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Quizzes > High School Quizzes > Mathematics

9th Grade Final Exam Practice Quiz

Ace Algebra and 9th Grade Math Review

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art representing a fun trivia quiz for 9th grade Math Challenge to assess key concepts.

Solve for x: 3x + 5 = 20.
x = 5
x = 3
x = 4
x = 15
To solve 3x + 5 = 20, first subtract 5 from both sides to obtain 3x = 15, and then divide by 3 to get x = 5. This problem reinforces the basic steps of linear equation solving.
Simplify the fraction 8/12.
2/3
4/5
3/4
1/2
Dividing both numerator and denominator by their greatest common divisor, 4, simplifies 8/12 to 2/3. This question tests basic fraction simplification skills.
What is 25% of 80?
20
25
30
15
To find 25% of 80, convert 25% to a decimal (0.25) and multiply by 80 to get 20. This problem reinforces the concept of percentages.
Calculate: 2(3 + 4).
14
10
12
18
First, add the numbers inside the parentheses (3 + 4 = 7) and then multiply by 2 to obtain 14. This exercise emphasizes the order of operations in arithmetic.
Find the area of a rectangle with a length of 7 and a width of 4.
28
11
32
14
The area of a rectangle is calculated by multiplying its length by its width. Thus, 7 multiplied by 4 gives 28, which is the correct area.
Solve the equation: 2x - 7 = 3x + 5.
x = -12
x = 12
x = -6
x = 6
Rearranging the equation by subtracting 2x from both sides results in -7 = x + 5, and subtracting 5 gives x = -12. This question tests basic skills in isolating variables.
Evaluate the expression: 4^2 - 2*5.
6
14
10
8
Calculate 4^2 to get 16, then compute 2*5 to get 10, and subtract 10 from 16 to obtain 6. This problem checks the proper application of the order of operations.
Simplify the expression: 2(x - 3) + 4x.
6x - 6
6x + 6
2x - 3
4x - 6
Distribute 2 across the terms in the parentheses to get 2x - 6 and then add 4x to combine like terms, resulting in 6x - 6. This exercise emphasizes the distributive property and combining like terms.
What is the slope of the line passing through the points (2, 3) and (5, 15)?
4
3
12
6
The slope is calculated by dividing the change in y by the change in x, so (15 - 3) divided by (5 - 2) gives 12/3, which simplifies to 4. This is a straightforward application of the slope formula.
Solve for y in the equation: 3y + 2 = 17.
5
3
7
15
Subtracting 2 from both sides yields 3y = 15, and then dividing by 3 results in y = 5. The solution demonstrates a basic method for solving linear equations.
Factor the quadratic expression: x^2 + 5x + 6.
(x + 2)(x + 3)
(x - 2)(x - 3)
(x + 1)(x + 6)
(x + 2)(x + 6)
The quadratic factors by finding two numbers that multiply to 6 and add up to 5, which are 2 and 3. Thus, the expression factors as (x + 2)(x + 3), reinforcing basic factorization skills.
Solve the proportion: 1/3 = x/9.
3
9
1
6
Using cross multiplication, 1 multiplied by 9 equals 3x, so x equals 3 after dividing both sides by 3. This reinforces understanding of proportional relationships.
In a triangle with angles of 60° and 70°, what is the measure of the third angle?
50°
60°
70°
80°
The sum of the angles in any triangle is 180°. Subtracting the sum of the two given angles (60° + 70°) from 180° gives 50° as the measure of the third angle.
Evaluate the expression: √49 + √16.
11
13
7
8
Taking the square roots, √49 equals 7 and √16 equals 4. Adding these results gives 7 + 4 = 11, which is the correct evaluation.
Solve the equation: 5(x - 1) = 20.
5
4
6
1
Dividing both sides by 5 simplifies the equation to x - 1 = 4, and adding 1 to both sides yields x = 5. This problem emphasizes the sequential steps needed to solve linear equations.
Solve the system of equations: 2x + y = 7 and x - y = 1.
x = 8/3, y = 5/3
x = 3, y = 1
x = 2, y = 3
x = 1, y = 6
Express y from the second equation as y = x - 1 and substitute into the first equation to obtain 2x + (x - 1) = 7. Solving this yields x = 8/3 and, consequently, y = 5/3. This problem combines substitution and simplification methods in solving systems of equations.
Find the vertex of the parabola defined by y = x^2 - 6x + 5.
(3, -4)
(3, 4)
(-3, -4)
(-3, 4)
The vertex of a parabola given by y = ax^2 + bx + c is found using the formula x = -b/(2a). Here, x calculates to 3 and substituting back gives y = -4, so the vertex is (3, -4). This requires applying the vertex formula correctly.
Simplify the radical expression: √50 + 2√8.
9√2
7√2
5√2
11√2
Express √50 as 5√2 and √8 as 2√2; multiplying the latter by 2 gives 4√2. Adding 5√2 and 4√2 results in 9√2. This question tests the ability to simplify and combine radical expressions.
If f(x) = 2x + 3 and g(x) = x^2, find f(g(2)).
11
14
7
9
First, evaluate g(2) by squaring 2 to get 4. Then substitute 4 into f(x) to compute 2(4) + 3, which equals 11. This demonstrates function composition clearly.
Determine the value of x that satisfies the proportion: (x - 2)/4 = (3x + 1)/10.
x = -12
x = 12
x = -8
x = 8
Cross-multiply to obtain 10(x - 2) = 4(3x + 1), which simplifies to 10x - 20 = 12x + 4. Rearranging the terms leads to 2x = -24, hence x = -12. This problem reinforces cross-multiplication and isolation of variables in a proportion.
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Study Outcomes

  1. Apply algebraic techniques to solve equations and inequalities.
  2. Analyze geometric relationships and properties in practical problems.
  3. Interpret graphical representations of functions and data.
  4. Synthesize problem-solving strategies to tackle multi-step mathematical challenges.
  5. Evaluate real-world scenarios using appropriate mathematical models.

9th Grade Math Test & Final Exam Review Cheat Sheet

  1. Master the Pythagorean Theorem - Dive into right triangles and see how the squares of the legs add up to the square of the hypotenuse. This golden rule is your secret weapon for finding missing side lengths and proving right angles in all sorts of shapes. Practice with real examples to build confidence and speed. Toppers Bulletin
  2. Understand the Distance Formula - Think of this as measuring a straight line between two points on a grid - it's just the Pythagorean Theorem in disguise! Use it to calculate exactly how far apart any two coordinates are, whether you're mapping points or tackling geometry puzzles. Give it a whirl on different point pairs to see it in action. Toppers Bulletin
  3. Learn the Slope Formula - The slope tells you how steep a line is - rise over run! By subtracting the y‑coordinates and dividing by the difference in x‑coordinates, you instantly know if your line climbs, falls, or stays flat. Graph some lines and watch how the slope number matches what you see on screen. Toppers Bulletin
  4. Apply the Quadratic Formula - When you see ax² + bx + c = 0, whip out x = ( - b ± √(b² - 4ac)) / (2a) to find your roots in a flash. This formula works like a charm for any quadratic, no factoring required! Tackle a few sample equations to master the plus‑minus magic. Toppers Bulletin
  5. Grasp the Law of Sines - For any triangle, the ratio of a side's length to the sine of its opposite angle is always the same. This powerful trick helps you solve triangles that aren't right‑angled by linking angles and sides effortlessly. Play with different triangles to see how it uncovers missing measurements. Toppers Bulletin
  6. Comprehend the Law of Cosines - Extend the Pythagorean Theorem to all triangles with a² = b² + c² - 2bc·cos A. It's perfect when you know two sides and the included angle, or when you need a third side. Mix and match your known values and watch this formula fill in the gaps. Toppers Bulletin
  7. Explore Exponential Growth and Decay - Model everything from bacteria populations to radioactive decay with A = A₀eᵝᵗ. Here, A₀ is your starting amount, k controls the growth or shrink rate, and t is time. Experiment with different k values to see charts shoot up or drop off dramatically. Toppers Bulletin
  8. Practice Solving Linear Equations - Get comfy rearranging ax + b = c by isolating x - subtract b, then divide by a. This fundamental skill unlocks a world of algebraic problem‑solving and keeps your symbol‑manipulation sharp. Try equations with fractions and decimals to level up your technique. GeeksforGeeks
  9. Understand Functions and Their Graphs - Functions are like machines: you feed in x and get out y. Learn how linear, quadratic, and other types of functions look when you plot them, and spot key features like intercepts and turning points. Sketching graphs helps you visualize how inputs transform into outputs. GeeksforGeeks
  10. Familiarize Yourself with Geometric Formulas - From perimeter to volume, knowing the right formula for triangles, circles, prisms, and more turns you into a geometry whiz. Memorize key area and surface‑area equations so you can tackle any shape quickly. Draw diagrams to link the formulas to real‑world objects. TeacherVision
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