12th Grade Math Questions with Answers
In this article, we will provide you with 12 math questions suitable for 12th-grade students, along with their answers and explanations. These questions cover various topics, including algebra, geometry, trigonometry, and calculus.
Question 1: Algebra
Solve for x: 2x^2 + 5x - 3 = 0
Answer: x = (-5 ± √(5^2 - 4(2)(-3))) / 2(2) = (-5 ± √49) / 4 = (-5 ± 7) / 4
Question 2: Geometry
In a triangle, the length of the hypotenuse is 10 cm and one of the legs is 6 cm. Find the length of the other leg.
Answer: Using the Pythagorean theorem, we get: √(10^2 - 6^2) = √(100 - 36) = √64 = 8 cm
Question 3: Trigonometry
If sin(x) = 3/5, find cos(x).
Answer: Using the identity sin^2(x) + cos^2(x) = 1, we get: cos^2(x) = 1 - 9/25 = 16/25 => cos(x) = ±√(16/25) = ±4/5
Question 4: Calculus
Find the derivative of f(x) = 3x^2 + 2x - 5.
Answer: Using the power rule, we get: f'(x) = d(3x^2)/dx + d(2x)/dx - d(5)/dx = 6x + 2
Question 5: Algebra
Solve the system of equations:
x + 2y = 7 3x - 2y = 5
Answer: Using substitution or elimination method, we get: x = 3, y = 2
Question 6: Geometry
In a circle, the central angle is 60 degrees and the arc length is 4π cm. Find the radius of the circle.
Answer: Using the formula: arc length = (central angle / 360) * 2πr, we get: 4π = (60/360) * 2πr => r = 12 cm
Question 7: Trigonometry
If cos(x) = 2/3, find tan(x).
Answer: Using the identity tan(x) = sin(x) / cos(x), we get: tan(x) = ±√(1 - 4/9) / (2/3) = ±√(5/9) / (2/3) = ±√(45) / 6 = ±1/√3
Question 8: Calculus
Find the area under the curve y = x^2 + 1 from x = 0 to x = 4.
Answer: Using integration, we get: ∫(x^2 + 1) dx from 0 to 4 = [x^3/3 + x] from 0 to 4 = (64/3 + 4) - (0 + 0) = 76/3
Question 9: Algebra
Solve for x: x^3 - 6x^2 + 11x - 6 = 0
Answer: Factorizing the equation, we get: (x - 1)(x - 2)(x - 3) = 0 => x = 1, 2, 3
Question 10: Geometry
In a triangle, the length of the hypotenuse is 15 cm and one of the legs is 9 cm. Find the length of the other leg.
Answer: Using the Pythagorean theorem, we get: √(15^2 - 9^2) = √(225 - 81) = √144 = 12 cm
Question 11: Trigonometry
If tan(x) = 3/4, find sin(x) and cos(x).
Answer: Using the identity sin(x) = tan(x) / √(1 + tan^2(x)), we get: sin(x) = 3/5. Using the identity cos(x) = 1 / √(1 + tan^2(x)), we get: cos(x) = 4/5.
Question 12: Calculus
Find the derivative of f(x) = (x^2 + 1) / (x + 1).
Answer: Using the quotient rule, we get: f'(x) = ((x + 1
