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Quizzes > High School Quizzes > Electives

Topic 8 Practice Quiz Answer Key

Practice for Topic 4 & 8 assessments with confidence

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Ace the Answer Keys, a 10th-grade math quiz.

Easy
What is the value of 5 + 3 * 2?
11
16
8
10
Multiplication is performed before addition. First, 3 multiplied by 2 equals 6, and then adding 5 results in 11.
Solve for x: x + 4 = 9.
5
4
3
6
Subtracting 4 from both sides gives x = 5. This is a basic linear equation.
What is the slope of the line defined by y = 2x + 3?
2
3
-2
-3
The slope-intercept form of a line is y = mx + b, where m is the slope. Here, m = 2.
What is the perimeter of a rectangle with a length of 5 and a width of 3?
16
15
13
18
The perimeter of a rectangle is given by 2*(length + width). Plugging in, we get 2*(5 + 3) = 16.
Reduce the fraction 8/12 to its simplest form.
2/3
4/6
3/4
8/12
Dividing the numerator and denominator by their greatest common divisor, 4, simplifies 8/12 to 2/3. This is the fraction in lowest terms.
Medium
Solve for x: 2(x - 3) + 4 = 10.
6
7
5
8
Distribute 2 over (x - 3) to obtain 2x - 6, then add 4 to get 2x - 2. Setting equal to 10 gives 2x = 12, so x equals 6.
Simplify the expression: 3(2x + 4) - 5x.
x + 12
8x + 12
5x - 12
6x + 4
First, distribute 3 to obtain 6x + 12, then subtract 5x to combine like terms, resulting in x + 12. This is the simplified form.
Solve the proportion: 6/9 = x/12.
8
9
7
10
Setting up a cross multiplication yields 6 × 12 = 9 × x. Solving for x gives x = 72/9, which equals 8.
Simplify the expression: (x^2 - 9) / (x - 3).
x + 3
x - 3
(x + 3) / (x - 3)
x^2 - 3
The numerator is a difference of squares, which factors to (x - 3)(x + 3). Canceling (x - 3) leaves the simplified expression x + 3.
Determine the slope of the line passing through the points (1, 2) and (3, 8).
3
2
4
6
Using the slope formula (y2 - y1) / (x2 - x1), we calculate (8 - 2) / (3 - 1) which simplifies to 6/2 = 3. This is the correct slope.
Solve the quadratic equation: x^2 - 5x + 6 = 0.
x = 2 or x = 3
x = -2 or x = -3
x = 1 or x = 6
x = 3 or x = 4
The quadratic factors as (x - 2)(x - 3) = 0, leading to the solutions x = 2 or x = 3. Factoring is the simplest method to solve this equation.
Find the area of a triangle with a base of 10 and a height of 7.
35
70
17.5
45
The area of a triangle is calculated as 1/2 × base × height. Thus, 1/2 × 10 × 7 equals 35.
Solve the absolute value equation: |2x - 4| = 6.
x = 5 or x = -1
x = 3
x = 5
x = -5 or x = 1
The equation |2x - 4| = 6 leads to two cases: 2x - 4 = 6 and 2x - 4 = -6. Solving these gives x = 5 and x = -1 respectively.
Solve the system of equations: x + y = 10 and x - y = 2.
x = 6, y = 4
x = 5, y = 5
x = 8, y = 2
x = 7, y = 3
Adding the two equations gives 2x = 12, so x = 6. Substituting x into one of the equations results in y = 4.
Simplify the sum: (2/3) + (1/4).
11/12
8/7
7/12
13/12
Converting 2/3 to 8/12 and 1/4 to 3/12, the sum becomes 8/12 + 3/12 = 11/12. This is the simplified result.
Hard
Solve for x: (3x - 2)/4 = (x + 1)/2.
4
2
6
8
Cross multiplying gives 2(3x - 2) = 4(x + 1). Simplifying leads to 6x - 4 = 4x + 4, and solving for x yields x = 4.
Solve for x: √(2x + 9) = 5.
8
7
9
6
Squaring both sides removes the square root, yielding 2x + 9 = 25. Subtracting 9 and solving gives x = 8.
Solve the quadratic equation by completing the square: x^2 + 6x + 5 = 0.
x = -1 or x = -5
x = 1 or x = 5
x = -2 or x = -3
x = 2 or x = 3
Completing the square transforms the equation into (x + 3)^2 = 4, leading to solutions x + 3 = 2 or x + 3 = -2, which yield x = -1 and x = -5. This method isolates the square of a binomial.
Find the composite function f(g(x)) if f(x) = 2x + 3 and g(x) = x^2 - 1.
2x^2 + 1
2x^2 - 1
x^2 + 2
2x^2 + 3
Substituting g(x) into f(x) gives f(g(x)) = 2(x^2 - 1) + 3, which simplifies to 2x^2 - 2 + 3 = 2x^2 + 1. This is the composite function.
Solve for x: 2^(x + 1) = 16.
3
4
5
2
Since 16 can be written as 2^4, equate the exponents: x + 1 = 4. Solving for x gives x = 3.
0
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Study Outcomes

  1. Analyze key math concepts to identify strengths and areas for improvement.
  2. Solve complex problems using systematic reasoning and direct feedback.
  3. Interpret detailed explanations to deepen understanding of mathematical principles.
  4. Apply learned strategies to boost confidence in upcoming tests and exams.

Topic 8 & 4 Assessment Answer Keys Cheat Sheet

  1. Quadratic Formula - Use x = (-b ± √(b² - 4ac))❄(2a) to solve any quadratic hurdle faster than you can say "math magic." It slices through ax² + bx + c = 0 like a hot knife through butter, ensuring you'll never get stuck on finding x. Grab more tricks here: Important Maths Formulae for CBSE Class 10
  2. Laws of Exponents - Powers get a lot simpler when you master rules like am × an = am+n and (am)n = amn. These laws turn dreadfully long expressions into neat, bite‑sized chunks that are way easier to handle. Supercharge your simplification game: Maths Formulas For Class 10
  3. Trigonometric Ratios - In any right triangle, sin θ = opposite❄hypotenuse, cos θ = adjacent❄hypotenuse, and tan θ = opposite❄adjacent. Think of these ratios as your secret decoder ring for all things angle and length in triangles. Unlock triangle mysteries: Maths Formulas For Class 10
  4. Pythagorean Identity - Remember sin² θ + cos² θ = 1 and you'll breeze through trigonometric simplification like a champ. This identity is like the foundation block in any trig tower - you build everything else on it. Solidify your trig foundation: Maths Formulas For Class 10
  5. Distance Formula - To find the gap between (x₝, y₝) and (x₂, y₂), use d = √[(x₂ − x₝)² + (y₂ − y₝)²]. It's your GPS for coordinate geometry, guiding you from point A to B with pinpoint accuracy. Navigate the grid: Important Maths Formulae for CBSE Class 10
  6. Arithmetic Progression (AP) Formulas - The nth term is aₙ = a + (n − 1)d, and the sum of the first n terms is Sₙ = n❄2 [2a + (n − 1)d]. These formulas are like a cheat code for sequences, making pattern‑spotting a total breeze. Decode AP secrets: Maths Formulas For Class 10
  7. Surface Area & Volume Formulas - For 3D shapes, formulas like SA of a sphere = 4πr² and Vol = (4❄3)πr³ are your toolkit. Whether you're wrapping a gift box or filling a balloon, these equations have you covered. Explore 3D magic: Maths Formulas For Class 10
  8. Logarithmic Properties - Rules like log(ab) = log a + log b and log(a❄b) = log a − log b turn complicated logs into manageable pieces. They're the ultimate brain‑saving shortcuts when you're up against gnarly exponential equations. Crack log puzzles: Math Formulas for Grade 10
  9. Binomial Theorem - Expand (a + b)❿ with Σ [C(n, k) · a❿❻ᵝ · bᵝ], where C(n, k) is your trusty binomial coefficient. This theorem is like the Swiss Army knife for polynomial expansions - always handy in exams. Go binomial bonkers: Math Formulas for Grade 10
  10. Law of Sines - In any triangle, sin A❄a = sin B❄b = sin C❄c, making it easy to find missing sides or angles in non-right triangles. It's like having a magic wand for every triangle problem that isn't a perfect right angle. Conquer all triangles: Ch. 10 Key Concepts - Algebra and Trigonometry 2e | OpenStax
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