Mathematics Quiz Class 10

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Find the value of x if, log5(x2 – 5x + 11) = 1

6 or -1

Find the value of sin(15°) using compound angles.

1/√2 - 1/2√2

Find the intercepts of the line 2x + 3y = 6 on both the axes.

x-intercept: (3, 0) and y-intercept: (0, 2)

State whether the function is even or odd if, f(x) = x3 + 4x + sin x.

<p>False (B)</p> Signup and view all the answers

At which point on the curve y = 3x – x2, the slope of the tangent is –5?

<p>(4, -4)</p> Signup and view all the answers

Divide 100 into two parts such that their product is maximum.

<p>50 and 50</p> Signup and view all the answers

If mean is 34.5 and standard deviation is 5, find the co-efficient of variance.

<p>(5/34.5)*100% or approximately 14.49%</p> Signup and view all the answers

Given the matrices A = [[-1, 7], [2, 4]] and B = [[-1, 2], [3, 0]], then find the matrix 'X' such that 2X + 3A - 4B = I, where I is the identity matrix of order 2.

<p>[[2, 1/2], [-5/2, -3/2]]</p> Signup and view all the answers

Given the matrices A = [[-2, 0, 2], [3, 4, 5]] and B = [[2, 1], [3, 5], [0, 2]], determine whether AB is singular or non-singular matrix.

<p>True (A)</p> Signup and view all the answers

Resolve into partial fraction (3x - 2) / ((x + 2)(x)(x2 + 4)).

<p>1/2*(1/<em>x</em>) + 3/8*(1/(<em>x</em> + 2)) - 1/8*((3<em>x</em> + 2) / (<em>x</em><sup>2</sup> + 4))</p> Signup and view all the answers

If A and B are obtuse angles and sin A = 5/13 and cos B = 4/5, then find sin(A + B).

<p>63/65</p> Signup and view all the answers

Prove that (sin 3A - sin A)/(cos 3A + cos A) = tan A

<p>Apply the sum-to-product identities for sine and cosine to simplify each expression and then simplify algebraically.</p> Signup and view all the answers

Prove that sin-1(5/13) - sin-1(17/85) = cos-1(84/85)

<p>Use the difference of arcsine formula (sin<sup>-1</sup> <em>x</em> - sin<sup>-1</sup> <em>y</em> = sin<sup>-1</sup>(<em>x</em>√(1-<em>y</em><sup>2</sup>)- <em>y</em>√(1-<em>x</em><sup>2</sup>)). Simplify by using the Pythagorean Identity and then use trigonometric identities to show the result.</p> Signup and view all the answers

Find the equation of a straight line passing through the point of intersection of lines 4x + 3y = 8 and x + y = 1; and parallel to the line 5x - 7y = 3.

<p>5<em>x</em> - 7<em>y</em> = -2</p> Signup and view all the answers

Find dy/ dx if x3 + x y2 = y3 + y x2.

<p>(<em>y</em><sup>3</sup> + 2<em>x</em> <em>y</em> - 3<em>x</em><sup>2</sup>) / (2<em>x</em> <em>y</em> - 3<em>y</em><sup>2</sup> - <em>x</em><sup>3</sup>)</p> Signup and view all the answers

If x = a(θ + sin θ) & y = a(1 - cos θ), find dy/ dx at θ = π/2.

<p>-1</p> Signup and view all the answers

If y = (x)sinx + (tanx)x, find dy/ dx.

<p>sin<em>x</em> + <em>x</em>cos<em>x</em> + (tan<em>x</em>)<sup><em>x</em></sup>(sec<sup>2</sup><em>x</em> <em>ln(tan</em>x*) + <em>x</em>sec<sup>2</sup><em>x</em>/tan<em>x</em>)</p> Signup and view all the answers

Find the range and co-efficient of range for the following data: Class Interval Frequency 10-19 15 20-29 25 30-39 13 40-49 17 50-59 10

<p>Range: 40, Coefficient of Range: 0.4</p> Signup and view all the answers

Calculate the mean deviation about mean of the following data: 17, 15, 18, 23, 25, 22, 11, 5

<p>4.14</p> Signup and view all the answers

The following data pertains to two workers doing the same job in a factory: Details Worker A Worker B Mean time of completing job 40 42 Standard deviation 8 6 Who is more consistent worker?

<p>Worker B</p> Signup and view all the answers

Solve the following system of equations by matrix inversion method: x + y + z = 3, 3x - 2y + 3z = 4, 5x + 5y + z = 11

<p>x = 1, y = 1, z = 1</p> Signup and view all the answers

If tan A = (2/√3) and A is in the first quadrant, find the value of cos A.

<p>1/√7</p> Signup and view all the answers

Evaluate tan 85° - tan 40° / 1 + tan 85° tan 40° without using a calculator.

<p>tan 45° = 1</p> Signup and view all the answers

Find the distance between the parallel lines 3x + 2y = 5 and 3x + 2y = 6.

<p>1/√13</p> Signup and view all the answers

Find the acute angle between the lines 3x = y - 4 and 2x + y + 3 = 0.

<p>tan<sup>-1</sup>(11/5) or approximately 65.56°</p> Signup and view all the answers

A manufacturer can sell 'x' items at a price of ₹ (330 - x) each. The cost of producing x items is ₹ (x2 + 10x + 12). Determine the number of items to be sold so that the manufacturer can make the maximum profit.

<p>150 items</p> Signup and view all the answers

A beam is bent in the form of curve y = 2sin x - sin 2x. Find the radius of curvature of the beam at x = π/2.

<p>1/2</p> Signup and view all the answers

Find the mean, standard deviation and co-efficient of variance of the following data: Class Interval Frequency 0-10 14 10-20 23 20-30 27 30-40 21 40-50 15

<p>Mean: 25.2, Standard Deviation: 14.39, Co-efficient of Variance: 0.57</p> Signup and view all the answers

Flashcards

Equation

A mathematical expression that can be used to represent a relationship between variables. It is a statement that two expressions are equal.

Logarithmic Equation

A type of equation that involves logarithmic functions. Logarithmic functions are the inverse of exponential functions.

Linear Relationship

A relationship between two variables where one variable increases or decreases at a constant rate as the other variable changes. It can be represented by a straight line on a graph.

Slope

A mathematical expression that can be used to find the slope of a line. The slope of a line represents the rate of change between two points.

Signup and view all the flashcards

Point of inflection

A point on a graph where the slope of a line changes. The slope of a line represents the rate of change between two points.

Signup and view all the flashcards

Rate of change

A measure of how much a variable changes in response to a change in another variable. It is represented by the slope of a line.

Signup and view all the flashcards

Trigonometric Function

A mathematical expression that can be used to represent an angle in terms of its sine, cosine, and tangent. Used to find the angles and side lengths of triangles.

Signup and view all the flashcards

Trigonometry

A technique used to determine the angles and side lengths of triangles. Utilizes trigonometric functions.

Signup and view all the flashcards

Sine Function

A mathematical function that can be used to represent an angle in terms of its sine, cosine, and tangent. Used to find the angle of a triangle.

Signup and view all the flashcards

Cosine Function

A mathematical function that can be used to represent an angle in terms of its sine, cosine, and tangent. Used to find the length of a side of a triangle.

Signup and view all the flashcards

Tangent Function

A mathematical function that can be used to represent an angle in terms of its sine, cosine, and tangent. Used to find the slope or gradient of a line.

Signup and view all the flashcards

Trigonometric Identity

A type of trigonometric function that involves simplifying trigonometric expressions by using identities.

Signup and view all the flashcards

Matrix

An arrangement of numbers in rows and columns. Matrices can be used to represent data, transformations, and systems of equations.

Signup and view all the flashcards

Square Matrix

A matrix that has the same number of rows and columns.

Signup and view all the flashcards

Row Matrix

A matrix that has only one row.

Signup and view all the flashcards

Column Matrix

A matrix that has only one column.

Signup and view all the flashcards

Zero Matrix

A matrix with all elements equal to zero.

Signup and view all the flashcards

Scalar Multiplication

A matrix that is obtained by multiplying each element of a matrix by a scalar.

Signup and view all the flashcards

Matrix Inversion Method

A method of solving a system of equations by using matrices. It involves finding the inverse of a matrix and using it to solve for the variables.

Signup and view all the flashcards

Inverse Matrix

A matrix that is the inverse of another matrix. The product of a matrix and its inverse is the identity matrix.

Signup and view all the flashcards

Singular Matrix

A type of matrix that has a determinant of zero. Singular matrices do not have an inverse.

Signup and view all the flashcards

Non-singular Matrix

A type of matrix that has a determinant that is not equal to zero. Non-singular matrices have an inverse.

Signup and view all the flashcards

Partial Fraction Decomposition

A method used to break down a complex fraction into simpler fractions. Used to simplify expressions and solve equations.

Signup and view all the flashcards

Standard Deviation

A measure of the spread or variability of a set of data. Measured in terms of how much the data points deviate from the mean.

Signup and view all the flashcards

Coefficient of variance

A statistical measure used to compare the variability of two different datasets. Calculated by dividing the standard deviation by the mean.

Signup and view all the flashcards

Mean

A measure of central tendency that represents the average of a set of data. Found by summing all the data points and dividing by the number of data points.

Signup and view all the flashcards

Median

A measure of the central tendency of a set of data. Represents the middle value of a dataset when the data is arranged in ascending order.

Signup and view all the flashcards

Mode

A measure of the central tendency of a set of data. Represents the data point that appears most frequently in a set of data.

Signup and view all the flashcards

Function

A type of mathematical function that describes the relationship between two or more variables. Can be used to model real-world phenomena.

Signup and view all the flashcards

Derivative

The rate of change of a function at a particular point. It is calculated by finding the slope of the tangent line to the curve at that point.

Signup and view all the flashcards

Differentiation

The process of finding the derivative of a function. Used to find the rate of change of a function.

Signup and view all the flashcards

Integration

The process of finding the original function from its derivative.

Signup and view all the flashcards

Radius of Curvature

A statistical measure that describes the amount of curvature in a graph.

Signup and view all the flashcards

Study Notes

Instructions

  • All questions are compulsory
  • Answer each question on a new page
  • Use sketches where necessary
  • Figures indicate marks
  • Non-programmable calculators are permitted
  • Mobile phones, pagers and electronic communication devices are not allowed

Question 1

  • Attempt five of the following
    • Find x if log₅(x² - 5x + 11) = 1
    • Find sin(15°) using compound angles
    • Find the intercepts of 2x + 3y = 6 on both axes
    • Determine if f(x) = x³ + 4x + sin x is even or odd
    • Find the point on y = 3x - x² where the tangent's slope is -5
    • Divide 100 into two parts where their product is maximum
    • If the mean is 34.5 and standard deviation is 5, find the coefficient of variance

Question 2

  • Attempt three of the following
    • Given A = [3 -4], B = [1 -3]
      • Solve for matrix X if 2X + 3A - 4B = I, where I is a 2x2 identity matrix
    • Given A = [2 -2 0], B = [3 5]
      • Determine if AB is singular or non-singular
    • Resolve (3x – 2)/((x+2)(x)(x² +4)) into partial fractions
    • If A and B are obtuse angles, sin A = 5/13 and cos B = 5/13, find sin(A+B)

Question 3

  • Attempt three of the following
    • Prove (sin3A - sinA)/(cos3A + cosA) = tanA
    • Prove sin⁻¹(3/5) - sin⁻¹(8/17) = cos⁻¹(84/85)
    • Find the equation of a line passing through the intersection of 4x + 3y = 8 and x+y =1, parallel to 5x -7y = 3
    • Find dy/dx if x³ + xy² = y³ + yx²

Question 4

  • Attempt three of the following
    • If x = a(θ + sin θ) and y = a(1 - cos θ), find dx/dθ at θ = π/2
    • If y = x sinx + (tan x)², find dy/dx

Question 5

  • Attempt two of the following
    • Solve x + y + z = 3, 3x - 2y + 3z = 4, 5x + 5y + z = 11 using matrix inversion
    • If tan A = 1/√3, find cos A
    • Evaluate tan 85° - tan 40°/1 + tan 85° tan 40°
    • Find the distance between the parallel lines 3x + 2y = 5 and 3x + 2y = 6
    • Find the acute angle between 3x = y − 4 and 2x + y + 3 = 0

Question 6

  • Attempt two of the following
    • A manufacturer sells x items at (330 - x) each. Cost of x items is x² + 10x +12. Find the number of items to maximize profit
    • A beam is bent in the form of y = 2 sinx sin2x. Find the radius of curvature at x = π/2
    • Find mean, standard deviation, and coefficient of variance of the following data:
      • Class interval | Frequency
        • 0-10 | 14
        • 10-20 | 23
        • 20-30 | 27
        • 30-40 | 21
        • 40-50 | 15

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Mathematics Past Paper 311302 - Winter 2023 PDF

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser