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Quizzes > High School Quizzes > Mathematics

Quiz Class Practice Test

Master key topics with practice questions

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Colorful paper art promoting Quiz Class Challenge, a high school math practice quiz.

Solve for x: 2x + 5 = 11.
x = 2
x = 4
x = 5
x = 3
Subtracting 5 from both sides gives 2x = 6, and then dividing by 2 yields x = 3. This is the straightforward solution to the linear equation.
Factor the expression: x² - 9.
(x - 3)²
(x - 9)(x + 1)
(x - 3)(x + 3)
(x + 3)²
x² - 9 is a difference of squares and factors into (x - 3)(x + 3). The other options do not correctly represent the factorization pattern for a difference of squares.
Simplify the expression: x³ * x².
x❻¹
x❵
x❹
x❶
When multiplying powers with the same base, you add the exponents: 3 + 2 equals 5. Therefore, x³ multiplied by x² simplifies to x❵.
Simplify the fraction: 2/4.
3/4
1/4
2/3
1/2
Divide both the numerator and denominator by their greatest common divisor, which is 2, to simplify 2/4 to 1/2. This is the simplest form of the given fraction.
Find the slope of the line that passes through the points (1, 2) and (3, 6).
2
4
1
3
The slope is calculated as (y₂ - y₝) divided by (x₂ - x₝), so (6 - 2)/(3 - 1) equals 4/2 which simplifies to 2. Thus, the slope of the line is 2.
Solve the quadratic equation: x² - 5x + 6 = 0.
x = -2 and x = -3
x = 1 and x = 6
x = 2 and x = 3
x = -1 and x = -6
Factoring the quadratic yields (x - 2)(x - 3) = 0. Setting each factor to zero gives the solutions x = 2 and x = 3.
Simplify the rational expression: (x² - 4)/(x - 2).
x + 2
x² + 2
x - 2
x² - 2
The numerator x² - 4 factors as (x - 2)(x + 2) using the difference of squares. Canceling the common factor (x - 2) with the denominator results in x + 2.
Find the vertex of the quadratic function: f(x) = 2x² - 8x + 3.
(-2, -5)
(4, 3)
(2, -5)
(2, 3)
The vertex of a parabola given by ax² + bx + c is found at x = -b/(2a). Here, x = 8/(4) = 2; substituting x = 2 into the function gives f(2) = -5, so the vertex is (2, -5).
Solve the system of equations: 2x + y = 7 and x - y = 1.
x = 2, y = 3
x = 3, y = 1
x = 4, y = -1
x = 8/3, y = 5/3
Solve the second equation for y to get y = x - 1 and substitute into the first equation: 2x + (x - 1) = 7, which simplifies to 3x = 8. Thus, x = 8/3 and y = 8/3 - 1 = 5/3.
Find the domain of the function: f(x) = √(x - 3).
x > 3
x < 3
x ≤ 3
x ≥ 3
For the square root to be defined in the real numbers, the expression inside must be non-negative. Setting x - 3 ≥ 0 gives x ≥ 3.
Evaluate the logarithm: log₂(16).
2
8
16
4
Since 2 raised to the 4th power equals 16, log₂(16) is 4. This demonstrates the basic concept of logarithms where the exponent is the answer.
If f(x) = 3x + 1, what is the value of f(5)?
18
16
15
14
Substituting x = 5 into f(x) = 3x + 1 produces f(5) = 3(5) + 1 = 15 + 1 = 16. This is a simple application of function evaluation.
Simplify the expression: (a² - b²)/(a - b).
a + b
a² - b²
a - b
ab
The numerator a² - b² factors into (a - b)(a + b) using the difference of squares. Canceling the common factor (a - b) yields the simplified expression a + b.
Determine if a triangle with side lengths 3, 4, and 5 is right-angled.
It is an acute triangle
Yes, it is right-angled
No, it is not right-angled
It is an equilateral triangle
The triangle satisfies the Pythagorean theorem because 3² + 4² equals 5². This confirms that the triangle is right-angled.
Find the x-intercept of the line described by y = 2x - 4.
x = 0
x = 2
x = -2
x = 4
The x-intercept occurs where y equals 0. Setting 2x - 4 to 0 and solving for x yields x = 2.
If log₃(x) = 4, what is the value of x?
81
12
16
64
The equation log₃(x) = 4 implies that 3 raised to the power of 4 equals x. Since 3❴ is 81, the correct value of x is 81.
Find the positive solution of the quadratic equation: x² + x - 1 = 0.
√2
(-1 - √5)/2
(-1 + √5)/2
1
Using the quadratic formula on x² + x - 1 = 0 gives solutions x = (-1 ± √5)/2. The positive solution is (-1 + √5)/2, which is the correct answer.
Find the equation of the line that is perpendicular to 2x - 3y = 6 and passes through the point (3, -1).
y = (-2/3)x + 1
y = (2/3)x + 1
y = (-3/2)x + 7/2
y = (3/2)x - 7/2
First, convert 2x - 3y = 6 to slope-intercept form to get a slope of 2/3; its perpendicular slope is -3/2. Using the point-slope form with point (3, -1) yields the equation y = (-3/2)x + 7/2.
Determine the sum of the infinite geometric series with first term 5 and common ratio 2/3.
10
5
15
20
The sum of an infinite geometric series is calculated using the formula a/(1 - r), provided |r| < 1. Here, a = 5 and r = 2/3, so the sum is 5/(1/3) which equals 15.
The function f(x) = (x² - 4)/(x - 2) is defined for all x ≠ 2. Simplify the function and determine its value at x = 2 using limits.
2
0
 
4
By factoring the numerator as (x - 2)(x + 2), the function simplifies to f(x) = x + 2 for x ≠ 2. Taking the limit as x approaches 2 gives 2 + 2, which equals 4.
0
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Study Outcomes

  1. Understand and explain core mathematical concepts covered in the quiz.
  2. Apply problem-solving strategies to tackle typical high school math challenges.
  3. Analyze various mathematical scenarios to identify underlying principles.
  4. Evaluate personal performance to build confidence for upcoming assessments.
  5. Interpret quiz results to guide further study and improvement in mathematics.

Quiz Class Practice Test Cheat Sheet

  1. Master the laws of exponents - Unlock the secrets behind product of powers, power of a product, and power of a power to breeze through complex expressions. Practice these rules until they're second nature for lightning-fast simplification. Quiz on exponents
    2. Try the quiz
  2. Understand the Pythagorean Theorem - Harness the power of a² + b² = c² to solve any right-angled triangle problem like a geometry ninja. Visualizing these relationships makes calculating missing sides a total breeze. Pythagorean theorem practice
    3. Dive into practice
  3. Solve linear equations & inequalities - Tackle one-variable equations and inequalities with confidence, then plot them on the coordinate plane for instant visual feedback. Understanding how algebra translates to graphs turns abstract problems into clear, colourful pictures. Linear equations quiz
    4. Check your skills
  4. Explore trig functions - Dive into sine, cosine, and tangent to master angle-to-length relationships in right-angled triangles. These functions unlock everything from simple height calculations to waves and circles in advanced applications. Video summary
    5. Watch the summary
  5. Factor quadratics & use the quadratic formula - Break down expressions like x² + bx + c into neat factors, or apply the quadratic formula when factoring gets tricky. This toolkit helps you find roots accurately, whether you're dealing with perfect squares or messy coefficients. Quadratics practice
    6. Give it a go
  6. Calculate perimeter & area - Measure triangles, quadrilaterals, and polygons by plugging side lengths into the right formulas. Visual aids and step‑by‑step breakdowns make geometry feel like playing with a puzzle. Area & perimeter quiz
    7. Practice now
  7. Use real number properties - Leverage commutative, associative, and distributive properties to rearrange and simplify algebraic expressions effortlessly. These core rules are your backstage pass to faster, cleaner calculations. Properties of real numbers
    8. Test yourself
  8. Create & interpret data plots - Build scatter plots and histograms to visualize data patterns, trends, and outliers in a snap. Seeing the story behind numbers transforms raw data into clear insights. Data visualization practice
    9. Start plotting
  9. Summarize data with mean, median, mode & range - Crunch numbers to find the average, the middle value, the most frequent data point, and the spread. Mastering these metrics makes interpreting any dataset a fun detective game. Descriptive statistics quiz
    10. Give it a try
  10. Grasp probability concepts - Explore experimental vs. theoretical probability, calculate conditional probabilities, and test for independence in real‑world scenarios. You'll see why probability is at the heart of games, weather forecasts, and decision‑making. Probability practice
    11. Check probabilities
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