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This document provides instructions and practice problems for students taking a quantitative tools course at the Indian School of Business. The problems cover topics like applying the order of operations, calculating areas of geometric shapes, graphing and deriving linear equations, solving systems of linear and quadratic equations, taking derivatives of functions, and solving optimization problems to find minimums and maximums. Students are instructed to watch video lectures and then attempt the practice problems, relying on additional materials and instructors as needed.

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134 views6 pages

Workbook PDF

This document provides instructions and practice problems for students taking a quantitative tools course at the Indian School of Business. The problems cover topics like applying the order of operations, calculating areas of geometric shapes, graphing and deriving linear equations, solving systems of linear and quadratic equations, taking derivatives of functions, and solving optimization problems to find minimums and maximums. Students are instructed to watch video lectures and then attempt the practice problems, relying on additional materials and instructors as needed.

Uploaded by

Ankit
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Workbook for Quantitative Tools for Economics

Kalyani Chaudhuri and Tarun Jain∗

Indian School of Business

April 8, 2018

Instructions: These problems correspond to the videos titled “Quantitative Tools for Economics”
for Managerial Economics students at ISB. Students should watch the videos and then attempt
the practice problems. You may rely on additional materials such as textbooks, the instructor and
academic associate to clarify any questions. The answers are not required to be turned in and will
not be graded.

∗
Comments and suggestions for improvement are welcome. Please email tarun jain@isb.edu

1
BODMAS Rule and Geometry
Simplify the following expressions using the BODMAS rule.

1. 17 + (8 − 5) ∗ 5
2. 25 − 48
6
+ 12 ∗ 2
3. 2 + (3∗15)−10
2
+ (5+1)
3

4. 7 + (6 ∗ 52 ) + 3
15
− 10 ∗ 33

2
Calculate the area of the triangle:
5.

6.

7.

Calculate the area of the rectangle ABCD and the triangle DCE:
8.

3
Functions
Graph the following linear functions.

1. y = x + 3
2. p = 2q + 4
3. f (x) = − 13 x − 1
2

Derive equations for the following lines.

4. The line passes through the points (3,4) and (5,1)


5. The line passes through the points (4,-3) and (3,1)
6. The line passes through the point (4,3) and has the slope -2
7. The line passes through the point (-2,5) and has the slope 3

Solve the following pairs of linear equations.

8. x − 2y = 0 and 3x + 4y = 20
9. x + 2y = 4 and 2x + 4y = 12

Solve for x in the following quadratic equations (Hint: Think of the graph of each equation).

10. y = x2 − 2
11. y = x2 + 4
12. y = 4x2 + 1

Solve for x in the following quadratic equations (Hint: Use the quadratic formula).

13. y = x2 + 6x − 14
14. y = 8x2 + 14x − 15
15. y = 16 x2 + 43 x − 2
3

4
Calculus
Find the derivative w.r.t. x for each of the following functions.

1. f (x) = 2x
2. f (x) = 4
3. f (x) = 5x + 10
4. f (x) = 3log(x) + 4x − 2
5. f (x) = 12x5 + 3x4 + 7x3 + x2 − 9x + 6
6. f (x) = 8x3 − 2
7. f (x) = 4xlogx (Hint: Use the product rule)
8. f (x) = x2 logx + 2x
9. f (x) = 2
x+1
(Hint: Use the quotient rule)
x2
10. f (x) = 3x−1

5
Optimization

Find the point at which the slope of this function is 0.

1. y = x2 − 4
2. y = 2x2 + 5

Find the point at which the function is minimized.

3. y = x2
4. y = −(x + 4)2 − 7

Find the point at which the function is maximized.

5. y = (x − 3)2 + 4
6. y = −12x2

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