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Quizzes > High School Quizzes > Mathematics

9th Grade Placement Test Practice Quiz

Boost your skills with 5th grade test tips

Difficulty: Moderate
Grade: Grade 5
Study OutcomesCheat Sheet
Colorful paper art promoting The Grade Leap Challenge, a high school math practice quiz.

What is 25 + 37?
60
62
65
63
Adding 25 and 37 gives 62 because when you break the numbers into tens and ones, 20+30 equals 50 and 5+7 equals 12, which sums to 62. This step-by-step process confirms that 62 is the correct answer.
What is the value of 8 - 7?
64
56
54
63
Multiplying 8 by 7 results in 56. The basic multiplication fact confirms that 8 - 7 equals 56.
What is the sum of 1/2 and 1/3?
2/3
1/2
1
5/6
To add 1/2 and 1/3, you convert them to a common denominator: 3/6 + 2/6 equals 5/6. This makes 5/6 the correct answer.
Solve for x: x + 5 = 12.
7
5
8
6
Subtracting 5 from both sides of the equation x + 5 = 12 results in x = 7. This simple subtraction confirms the correct value for x.
What is the area of a rectangle with a length of 5 and a width of 3?
15
10
8
18
The area of a rectangle is calculated as length multiplied by width. Here, 5 multiplied by 3 equals 15, which is the correct area.
Solve the equation: 2x - 3 = 7.
7
5
10
3
First, add 3 to both sides to get 2x = 10. Dividing both sides by 2 gives x = 5, confirming the correct solution.
What is the slope of a line passing through the points (1, 2) and (3, 6)?
3
1
4
2
The slope is calculated by the formula (y2 - y1) / (x2 - x1). Using the given points, (6 - 2) divided by (3 - 1) equals 4/2, which simplifies to 2.
Find the area of a triangle with a base of 8 cm and a height of 5 cm.
15
40
20
13
The area of a triangle is found by using the formula 1/2 - base - height. Substituting the given values, 1/2 - 8 - 5 equals 20, which is the correct answer.
What is the value of 3³?
27
36
18
9
Raising 3 to the third power means multiplying 3 by itself three times: 3 - 3 - 3, which equals 27. This confirms that 27 is the correct answer.
Simplify the expression: 4(2x + 3) - 8x.
12
8
2
4x
First, distribute the 4 to get 8x + 12. Subtracting 8x cancels the variable part, leaving only 12 as the simplified result.
Solve for y in the equation: (3y)/4 = 9.
15
11
12
9
Multiply both sides of the equation by 4 to obtain 3y = 36. Then, dividing by 3 yields y = 12, which is the correct solution.
Which of these formulas represents the Pythagorean theorem?
a² - b² = c²
a + b = c
a² + b² = c²
2a + 2b = c
The Pythagorean theorem for right triangles states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, written as a² + b² = c². This is the precise formula among the given options.
If a rectangle has a perimeter of 20 and one side is 6, what is the length of the adjacent side?
3
4
6
5
The perimeter of a rectangle is calculated as 2 - (length + width). If one side is 6 and the total of the two different sides is 10 (since 2 - (6 + x) = 20), then the other side must be 4.
Evaluate the expression: 12/3 + 2 - 5.
12
14
16
10
First, divide 12 by 3 to obtain 4, then multiply 2 by 5 to get 10. The sum of 4 and 10 is 14, which is the correct result.
What is the next prime number after 7?
9
11
10
13
After 7, the numbers 8, 9, and 10 are not prime. The next prime number in the sequence is 11, making it the correct answer.
What are the solutions to the quadratic equation x² - 5x + 6 = 0?
x = -2 and x = -3
x = 1 and x = 6
x = -1 and x = -6
x = 2 and x = 3
The equation factors into (x - 2)(x - 3) = 0, which yields the solutions x = 2 and x = 3. This factorization confirms that the correct solutions are x = 2 and x = 3.
Given the function f(x) = 2x + 3, what is the value of f(4)?
11
10
12
14
By substituting x = 4 into the function, we have f(4) = 2 - 4 + 3 = 11. This calculation confirms that 11 is the correct answer.
Simplify the expression: (x² - 9) / (x + 3).
x - 3
x² - 3
x + 3
(x - 3)/(x + 3)
The numerator is a difference of squares and can be factored into (x - 3)(x + 3). Canceling the common factor (x + 3) results in x - 3, provided that x is not -3.
Find the value of the expression: 2/(1/4) + 3/(1/6).
24
26
28
20
Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus, 2 divided by 1/4 is 2 - 4 (which is 8) and 3 divided by 1/6 is 3 - 6 (which is 18), and their sum is 26.
In the arithmetic sequence 3, 7, 11, ..., what is the 10th term?
35
42
39
40
The sequence increases by a common difference of 4. Using the formula for the nth term, the 10th term is calculated as 3 + (10 - 1) - 4, which equals 39.
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Study Outcomes

  1. Apply high school-level mathematics concepts to solve challenging problems.
  2. Analyze problem statements to identify underlying mathematical principles.
  3. Evaluate various strategies for effective problem solving.
  4. Demonstrate proficiency in algebraic manipulation and logical reasoning.
  5. Assess personal understanding and readiness for upcoming tests and exams.

9th Grade Placement Test Review Cheat Sheet

  1. Master the Quadratic Formula - Think of it as your algebraic detective tool: plug in a, b, and c into x = (-b ± √(b² - 4ac)) / 2a and reveal the hidden solutions of any quadratic mystery! This formula works every time for ax² + bx + c = 0. Albert.io reference sheet
  2. Understand Slope and Slope-Intercept Form - Picture slope (m) as the steepness of a rollercoaster track: m = (y₂ - y₝) / (x₂ - x₝). Then use y = mx + b to pinpoint where your ride starts on the y-axis and how it's angled. Agrade Ahead blog
  3. Learn the Midpoint Formula - This is your geometry GPS: the midpoint between (x₝, y₝) and (x₂, y₂) is simply ((x₝ + x₂)/2, (y₝ + y₂)/2). It's like finding the perfect halfway house between two coordinate points! Agrade Ahead blog
  4. Grasp the Pythagorean Theorem - In any right triangle, a² + b² = c² unlocks the length of the hypotenuse (c) when you know the other two sides. Think of it as the triangle's secret code for side lengths! Albert.io reference sheet
  5. Familiarize Yourself with Area and Circumference of a Circle - Calculate area with A = πr² to see how much space is inside, and use C = 2πr to measure the outer edge. Circles never felt so simple! Albert.io reference sheet
  6. Understand Arithmetic Sequences - These are number staircases with a constant difference (d) between steps. To find the nth stair, use aₙ = a₝ + (n - 1)d and climb with confidence! Albert.io reference sheet
  7. Learn Geometric Sequences - Each term multiplies by a fixed ratio (r), like shooting up or shrinking fast. Discover any term with aₙ = a₝ · r^(n - 1) and watch the pattern unfold! Albert.io reference sheet
  8. Master Exponential Growth and Decay - Model wild population booms or slow radioactive decay with A = A₀e^(kt), where A₀ is your starting amount, k is the growth/decay rate, and t is time. Science and math unite! Albert.io reference sheet
  9. Understand Radians and Degrees - Switch between rad (180/π°) and degrees (π/180 rad) to ace trigonometry. Whether you're spinning circles or solving sine waves, conversions are key! Albert.io reference sheet
  10. Familiarize Yourself with Volume Formulas - From V = πr²h for cylinders to V = (4/3)πr³ for spheres, these equations tell you how much space an object occupies. Perfect for all your 3D shape adventures! Albert.io reference sheet
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