Applied mathematics is an essential subject for students in various fields. It focuses on applying mathematical methods to solve real-world problems.
All subjects applied mathematics question paper mypractically
Algebra
Question: What is the solution to the system of equations: 2x + 3y = 6 and 4x – y = 8?
Answer: x = 2, y = 0.
Question: Simplify the expression: (x^2 – 4)/(x + 2).
Answer: x – 2.
Question: Solve for x: 3x – 5 = 10.
Answer: x = 5.
Question: What is the quadratic formula used to solve the equation ax^2 + bx + c = 0?
Answer: x = (-b ± √(b^2 – 4ac)) / 2a.
Question: If a function is f(x) = 2x + 3, what is f(4)?
Answer: f(4) = 11.
Question: Factorize the quadratic equation x^2 + 5x + 6.
Answer: (x + 2)(x + 3).
Question: Solve the inequality: 2x – 3 > 5.
Answer: x > 4.
Question: What is the sum of the arithmetic sequence 2, 4, 6, …, 20?
Answer: 110.
Question: Find the value of x: x^2 = 49.
Answer: x = ±7.
Question: Solve for x: 5x + 2 = 17.
Answer: x = 3.
Question: Expand the binomial (x + 3)^2.
Answer: x^2 + 6x + 9.
Question: What is the determinant of the matrix: [1, 2; 3, 4]?
Answer: -2.
Question: Solve the equation: x^2 – 4x + 4 = 0.
Answer: x = 2.
Question: What is the value of x in the equation: log(x) + log(2) = 1?
Answer: x = 5.
Question: Factorize x^2 – 9.
Answer: (x – 3)(x + 3).
Question: What is the inverse of the matrix [1, 2; 3, 4]?
Answer: [ -2, 1; 1.5, -0.5].
Question: Solve for y: 2y + 5 = 15.
Answer: y = 5.
Question: Find the value of x in the equation 3x^2 – 12 = 0.
Answer: x = ±2.
Question: What is the sum of the roots of the quadratic equation x^2 + 7x + 12 = 0?
Answer: -7.
Calculus
Question: What is the derivative of f(x) = x^3?
Answer: 3x^2.
Question: Calculate the integral of f(x) = 2x.
Answer: x^2 + C.
Question: What is the second derivative of f(x) = x^4?
Answer: 12x^2.
Question: Find the critical points of f(x) = x^3 – 3x^2 + 2.
Answer: x = 0 and x = 2.
Question: Evaluate the limit: lim(x→2) (x^2 – 4)/(x – 2).
Answer: 4.
Question: What is the area under the curve of f(x) = x from x = 0 to x = 3?
Answer: 4.5.
Question: Find the derivative of f(x) = sin(x).
Answer: cos(x).
Question: Calculate the integral of f(x) = e^x.
Answer: e^x + C.
Question: What is the derivative of f(x) = ln(x)?
Answer: 1/x.
Question: Determine the local maximum of f(x) = -x^2 + 4x – 3.
Answer: x = 2.
Question: Find the slope of the tangent line to the curve y = x^2 at x = 1.
Answer: 2.
Question: What is the antiderivative of f(x) = 3x^2?
Answer: x^3 + C.
Question: Solve the differential equation: dy/dx = 2x.
Answer: y = x^2 + C.
Question: What is the value of the definite integral ∫(2 to 5) (3x + 2) dx?
Answer: 49.5.
Question: Determine the concavity of f(x) = x^3 at x = 1.
Answer: Concave up.
Question: Find the inflection point of f(x) = x^3 – 3x^2 + 4.
Answer: x = 2.
Question: Calculate the derivative of f(x) = cos(x).
Answer: -sin(x).
Question: What is the integral of f(x) = 1/x?
Answer: ln|x| + C.
Question: Find the derivative of f(x) = e^(2x).
Answer: 2e^(2x).
Question: What is the limit as x approaches infinity for the function f(x) = 1/x?
Answer: 0.
Probability
Question: What is the probability of getting a heads in a single coin toss?
Answer: 1/2.
Question: If a die is rolled, what is the probability of getting an even number?
Answer: 1/2.
Question: What is the probability of drawing a red card from a standard deck of cards?
Answer: 1/2.
Question: Calculate the probability of getting a sum of 7 when rolling two dice.
Answer: 1/6.
Question: What is the probability of selecting a king from a deck of 52 cards?
Answer: 1/13.
Question: If two coins are tossed, what is the probability of getting two heads?
Answer: 1/4.
Question: What is the probability of drawing an ace from a deck of 52 cards?
Answer: 1/13.
Question: If a die is rolled, what is the probability of getting a number less than 4?
Answer: 1/2.
Question: What is the probability of getting exactly one head in two coin tosses?
Answer: 1/2.
Question: If two dice are rolled, what is the probability of getting doubles?
Answer: 1/6.
Question: What is the probability of getting a number greater than 5 on a single die roll?
Answer: 1/3.
Question: What is the probability of drawing a black card from a deck of cards?
Answer: 1/2.
Question: If a die is rolled twice, what is the probability of getting a 6 both times?
Answer: 1/36.
Question: What is the probability of drawing a heart from a deck of 52 cards?
Answer: 1/4.
Question: What is the probability of selecting a face card from a deck of 52 cards?
Answer: 3/13.
Question: If three coins are tossed, what is the probability of getting all heads?
Answer: 1/8.
Question: What is the probability of drawing two aces consecutively from a deck of cards without replacement?
Answer: 1/221.
Question: If a die is rolled, what is the probability of getting a 3?
Answer: 1/6.
Question: What is the probability of drawing a spade from a deck of cards?
Answer: 1/4.
Question: If two dice are rolled, what is the probability of getting a sum less than 5?
Answer: 1/9.
Geometry
Question: What is the area of a triangle with base 6 cm and height 8 cm?
Answer: 24 cm².
Question: Calculate the circumference of a circle with a radius of 7 cm.
Answer: 44 cm.
Question: What is the volume of a sphere with a radius of 5 cm?
Answer: 523.6 cm³.
Question: Find the length of the diagonal of a rectangle with sides 3 cm and 4 cm.
Answer: 5 cm.
Question: What is the perimeter of a square with a side length of 6 cm?
Answer: 24 cm.
Question: Calculate the area of a circle with a radius of 10 cm.
Answer: 314 cm².
Question: Find the volume of a cylinder with a radius of 3 cm and height of 10 cm.
Answer: 282.74 cm³.
Question: What is the surface area of a cube with a side length of 4 cm?
Answer: 96 cm².
Question: Calculate the length of the hypotenuse of a right triangle with sides 9 cm and 12 cm.
Answer: 15 cm.
Question: What is the area of a rectangle with length 8 cm and width 5 cm?
Answer: 40 cm².
Question: Find the circumference of a circle with a diameter of 12 cm.
Answer: 37.68 cm.
Question: What is the volume of a cone with a radius of 4 cm and height of 9 cm?
Answer: 150.8 cm³.
Question: Calculate the perimeter of a regular hexagon with a side length of 7 cm.
Answer: 42 cm.
Question: What is the area of a parallelogram with base 10 cm and height 6 cm?
Answer: 60 cm².
Question: Find the volume of a rectangular prism with length 4 cm, width 5 cm, and height 6 cm.
Answer: 120 cm³.
Question: What is the surface area of a sphere with a radius of 3 cm?
Answer: 113.1 cm².
Question: Calculate the area of a trapezoid with bases 8 cm and 10 cm and height 5 cm.
Answer: 45 cm².
Question: What is the length of the side of a square with an area of 49 cm²?
Answer: 7 cm.
Question: Find the volume of a pyramid with a base area of 25 cm² and a height of 12 cm.
Answer: 100 cm³.
Question: What is the area of a sector with a radius of 6 cm and an angle of 60°?
Answer: 18.84 cm².
