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Quizzes > High School Quizzes > Social Studies

4.14 Unit Test: New Century Practice Quiz

Ace Part 1 with our unit test practice

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Colorful paper art promoting a trivia quiz for ninth-grade mathematics self-assessment.

Simplify: 2(x + 3).
2x
2x + 3
2x + 6
x + 5
Using the distributive property, multiply 2 by both x and 3 to get 2x + 6. This shows that each term inside the parentheses must be multiplied by 2.
Solve for x: x + 5 = 10.
15
5
0
10
Subtract 5 from both sides to isolate x, resulting in x = 5. This simple linear equation demonstrates basic algebraic manipulation.
Which formula represents the slope-intercept form of a linear equation?
y = ax^2 + bx + c
x = my + b
ax + by = c
y = mx + b
The slope-intercept form of a linear equation is written as y = mx + b, where m represents the slope and b represents the y-intercept. This form is particularly useful for graphing linear equations.
Simplify the fraction 8/12.
8/3
2/3
3/4
4/6
Divide both the numerator and the denominator by their greatest common divisor, which is 4, to simplify 8/12 to 2/3. This results in the fraction in its simplest form.
What is the result of 12 ÷ 4?
3
2
6
4
Dividing 12 by 4 gives a quotient of 3. This is a fundamental arithmetic operation useful in many mathematical contexts.
Solve for x: 2x - 4 = 10.
7
8
6
9
Add 4 to both sides to obtain 2x = 14, then divide both sides by 2 to find x = 7. This problem reinforces the steps of solving a simple linear equation.
Which of these expressions correctly demonstrates the distributive property for a(b + c)?
ab + ac
a + bc
ab + c
a + b + c
The distributive property means multiplying a by each term inside the parentheses: a(b + c) = ab + ac. This is a fundamental property used in algebra.
Factor the expression: x² + 5x + 6.
(x+3)(x-2)
(x+1)(x+6)
(x+2)(x+3)
(x-2)(x-3)
To factor x² + 5x + 6, look for two numbers that multiply to 6 and add up to 5, which are 2 and 3. This leads to the factorization (x+2)(x+3).
Solve for y: (3y)/2 = 9.
5
7
6
4
Multiply both sides of the equation by 2 to get 3y = 18, then divide by 3 to obtain y = 6. This problem requires manipulating an equation with a fractional coefficient.
What is the slope of the line passing through the points (2, 3) and (5, 11)?
2
8/3
9/2
3
The slope is calculated by the formula (y2 - y1) / (x2 - x1), which gives (11 - 3)/(5 - 2) = 8/3. This measures the rate of change between two points.
If a line has the equation y = 2x - 5, what is its y-intercept?
5
-5
2
0
In the slope-intercept form y = mx + b, the term b represents the y-intercept. Here, b is -5, which means the line crosses the y-axis at -5.
What is the area of a triangle with a base of 8 units and a height of 5 units?
18
20
30
40
The area of a triangle is calculated with the formula 1/2 - base - height. Substituting the values, 1/2 - 8 - 5 gives an area of 20 square units.
Simplify the expression: 4(x - 3) + 2x.
4x + 12
4x - 12
6x - 12
6x + 12
First, apply the distributive property to 4(x - 3) to obtain 4x - 12, then add 2x to get 6x - 12. Combining like terms is essential in simplifying algebraic expressions.
What is the probability of drawing a red card from a standard 52-card deck?
1/3
1/2
2/3
1/4
A standard deck has 52 cards, of which 26 are red, so the probability is 26/52, which simplifies to 1/2. This question assesses basic probability knowledge.
Solve the proportion: 2/3 = x/9.
5
3
6
4
Cross-multiply to obtain 2 - 9 = 3x, which simplifies to 18 = 3x. Dividing both sides by 3 gives x = 6.
Solve the equation: 3(x - 2) + 4 = 2(2x + 1).
2
4
-4
-2
First, distribute the multiplication on each side: 3x - 6 + 4 becomes 3x - 2, and 2(2x + 1) becomes 4x + 2. Rearranging the equation leads to x = -4.
Solve for x: (x/4) - (x/6) = 1.
12
14
10
8
Find a common denominator (12) to combine the fractions: (3x - 2x)/12 simplifies to x/12, and then multiply both sides by 12 to get x = 12. This problem tests fraction manipulation.
The sum of two consecutive even integers is 46. What is the smaller integer?
18
24
20
22
Let the smaller even integer be n, so the next consecutive even integer is n + 2. The equation n + (n + 2) = 46 simplifies to 2n + 2 = 46, yielding n = 22.
The area of a rectangle is 48 square units, and its length is 3 times its width. What is the width?
6
3
5
4
Let the width be w and the length be 3w. The area is given by 3w² = 48, so w² = 16 and the width w is 4. This problem applies both algebra and geometric reasoning.
If f(x) = 2x² - 3x + 1, what is f(2)?
2
4
5
3
Substitute x = 2 into the function: f(2) = 2(2²) - 3(2) + 1, which computes to 8 - 6 + 1 = 3. Evaluating the function at a specific input tests understanding of function notation.
0
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Study Outcomes

  1. Analyze a variety of math problems to pinpoint strengths and areas for improvement.
  2. Apply problem-solving strategies to solve grade-level mathematical challenges.
  3. Evaluate understanding of core mathematical concepts from ninth-grade curriculum.
  4. Interpret exam-style questions to develop deeper conceptual insights.
  5. Synthesize feedback from self-assessment to enhance exam readiness.
  6. Reflect on error patterns to guide targeted practice and improvement.

4.14 Unit Test: A New Century Part 1 Cheat Sheet

  1. Pythagorean Theorem - This is your go‑to shortcut for right triangles: the square of the hypotenuse equals the sum of the squares of the other two sides. Picture yourself measuring walls and floors and presto - you'll always get the right length! Math Formulas for Grade 9 - Toppers Bulletin
  2. Distance Formula - Wondering how far apart two points are on a coordinate plane? Plug them into d = √((x₂ - x₝)² + (y₂ - y₝)²) and voilà, you have your distance. It's like using a ruler in math world! Math Formulas for Grade 9 - Toppers Bulletin
  3. Slope Formula - Find the steepness of any line by calculating m = (y₂ - y₝) / (x₂ - x₝). Whether you're climbing a hill or plotting a graph, this formula tells you if your line is rising, falling, or perfectly flat. Math Formulas for Grade 9 - Toppers Bulletin
  4. Quadratic Formula - Never fear a quadratic equation again! Use x = [ - b ± √(b² - 4ac)] / (2a) to solve any equation of the form ax² + bx + c = 0. It's like having a one‑stop solution shop for finding roots. Math Formulas for Grade 9 - Toppers Bulletin
  5. Law of Sines - In any triangle, the ratios of a side length to the sine of its opposite angle are all equal: a/sin A = b/sin B = c/sin C. This is your secret weapon for missing‑angle or missing‑side problems! Math Formulas for Grade 9 - Toppers Bulletin
  6. Law of Cosines - Generalize Pythagoras for any triangle using a² = b² + c² - 2bc·cos A. Perfect for when you know two sides and the included angle, and need that third side in a flash. Math Formulas for Grade 9 - Toppers Bulletin
  7. Exponential Growth & Decay - Model populations, interest, and radioactive decay with A = A₀ekt, where A₀ is your starting amount, k is the rate, and t is time. Watch your numbers skyrocket or dwindle with every t‑unit! Math Formulas for Grade 9 - Toppers Bulletin
  8. Quadratic Equation Practice - Master factoring, completing the square, and the quadratic formula to tackle every quadratic you meet. With regular practice, those puzzles become pure pleasure! Ch. 9 Key Concepts - Intermediate Algebra | OpenStax
  9. Area & Volume Formulas - From ½ × base × height for triangles to πr²h for cylinders, these formulas help you measure flat shapes and 3D solids alike. Keep them handy for everything from art projects to science fair models! Maths Formulas For Class 9 | List of Important Formulas for Grade 9
  10. Probability Basics - Calculate the chance of an event by dividing the number of favorable outcomes by the total outcomes. Whether you're rolling dice or drawing cards, this keeps your odds crystal‑clear! Maths Formulas For Class 9 | List of Important Formulas for Grade 9
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