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Quizzes > High School Quizzes > Mathematics

PERT Math Practice Quiz

Sharpen Your Skills With Exam-Style Practice

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Paper art illustrating a trivia quiz on PERT Math Mastery for high school students.

Solve: 2x - 4 = 10.
x = 5
x = 8
x = 6
x = 7
To solve the equation, add 4 to both sides to obtain 2x = 14, then divide both sides by 2 to get x = 7. This approach uses the basic principles of linear equation solving.
What is the area of a triangle with a base of 8 and a height of 5?
30
20
40
13
The area of a triangle is calculated using the formula 1/2 * base * height. Substituting the given values: 1/2 * 8 * 5 equals 20.
Find the slope of the line that passes through the points (1, 2) and (3, 6).
4
2
3
1
The slope is found by using the formula (y2 - y1) / (x2 - x1). For the points given, the calculation is (6 - 2) / (3 - 1) = 4/2, which simplifies to 2.
What is the sum of the solutions of the equation (x - 3)(x + 2) = 0?
-6
6
5
1
The solutions of the equation are x = 3 and x = -2. Adding these values gives 3 + (-2) = 1, which is the correct sum.
If f(x) = 2x + 5, what is the value of f(3)?
11
9
10
8
Substitute x = 3 into the function f(x) = 2x + 5 to obtain 2(3) + 5 = 6 + 5 = 11. This direct substitution confirms the correct result.
Which factorization is equivalent to the quadratic expression x^2 - 5x + 6?
(x - 2)(x + 3)
(x - 2)(x - 3)
(x + 2)(x + 3)
(x + 2)(x - 3)
The quadratic x^2 - 5x + 6 factors into (x - 2)(x - 3) because -2 and -3 sum to -5 and multiply to 6. This factoring technique is a standard method for solving quadratics.
Solve the system of equations: 2x + y = 7 and x - y = 1. What is the value of x?
8/3
5/3
3
7/3
First, express x from the second equation as x = y + 1 and substitute into the first equation to obtain 2(y + 1) + y = 7. Solving for y gives y = 5/3 and therefore x = 8/3.
Simplify the expression: (3x^2y) / (6xy^2).
x/(3y)
2x/y
3x/(2y)
x/(2y)
Cancel the common factors: 3/6 simplifies to 1/2, one x cancels out from x^2/x, and one y cancels leaving y in the denominator. The simplified expression is x/(2y).
For the function f(x) = x^2 - 4, what is the value of f(3)?
-5
5
9
7
Substitute x = 3 into the function to get 3^2 - 4, which equals 9 - 4 = 5. This shows a straightforward evaluation of the function at x = 3.
If the perimeter of a rectangle is 32 and its length is 3 times its width, what is the area of the rectangle?
64
48
32
36
Let the width be w and the length be 3w. With a perimeter of 32, the equation 2(w + 3w) = 32 gives 8w = 32, so w = 4 and length = 12. The area is width multiplied by length, 4 x 12 = 48.
What is the area of a circle with radius 5?
5π
50π
10π
25π
The area of a circle is given by A = πr^2. With a radius of 5, the area calculates to π(5)^2, which is 25π.
Solve the equation: 3(x - 2) = 2x + 1.
-7
1
5
7
Distribute 3 on the left side to get 3x - 6 = 2x + 1. Subtract 2x from both sides to yield x - 6 = 1 and then add 6 to find x = 7.
What is the sum of the solutions for the equation |x - 3| = 5?
6
8
-2
10
The equation |x - 3| = 5 produces two solutions: x - 3 = 5 and x - 3 = -5, yielding x = 8 and x = -2 respectively. The sum of these solutions is 8 + (-2) = 6.
If 5^(2x) = 125, what is the value of x?
2/3
1/2
5/2
3/2
Recognize that 125 can be expressed as 5^3. Equating the exponents in 5^(2x) = 5^3 gives 2x = 3, hence x = 3/2. This shows the application of exponent rules.
Determine the vertex of the parabola given by the equation y = x^2 - 6x + 8.
(1, -6)
(3, 1)
(3, -1)
(-3, 1)
The x-coordinate of the vertex is calculated using -b/(2a), which gives 6/2 = 3. Substituting x = 3 into the equation results in y = -1, so the vertex is (3, -1).
Find the product of the solutions of the equation x^2 + 4x - 21 = 0.
-21
-10
21
10
The equation factors into (x + 7)(x - 3), which gives solutions x = -7 and x = 3. Multiplying these solutions results in (-7) * 3 = -21.
The quadratic equation x^2 + kx + 9 = 0 has exactly one real solution. What is the sum of all possible values of k?
18
0
-9
9
A quadratic equation has exactly one real solution if the discriminant is zero. Setting k^2 - 36 = 0 yields k = 6 or k = -6, and their sum is 6 + (-6) = 0.
A cylinder has a volume of 150π and a height of 10. What is the radius of the cylinder?
15
5√3
√15
3
The volume formula for a cylinder is V = πr²h. Substituting the given values, 150π = πr²(10) leads to r² = 15, so the radius is √15.
Find the equation of the line perpendicular to y = -2x + 3 that passes through the point (4, 1).
y = (1/2)x - 1
y = -2x - 1
y = 2x + 1
y = -(1/2)x + 1
The slope of the given line is -2, so the perpendicular line must have a slope of 1/2 (the negative reciprocal). Using the point-slope form with the point (4, 1) leads to the equation y = (1/2)x - 1.
Solve for x: log₂(x) + log₂(x - 2) = 3.
2
-2
4
8
Combine the logarithms using the property log₂(a) + log₂(b) = log₂(ab) to get log₂[x(x - 2)] = 3. This implies x(x - 2) = 2³ = 8. Solving the resulting quadratic yields the valid solution x = 4.
0
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Study Outcomes

  1. Analyze algebraic expressions and equations to identify key components relevant for problem solving.
  2. Solve geometric problems using foundational principles to enhance spatial reasoning.
  3. Apply critical reasoning skills to tackle high school-level math challenges effectively.
  4. Evaluate performance to identify strengths and weaknesses in algebra and geometry concepts.

PERT Math Practice Cheat Sheet

  1. Master the Order of Operations - Having PEMDAS in your toolkit means you'll tackle math like a pro detective solving a mystery step-by-step. Remember: Parentheses first, then Exponents, Multiplication/Division (left to right), and finally Addition/Subtraction (left to right). Get hands-on practice and catchy mnemonic tips to lock in your PEMDAS skills. Explore PEMDAS with MathHelp
  2. Understand Linear Equations - Solving 2x + 3 = 7 feels like cracking a secret code: isolate x by subtracting 3 and dividing by 2. You'll see patterns emerge as you rearrange terms and balance both sides. Build confidence with step-by-step examples that make variables fun. Dive into linear equations at MathHelp
  3. Grasp the Distance Formula - Turn the distance formula d = √((x₂ - x₝)² + (y₂ - y₝)²) into your own treasure map for points on a graph. Practice with pairs like (1,2) and (4,6) to see √25 pop out as 5. Interactive exercises make pinpointing distances a breeze. Practice distance formula at PERT Practice Test
  4. Know the Slope-Intercept Form - y = mx + b is your golden ticket to graphing lines: m is the slope, b is the y-intercept. For example, y = 2x + 3 shoots through (0,3) and rises 2 for every 1 step to the right. Fun graphing tools help you sketch with style. Master slope-intercept form at PERT Practice Test
  5. Calculate Areas of Shapes - Whether you're finding a rectangle's area (length×width) or a triangle's (½×base×height), these formulas unlock the secrets of space. A 10×5 triangle yields 25 square units - easy math magic! Shape puzzles and visuals boost your spatial smarts. Explore shape areas at PERT Practice Test
  6. Understand Volume Calculations - From rectangular prisms (length×width×height) to cylinders (π×radius²×height), volume formulas let you stack and fill like a pro. A cylinder with r=3,h=7 gives about 197.92 cubic units. Watch 3D models spin to cement the concept. Dive into volume formulas at PERT Practice Test
  7. Interpret Graphs and Tables - Decode bar graphs, line charts, and pie graphs to spot trends, calculate growth, or find percentages in seconds. If a sales line shows steady climbs, you'll forecast the next big leap. Quizzes with real-world data sharpen your interpretation skills. Decode graphs at PERT Practice Test
  8. Calculate Mean, Median, and Mode - Stats come alive when you find the mean (average), median (middle), and mode (most frequent) of a dataset. For {2,3,3,5,7}, mean=4, median=3, mode=3. Engaging drills help you spot these measures in everyday numbers. Practice stats basics at PERT Practice Test
  9. Understand Basic Probability - Chance rules your world - from rolling dice to drawing cards. Probability = favorable outcomes ÷ total outcomes, so rolling a 4 on a die is 1/6. Flashcards and mini-games turn probability into your playground. Explore probability at PERT Practice Test
  10. Practice with Sample Questions - The more you solve, the sharper you get! Factor quadratics, simplify expressions, and tackle fun challenge problems to build speed and accuracy. Regular practice cements concepts so they stick during exam time. Get PERT practice questions at Effortless Math
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