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Quizzes > High School Quizzes > Mathematics

Conquer SAT Math Practice Quiz

Practice comprehensive ACT, Math 1, and Math 2 tests

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Paper art illustrating trivia for Ace ACT Math, challenging high school students for exams.

Solve for x: 2x + 3 = 11.
x = 3
x = 5
x = 6
x = 4
Subtracting 3 from both sides yields 2x = 8, and dividing by 2 gives x = 4. This is a standard method for solving linear equations.
Solve for y: (y/3) = 4.
y = 7
y = 12
y = 4
y = 16
Multiplying both sides of the equation by 3 gives y = 12. This is a basic multiplication operation to isolate the variable.
Evaluate: 5 × (2 + 3).
20
10
15
25
First solve the expression in the parentheses (2 + 3 = 5) and then multiply by 5 to get 25. This ensures that the order of operations is followed.
Find the value of 2^3.
8
5
6
9
2 raised to the power of 3 means 2 × 2 × 2 which equals 8. Exponentiation is a repeated multiplication process.
What is the area of a rectangle with a length of 4 and a width of 3?
12
10
7
14
The area of a rectangle is calculated as length multiplied by width, so 4 × 3 = 12. This follows the standard formula for area.
Find the sum of the solutions for the equation x² - 5x + 6 = 0.
3
5
6
2
Factoring the equation gives (x - 2)(x - 3) = 0, so x = 2 and x = 3. Their sum is 2 + 3 = 5.
Factor completely: 2x² + 8x.
2x(x + 4)
2(x + 4)x
4x(x + 2)
x(2x + 8)
The common factor in both terms is 2x. Factoring it out yields 2x(x + 4). This is an application of factoring by a common term.
Simplify the expression: (3x²y) / (xy).
3xy
3y
3x
3x²
Canceling the common factors x and y in the numerator and denominator leaves 3x. This demonstrates the simplification of rational expressions.
Solve for x: (x/2) + 1 = 3.
6
2
4
3
Subtract 1 from both sides to get x/2 = 2, then multiply by 2 to solve for x, resulting in x = 4. This is a straightforward linear equation.
Find the length of the hypotenuse of a right triangle with legs of lengths 3 and 4.
7
5
4
6
Using the Pythagorean theorem, the hypotenuse is √(3² + 4²) = √(9 + 16) = √25 = 5. This classic triple confirms the correctness of the computation.
Find the value of y that satisfies the system: y = 2x + 3 and y = x + 5.
3
8
5
7
By setting 2x + 3 equal to x + 5, we solve for x obtaining x = 2. Substituting back into y = 2x + 3 gives y = 7.
What is the slope of the line passing through the points (2, 3) and (6, 11)?
2
4
3
8
The slope is calculated as (11 - 3)/(6 - 2) = 8/4 = 2. This represents the rate of change between the two points.
Evaluate the expression: √49 + √16.
10
13
7
11
√49 is 7 and √16 is 4, so their sum is 7 + 4 = 11. This uses the property of square roots for perfect squares.
Solve for x: 4^x = 64.
2
3
6
4
Since 64 is 4 raised to the power of 3 (4³ = 64), the value of x is 3. This question tests understanding of exponential equations.
Simplify the expression: (x² - 9)/(x - 3).
x² - 3
x + 3
x - 3
x² + 3
The numerator factors as (x - 3)(x + 3), and canceling the common factor (x - 3) yields x + 3. This demonstrates factoring and simplification skills.
Evaluate f(3) for the function f(x) = 2x² - 3x + 5.
11
10
14
13
Substitute x = 3 into the function: 2(3²) - 3(3) + 5 equals 18 - 9 + 5, which simplifies to 14. This problem tests function evaluation skills.
Solve for x: ln(x) + ln(2) = ln(8).
2
8
4
6
Using the logarithm property ln(a) + ln(b) = ln(ab), we have ln(2x) = ln(8). Hence, 2x = 8, which gives x = 4. This requires understanding properties of logarithms.
For the function f(x) = (x - 2) / (x + 3), find the value of x that makes f(x) = 0.
-3
2
5
0
A rational function equals zero when its numerator is zero (and the denominator is not zero). Setting x - 2 = 0 yields x = 2, which is the correct solution.
Which of the following lines is perpendicular to the line 2x - 3y = 6?
2x - 3y = 0
3x + 2y = 0
3x - 2y = 0
2x + 3y = 6
The given line has a slope of 2/3 when rewritten in slope-intercept form. The perpendicular line must have a slope of -3/2, which corresponds to the line 3x + 2y = 0.
Solve for x: 2(x - 1) > 3(x + 4).
x < 14
x < -14
x > 14
x > -14
Expanding the inequality gives 2x - 2 > 3x + 12. Simplifying leads to -14 > x, or equivalently x < -14. This question tests the ability to solve linear inequalities.
0
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Study Outcomes

  1. Understand key ACT math concepts through targeted practice questions.
  2. Analyze and solve ACT-style problems to improve mathematical reasoning.
  3. Apply strategies to effectively address challenges in exam scenarios.
  4. Evaluate personal strengths and areas for improvement based on quiz performance.
  5. Integrate learned techniques to enhance overall test preparation skills.

Math SAT Practice Test & ACT Questions Cheat Sheet

  1. Master the Pythagorean Theorem - By mastering a² + b² = c², you can solve for the hypotenuse or one of the legs effortlessly. This trusty formula turns right triangle problems into simple, satisfying puzzles. Princeton Review
  2. Understand SOHCAHTOA for trigonometry - Remember that Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent, and you'll never get lost in wave or rotation problems again. This little mnemonic acts like a GPS for angles, guiding you to the right ratio every time. PrepScholar Blog
  3. Know the slope formula - The slope formula (y₂ - y₝) / (x₂ - x₝) is your go-to when you need to find steepness or direction between two points. Think of it as a skateboard ramp calculator: positive slopes go uphill, negative ones downhill, and zero makes a flat line. PrepScholar Blog
  4. Familiarize yourself with the quadratic formula - x = (-b ± √(b² - 4ac)) / (2a) is like the ultimate cheat code for ax² + bx + c = 0. No matter how gnarly the equation, just plug and chug to unlock the roots in seconds, paying close attention to the discriminant under the radical. Magoosh
  5. Learn the area formulas - From triangles (½ × base × height) to rectangles (length × width) and circles (π × radius²), area formulas are your backstage passes to all things shapes. Memorize them and you'll breeze through territory questions faster than a speedster! Princeton Review
  6. Practice the distance formula - Compute √((x₂ - x₝)² + (y₂ - y₝)²) to find the straight-line distance between any two points like a math ninja measuring leaps across a coordinate grid. This key tool helps you crack coordinate geometry challenges with style. PrepScholar Blog
  7. Understand the properties of special right triangles - In a 45°-45°-90° triangle, the sides sing in a 1:1:√2 ratio, and in a 30°-60°-90° triangle, they groove in a 1:√3:2 pattern. These patterns let you skip the calculator and solve angle‑side mysteries in a snap! Magoosh
  8. Review logarithm properties - Logarithms are the ultimate reversal of exponent rules: log_b(xy) = log_b(x) + log_b(y) and log_b(x/y) = log_b(x) - log_b(y), turning multiplication and division into easy additions and subtractions. Master these identities to simplify crazy expressions and tame exponential equations like a seasoned pro. PrepScholar Blog
  9. Understand the equation of a circle - (x - h)² + (y - k)² = r² shows any circle's center at (h, k) and radius r, like a secret map revealing its exact location and size. Use this form to rewrite or graph circles in a flash and conquer coordinate geometry circles effortlessly. Magoosh
  10. Practice probability basics - Probability = Number of desired outcomes / Total number of outcomes gives you the lowdown on your odds, whether you're rolling dice or picking cards. Think of it as your personal chance meter, helping you make smart guesses and dodge surprises! Magoosh
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