividing both sides by π gives r² = 50, so r = √50 which simplifies to 5√2.
The function f(x) = x² - 4x + k has a repeated root. Find the value of k.
0
2
4
-4
A quadratic has a repeated root when its discriminant is zero. For the equation x² - 4x + k, the discriminant is 16 - 4k; setting this equal to zero yields k = 4.
0
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Study Outcomes

  1. Analyze exam-style questions to identify underlying mathematical concepts.
  2. Apply learned techniques to solve problems similar to past exam questions.
  3. Evaluate multiple problem-solving approaches to determine the most effective method.
  4. Identify key mathematical pitfalls and common errors in exam situations.
  5. Enhance test performance by practicing under simulated exam conditions.

After Twenty Years Q&A PDF Cheat Sheet

  1. Master the Pythagorean Theorem - This fundamental principle shows how the squares of the legs add up to the square of the hypotenuse, perfect for right triangles. It's like puzzle pieces fitting together - if you know two sides, you can always find the third. Try plugging 3 and 4, you get 5, a classic 3 - 4 - 5 triangle. visitmath.eu
  2. Understand the Quadratic Formula - The Quadratic Formula is your one-stop shop for finding x in ax² + bx + c = 0. It even hints at root nature: if the discriminant (b² − 4ac) is negative, you dive into imaginary territory. Memorize the song "minus b, plus or minus sqrt, over two a," and you're golden. library.fiveable.me
  3. Get comfortable with the Distance Formula - Think of this as the 2D ruler: √((x₂ − x₝)² + (y₂ − y₝)²) gives you the straight-line distance between two dots on a grid. It's just the Pythagorean Theorem wearing coordinate clothes. Use it to track how far you've "walked" in a coordinate plane adventure! library.fiveable.me
  4. Learn the Slope Formula - Slope m = (y₂ − y₝)/(x₂ − x₝) tells you if your line is hiking uphill, gliding downhill, or chilling flat. It's like speed: rise over run. A positive m means uphill, negative m means a downhill dash, and zero m means a lazy stroll. library.fiveable.me
  5. Familiarize yourself with the Midpoint Formula - Midpoint M = ((x₝ + x₂)/2, (y₝ + y₂)/2) is your digital compass finding the exact halfway point. Perfect for bisecting segments or centering your graphics. Think of it as the checkpoint right in the middle! library.fiveable.me
  6. Remember the Area of a Circle - A = πr² reveals the space inside a circle fortress, where r is the distance from center to wall. Double the radius, quadruple the area - circles pack major punch! Great for pizza slices, garden beds, and any round masterpiece. visitmath.eu
  7. Know the Slope-Intercept Form - y = mx + b is your graphing sidekick: m gives the tilt, b gives the y-crossing. Slide b up or down to shift the line, change m to tweak the angle. It's like controlling the steering wheel and accelerator of your graph! library.fiveable.me
  8. Understand Exponential Growth and Decay - y = y₀e^(kt) models viral videos and radioactive atoms alike. Positive k means your curve skyrockets; negative k means it fades out Halloween-flashlight style. Welcome to the world where numbers can go boom or bust! library.fiveable.me
  9. Learn the Law of Sines - a/sin(A) = b/sin(B) = c/sin(C) lets you solve triangles that aren't 90°-bound when you know some angles and sides. It's like tuning three dials in sync. Perfect for navigation puzzles and triangulating your pizza delivery spot! visitmath.eu
  10. Master the Law of Cosines - c² = a² + b² − 2ab cos(C) generalizes Pythagoras to any triangle angle. Use it when you know two sides and the included angle, and voilà, you get the third side. It's the detective of triangle world! visitmath.eu
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