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1.

Using the Quotient Rule, the derivative of y = (x + 3) / (x - 2) for x != 2 is:

1 / (x - 2)²

5 / (x - 2)²

-5 / (x - 2)²

(2x + 1) / (x - 2)²

2.

According to the Chain Rule, if y = (3 x² - 5)⁴, then dy/dx is:

24 x (3 x² - 5)³

12 x (3 x² - 5)⁴

6 x (3 x² - 5)³

4 (3 x² - 5)³

3.

The second derivative d²y/dx² of the function y = x⁴ - 2 x³ + 5 is:

12 x² - 6 x

12 x² - 12 x

4 x³ - 6 x²

24 x - 12

4.

If $^nP_2 = 56$, then the value of $n$ is:

D) 10

A) 7

B) 8

C) 9

5.

If two vectors $\vec{A} = (2, k, -3)$ and $\vec{B} = (4, 2, 6)$ are perpendicular, then the value of $k$ is:

A) 5

C) 10

B) -5

D) -10

6.

When using integration by parts on $\int x \ln x\, dx$, according to the LIATE rule, the choice for $u$ should be:

C) $x ln x$

B) $ln x$

A) $x$

D) $dx$

7.

What is the rigorous mathematical principle for: Chain Rule and Implicit Differentiation?

The derivative of a product is simply the product of individual derivatives

dy/dx equals (du/dx) divided by (dy/du)

If y = f(u) and u = g(x), then dy/dx = (dy/du) * (du/dx); for implicit curves f(x, y) = c, differentiate term by term treating y as a function of x

Implicit differentiation requires isolating y explicitly in every case

Curriculum

Mathematics

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Unit 6

Unit 7

Lesson 1 Quiz: Counting Principle, Permutations (nPr) and Combinations (nCr)

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