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Questions and Answers
If $b^2 - 4ac = 0$, what can be said about the roots of the equation $ax^2 + bx + c = 0$?
If $b^2 - 4ac = 0$, what can be said about the roots of the equation $ax^2 + bx + c = 0$?
What value of $a$ makes the roots of $x^2 - 5x + a = 0$ equal?
What value of $a$ makes the roots of $x^2 - 5x + a = 0$ equal?
What is the value of $ an heta$ if $ an heta = 2$?
What is the value of $ an heta$ if $ an heta = 2$?
What is the slope of two parallel lines?
What is the slope of two parallel lines?
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If $ heta$ is the angle between the lines whose slopes are $m_1$ and $m_2$, what is the formula for $ an heta$?
If $ heta$ is the angle between the lines whose slopes are $m_1$ and $m_2$, what is the formula for $ an heta$?
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What is the diameter of a circle with a radius of 4 cm?
What is the diameter of a circle with a radius of 4 cm?
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What is the sum of the roots of the equation $x^2 - 6 = 0$?
What is the sum of the roots of the equation $x^2 - 6 = 0$?
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The general formula for the equation of a straight line perpendicular to another line with slope $ rac{2}{3}$ is?
The general formula for the equation of a straight line perpendicular to another line with slope $ rac{2}{3}$ is?
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Study Notes
First Semester Examination - December 2019
- Subject: Workshop Mathematics
- Duration: 3 hours
- Max Marks: 60
- Date: 23.12.2019
- Time: 02:00 p.m. to 05:00 p.m.
Part A
- Question 1: If b² - 4ac = 0, then the roots of ax² + bx + c = 0 are equal.
- Question 2: If the roots of x² - 5x + a = 0 are equal, then a = 25/4.
- Question 3: If sin A = ½, cos A = ½, then sin 2A = √3/2.
- Question 4: Find the value of cos A - sin A.
- Question 5: cot(90+θ) = -tanθ
- Question 6: Find 4² = 4
- Question 7: The sum of the coefficients in the expansion of (1-x)¹⁰ = 1³
- Question 8: If two straight lines are parallel, then their slopes are equal.
- Question 9: Slope-point formula: y - y₁ = m(x - x₁).
- Question 10: If θ is the angle between two straight lines, then tan θ...
- Question 11: Equation of a line perpendicular to 3x-2y+9 = 0.
- Question 12: Find the center and radius of circle x² + y² + 2x - 4y + 3 = 0
- Question 13: Find the equation of a circle with center (0,0).
- Question 14: Equations of two diameters, then the center...(this requires further explanation or context).
- Question 15: If radius of a circle is 4cms, then diameter is 8cms.
- Question 16: Sum of roots of quadratic eq. x² -6 = 0 = 0.
- Question 17: Roots of a quadratic equation... (needs expanded answer or context)
- Question 18: Write into degrees... (needs additional information for a complete question)
- Question 19: cos(A + B)= ... (needs additional information for a complete question)
- Question 20: Slope of line perpendicular to a line with slope m is -1/m
- Question 21: Sum of binomial coefficients = True.
- Question 22: (needs additional information for a complete question)
- Question 23: Equations differ by constant term = True.
- Question 24: Length of diameter of a circle… = True
- Question 25: In formula 2πr, 'r' is area = False
- Question 26: Formula for tan(A+B) = ...
- Question 27: Diameter of circle = 2(radius)
- Question 28: Area of a circle = πr²
- Question 29: Sin n = ... (needs additional info)
- Question 30: Write π... (needs additional info)
Part B
- Instructions: Answer all questions (Max 40 words)
- Multiple questions requiring 40-word answers (needs expanded questions)
Part C
- Instructions: Answer any four questions (Max 100 words)
- Multiple questions requiring detailed answers.
Other Information
- Paper Code: 18-1112
- Exam: First Semester Examination
- Institution: Central Institute of Plastics Engineering and Technology
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Description
Test your knowledge with this comprehensive examination from the December 2019 Workshop Mathematics first semester. This quiz covers a variety of topics including quadratic equations, trigonometry, and geometry. Challenge yourself with questions that test your understanding of mathematical principles and formulas.
