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Quizzes > High School Quizzes > Mathematics

Math Final Practice Quiz

Sharpen skills with focused exam practice

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Colorful paper art promoting the Math Final Frenzy high school-level trivia quiz

What is the value of x in the equation 2x + 3 = 11?
x = 4
x = 3
x = 5
x = 8
Subtracting 3 from both sides gives 2x = 8. Dividing by 2 results in x = 4.
Simplify the expression 3(2x - 4).
6x - 12
6x - 4
2x - 12
3x - 4
Distributing 3 across the terms inside the parentheses gives 3×2x - 3×4, which simplifies to 6x - 12. This is the fully simplified expression.
What is the value of y if y/5 = 3?
y = 15
y = 3
y = 8
y = 5
Multiplying both sides of the equation by 5 gives y = 15. This is a straightforward application of the multiplication property of equality.
Calculate 15% of 200.
30
15
20
35
15% of 200 is computed by multiplying 0.15 by 200, which equals 30. This calculation reinforces the concept of percentages in basic arithmetic.
What is the area of a rectangle with a length of 8 and a width of 5?
40
13
20
80
The area of a rectangle is calculated by multiplying its length by its width. Therefore, 8 multiplied by 5 gives an area of 40.
What are the solutions to the quadratic equation x² - 5x + 6 = 0?
x = 2 and x = 3
x = -2 and x = -3
x = 1 and x = 6
x = -1 and x = -6
Factoring x² - 5x + 6 results in (x - 2)(x - 3) = 0, which means the solutions are x = 2 and x = 3. Factoring is an essential technique for solving quadratic equations.
Solve the inequality 2x - 3 < 7 for x.
x < 5
x > 5
x < 2
x > 2
Adding 3 to both sides gives 2x < 10, and dividing both sides by 2 results in x < 5. This problem highlights the process of isolating the variable in an inequality.
Find the slope of the line that passes through the points (2, 3) and (6, 11).
2
4
3
-2
The slope is calculated as the change in y divided by the change in x: (11 - 3) / (6 - 2) equals 8/4, which simplifies to 2. This demonstrates the core concept of slope in coordinate geometry.
Simplify the expression (3x² - 2x + 4) - (x² + 5x - 2).
2x² - 7x + 6
4x² + 3x + 2
2x² - 3x + 2
3x² - 7x + 2
By subtracting like terms, (3x² - x²) yields 2x², (-2x - 5x) gives -7x, and (4 - (-2)) results in 6. This shows the proper method of combining like terms in an algebraic expression.
Solve the system of equations: 2x + y = 7 and x - y = 1.
x = 8/3, y = 5/3
x = 3, y = 1
x = 2, y = 3
x = 4, y = -1
Using elimination or substitution, you can solve the system to find x = 8/3 and y = 5/3. This problem applies the method of solving linear systems in two variables.
Factor the expression x² - 9.
(x - 3)(x + 3)
x(x - 9)
(x - 3)²
x² - 3
Recognizing the difference of squares, x² - 9 can be factored into (x - 3)(x + 3). This technique is fundamental for simplifying algebraic expressions.
If f(x) = 2x + 1, what is the value of f(3)?
7
6
5
8
Substituting x = 3 into the function f(x) = 2x + 1 gives 2(3) + 1, which equals 7. This question reinforces the concept of function evaluation.
Solve for x in the equation 3^x = 81.
4
3
5
6
Since 81 can be expressed as 3^4, equating the exponents gives x = 4. This problem demonstrates the relationship between exponential expressions and their bases.
Find the median of the data set: {3, 7, 8, 5, 12}.
7
8
5
12
Arranging the data in order gives {3, 5, 7, 8, 12}, where the middle value is 7. The median is a fundamental measure of central tendency in statistics.
What is the probability of flipping a fair coin and it landing on heads?
1/2
1/3
2/3
1/4
A fair coin has two equally likely outcomes: heads or tails. Hence, the probability of getting heads is 1 out of 2, or 1/2.
Solve the quadratic equation 2x² - 4x - 6 = 0 using the quadratic formula.
x = 3 and x = -1
x = 2 and x = -3
x = 1 and x = -6
x = 4 and x = -2
Dividing the equation by 2 simplifies it to x² - 2x - 3 = 0. Applying the quadratic formula gives the solutions x = 3 and x = -1, which are the correct roots.
Find the vertex of the parabola given by the equation y = x² - 6x + 5.
(3, -4)
(3, 5)
(-3, -4)
(-3, 4)
The vertex of a parabola given by y = ax² + bx + c is found at x = -b/(2a). Here, x = 6/2 = 3, and substituting back into the equation gives y = -4, so the vertex is (3, -4).
Determine the value of log₂(32).
5
4
3
6
Since 32 can be expressed as 2^5, the logarithm log₂(32) equals 5. This exercise reinforces the basic properties of logarithms and exponents.
If sin θ = 1/2 and θ is in the first quadrant, what is the value of cos θ?
√3/2
1/2
√2/2
1
In the first quadrant, standard trigonometric values indicate that if sin θ = 1/2, then cos θ must be √3/2. This is derived using the Pythagorean identity, a foundational concept in trigonometry.
Solve for x in the equation |2x - 5| = 9.
x = 7 or x = -2
x = 2 and x = -7
x = 9 or x = -9
x = 7 or x = 2
The absolute value equation splits into two cases: 2x - 5 = 9 and 2x - 5 = -9. Solving these equations yields x = 7 and x = -2, respectively, which are the correct solutions.
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Study Outcomes

  1. Apply algebraic techniques to solve equations and inequalities.
  2. Analyze geometric properties to address problem-solving challenges.
  3. Evaluate function behavior using graphing and numerical methods.
  4. Utilize problem-solving strategies to identify strengths and areas for improvement.
  5. Synthesize mathematical concepts to build confidence for final exams.

Math Final Test Review Cheat Sheet

  1. Master the quadratic formula - The quadratic formula x = ( - b ± √(b² - 4ac)) / (2a) lets you solve any quadratic equation in a snap. Use the discriminant D = b² - 4ac to predict whether roots are real, equal, or complex, giving you a roadmap to the solution. Regular practice with different coefficients makes the process second nature. GeeksforGeeks - Maths Formulas
  2. Understand the Pythagorean identity - The identity sin²θ + cos²θ = 1 is the cornerstone of trigonometry, simplifying complex expressions into something you can handle. It lets you swap between sine and cosine effortlessly and solve equations faster. Mastering this also helps with advanced identities and calculus topics later on. GeeksforGeeks - Maths Formulas
  3. Familiarize yourself with the distance formula - The distance formula d = √[(x₂ - x₝)² + (y₂ - y₝)²] calculates the straight-line gap between two points on a plane. It's your go‑to tool in coordinate geometry for finding lengths and proving geometric relationships. Visualizing points and plotting them can turn abstract numbers into clear geometric insights. GeeksforGeeks - Maths Formulas
  4. Learn circle area and circumference - Knowing that Area = πr² and Circumference = 2πr lets you tackle any circle problem with confidence. From computing plots of land to engineering designs, these formulas are everywhere. Remembering r as the bridge between area and perimeter keeps things in perspective. BYJU'S - Maths Formulas
  5. Grasp arithmetic progression formulas - The nth term aₙ = a + (n - 1)d and sum Sₙ = n/2 [2a + (n - 1)d] unlocks the world of sequences and series. You'll spot patterns, make predictions, and sum long lists of numbers with ease. These formulas also appear in finance for calculating installments and interests. BYJU'S - Maths Formulas
  6. Master surface area & volume of 3D shapes - Surface area and volume formulas for spheres, cylinders, and cones are crucial in mensuration: sphere SA=4πr², V=4/3πr³; cylinder SA=2πr(h+r), V=πr²h; cone SA=πr(l+r), V=1/3πr²h. Applying them helps you solve real‑world engineering and physics problems. Visual aids and practice sketches make these formulas stick. BYJU'S - Maths Formulas
  7. Memorize basic trigonometric ratios - sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent form the backbone of trigonometry. These ratios let you link angles with side lengths in right‑angled triangles instantly. Flashcards and triangle sketches can speed up recall in exams. GeeksforGeeks - Maths Formulas
  8. Understand probability fundamentals - Probability P(E) = number of favorable outcomes / total outcomes quantifies the chance of an event happening. It's essential for statistics, games of chance, and real‑world risk analysis. Simulating experiments or rolling dice helps you see theory turn into practice. BYJU'S - Probability Formulas
  9. Learn sum & product of roots of quadratics - For ax² + bx + c = 0, the sum of roots α + β = - b/a and product αβ = c/a are handy shortcuts. You can solve or check equations without calculating roots directly, saving time in complex algebra problems. These relations also pop up in polynomial theory and proofs. GeeksforGeeks - Maths Formulas
  10. Master triangle area formulas - Use Area = ½ × base × height for classic problems or the coordinate form ½|x₝(y₂ - y₃) + x₂(y₃ - y₝) + x₃(y₝ - y₂)| in the plane. Both methods are key to solving geometry questions accurately. Drawing diagrams and labeling points makes these formulas intuitive. GeeksforGeeks - Maths Formulas
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