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Quizzes > High School Quizzes > Mathematics

MAT 144 Practice Quiz 1

Boost your understanding and ace the exam.

Difficulty: Moderate
Grade: Grade 12
Study OutcomesCheat Sheet
Colorful paper art promoting a MAT-144 college math practice quiz

Solve for x: 2x + 3 = 7.
1
4
3
2
Subtracting 3 from both sides gives 2x = 4, and dividing by 2 results in x = 2. Option A is correct because it satisfies the equation exactly.
Find the value of f(3) if f(x) = 2x + 1.
6
7
8
5
Substitute x = 3 into the function: f(3) = 2(3) + 1 = 7. Option A is correct as it is the result obtained by proper substitution and arithmetic.
Identify the slope of the line given by the equation y = 3x - 2.
-3
3
-2
2
In the slope-intercept form y = mx + b, the coefficient m is the slope. Since m is 3 in this equation, Option A is the correct answer.
Simplify the expression: 3(x + 2) - 2x.
5x + 6
x + 2
x + 6
3x - 2
Expanding 3(x + 2) yields 3x + 6 and subtracting 2x results in x + 6. Option A is correct as it represents the simplified form of the expression.
Solve for x: 5 - x = 2.
3
5
2
0
Subtracting 5 from both sides gives -x = -3, and multiplying by -1 shows that x = 3. This clear step-by-step solution confirms Option A as the correct answer.
Solve the quadratic equation: x² - 5x + 6 = 0.
x = 2 and x = 3
x = -2 and x = -3
x = 1 and x = 6
x = 2 and x = -3
The equation factors as (x - 2)(x - 3) = 0, which gives the solutions x = 2 and x = 3. Option A is correct as both roots satisfy the original equation.
Find (f ∘ g)(2) if f(x) = x² - 3 and g(x) = 2x + 1.
18
22
16
20
First, compute g(2) = 2(2) + 1 = 5, then evaluate f(5) = 5² - 3 = 22. Option A is correct because it reflects the proper composition of functions.
Determine the domain of the function f(x) = √(2x - 4).
x > 2
x < 2
x ≥ 2
x ≤ 2
Since the radicand of a square root must be non-negative, set 2x - 4 ≥ 0, which simplifies to x ≥ 2. Option A is correct as it correctly represents the acceptable x-values.
Solve the system of equations: x + y = 10 and x - y = 2.
x = 6, y = 4
x = 7, y = 3
x = 5, y = 5
x = 4, y = 6
Adding the two equations yields 2x = 12, so x = 6; substituting back into one of the equations gives y = 4. Thus, Option A is correct as these values satisfy both equations.
Solve for x: 3^x = 27.
9
3
27
2
Recognize that 27 can be written as 3^3, hence the equation becomes 3^x = 3^3. Equating the exponents shows that x = 3, making Option A the correct choice.
Evaluate log₃(81).
4
5
81
3
Since 81 is 3 raised to the power of 4 (3^4), log₃(81) is equal to 4. Option A is correct by applying the definition of a logarithm.
Simplify the rational expression: (x² - 9) / (x + 3).
x - 9
x + 3
x² - 9
x - 3
The numerator factors as (x - 3)(x + 3), and canceling the (x + 3) term with the denominator leaves x - 3. Therefore, Option A is the correct simplified form.
Find the slope of the line passing through the points (1, 2) and (3, 10).
6
2
8
4
The slope is calculated using the formula (y₂ - y₝) / (x₂ - x₝). Substituting the given points results in a slope of (10 - 2)/(3 - 1) = 4, which makes Option A correct.
Solve the quadratic equation: 2x² - 4x - 6 = 0 using the quadratic formula.
x = 4 or x = -4
x = 2 or x = -3
x = 3 or x = -1
x = 1 or x = -6
Using the quadratic formula, the discriminant is 64, and the solutions are given by x = (4 ± 8)/4, which simplify to x = 3 and x = -1. Option A correctly represents these solutions.
Factor the polynomial: x³ + 3x² - x - 3.
(x + 1)(x - 3)
x(x + 3)(x - 1)
x³ - 1
(x + 3)(x - 1)(x + 1)
By grouping the terms as (x³ + 3x²) and (-x - 3) and factoring common factors, you obtain (x + 3)(x² - 1). Since x² - 1 factors further to (x - 1)(x + 1), Option A is the complete correct factorization.
Find the inverse of the function f(x) = (2x + 3)/(x - 1).
(x + 3)/(x - 2)
(x - 3)/(x + 2)
(2x + 3)/(x - 2)
(x + 2)/(x - 3)
Start by writing y = (2x + 3)/(x - 1) and then solve for x by cross multiplying and isolating x. After switching the roles of x and y, the inverse function is found to be f❻¹(x) = (x + 3)/(x - 2), which corresponds to Option A.
Solve the inequality: x² - 4x + 3 < 0.
x > 3
1 < x < 3
x < 1 or x > 3
1 ≤ x ≤ 3
Factoring the quadratic gives (x - 1)(x - 3) < 0, which is true when x is between 1 and 3. Thus, Option A correctly identifies the interval where the inequality holds.
Simplify the expression: (√50 + √18) / √2.
4
5 + 3√2
8
√68
Express √50 as 5√2 and √18 as 3√2, so the numerator becomes 8√2. Dividing by √2 results in 8, making Option A the correct simplified result.
Using compound interest, calculate the amount after 3 years if $1000 is invested at 5% annual interest compounded annually.
1100.00
1200.00
1150.00
1157.63
Using the compound interest formula A = P(1 + r)❿ with P = 1000, r = 0.05, and n = 3 gives A = 1000 × (1.05)³ ≈ 1157.63. Option A is correct as it is the closest approximation.
Solve the absolute value inequality: |2x - 5| ≥ 7.
-1 < x < 6
x ≤ -1 or x ≥ 6
x > -1 or x < 6
x ≥ -1 or x ≤ 6
The absolute value inequality splits into two cases: 2x - 5 ≥ 7, which simplifies to x ≥ 6, and 2x - 5 ≤ -7, which simplifies to x ≤ -1. Therefore, the solution is x ≤ -1 or x ≥ 6, making Option A correct.
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Study Outcomes

  1. Analyze problem statements to identify key mathematical concepts.
  2. Apply problem-solving techniques to resolve complex mathematical queries.
  3. Evaluate and interpret results to ensure accuracy and clarity in solutions.
  4. Integrate multiple methods to tackle and simplify challenging problems.

MAT-144 Quiz 1 Review Cheat Sheet

  1. Compound Interest Formula - Get ready to watch your savings skyrocket with A(t) = P(1 + r/n)nt. This formula shows how your principal P grows over time t when interest rate r is compounded n times per year. Experiment with different values to see compounding in action! CliffsNotes Compound Interest
  2. Future Value of Periodic Payments - Discover how regular deposits pile up with A(t) = P × ((1 + r/n)nt - 1) / (r/n). Perfect for planning your dream vacation or retirement fund, this formula calculates the total value of a series of equal payments P over time. Watch your small contributions turn into big rewards! CliffsNotes Future Value
  3. Loan Payment Formula - Say goodbye to confusing bills using PMT = P × (r/n) / (1 - (1 + r/n) - nt). This handy equation tells you exactly how much you'll pay each period to clear a loan of size P at rate r over t years. Master it, and you'll never be surprised by your monthly statement again! CliffsNotes Loan Payments
  4. Graphing Piecewise-Defined Functions - Ready to unleash your inner artist? Piecewise functions let you draw different rules on separate intervals. Practice identifying breakpoints and sketching each segment to become a graphing guru! College Sidekick Piecewise Functions
  5. Function Behavior Analysis - Become a function detective by spotting where curves rise (increasing) or fall (decreasing) and pinpointing local highs and lows. This skill is key for optimization problems and understanding real-world trends. Grab your magnifying glass and dive in! College Sidekick Function Behavior
  6. Average Rate of Change - Think of this as your function's "speedometer" between two points. Calculate [f(b) - f(a)]/(b - a) to see how fast values change over an interval - crucial for everything from physics to finance. Get ready to track those slopes like a pro! College Sidekick Rate of Change
  7. Transformations of Functions - Shift, stretch, reflect, or compress graphs with simple tweaks to f(x). Understanding these moves turns graphing into a fun puzzle where each adjustment has a clear rule. Start flexing those transformation muscles today! College Sidekick Transformations
  8. Difference Quotients - Lay the groundwork for calculus by mastering [f(x + h) - f(x)]/h. Simplifying this quotient is your first step toward finding derivatives and understanding instantaneous rates. Embrace the challenge and step into the world of limits! College Sidekick Difference Quotient
  9. Box Plot Interpretation - Box plots are like the Twitter feed of data: quick snapshots of medians, quartiles, and outliers. Learn to read these "five-number summaries" to uncover distribution shapes and spot anomalies instantly. Crunch those numbers and tell the data story! CliffsNotes Box Plots
  10. Probability Concepts - Roll the dice and explore the world of chance with compound, conditional, and complementary probabilities. Whether you're predicting card draws or weather events, these tools help you quantify uncertainty. Get ready for some thrilling "what are the odds?" moments! CliffsNotes Probability
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