SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Calculus

Grade: Top-SAT3 Lesson: S6-P1

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: in Class

Problem Id	Problem	Options
1	Solve the equation \$ (x^2 + 3x + 2)/(x + 2) \$ = 4.	A) x = 4 and x = - 3 B) x = 3 and x = 2 C) x = - 5 and x = 4 D) x = 3 and x = - 2
2	The equation \$e^4x + 8e^3x + 13e^2x - 8e^x + 1 = 0\$, x ∈ R has:	A) Two solutions and only one of them is negative. B) Two solutions and both are negative. C) Four solutions two of which are negative. D) No solution.
3	Find the limit \$lim_(x->∞) ((x^2 + x + 1) / (3x + 2)^2)\$.	A) 0 B) \$1/9\$ C) 1 D) \$1/3\$
4	Let λ ≠ 0 be a real number. Let α, β be the roots of the equation \$14x^2 - 31x + 3λ\$ = 0 and α, γ be the roots of the equation \$35x^2 - 53x + 4λ\$ = 0. Then \$(3α) / β\$ and \$(4α) / γ\$ are the roots of the equation.	A) \$7x^2 - 245x + 250 = 0\$ B) \$49x^2 + 245x + 250 = 0\$ C) \$49x^2 - 245x + 250 = 0\$ D) \$7x^2 + 245x - 250 = 0\$
5	Which of the following could be the graph of \$y = k(x - 2 )^m (x + 1)^n\$, where k is a real number, m is an even integer, and n is an odd integer?	A) $5a$ B) $5b$ C) $5c$ D) $5d$
6	Find the x-values for which \$"f(x)" = 2/(sqrt(1 - x))\$ continuous.	A) (∞, 4) B) (− ∞, 3) C) (− ∞, 1) D) (∞, 2)
7	Solve each of the inequalities \$x^6 - 4x^4 - 16x^2 + 64 ≥ 0\$.	A) \$ x ∈ (- ∞, - 2) ∪ (2, ∞)\$ B) \$ x ∈ (- ∞, - 1) ∪ (1, ∞)\$ C) \$ x ∈ (- ∞, - 2) \$ D) \$ x ∈ (2, ∞)\$
8	If the quadratic equation \$x^2 + px + q = 0\$ has roots α and 𝛽, \$α^2 + β ^2 = 7\$ and α + β =3 , find the values of p and q.	A) p = - 3 and q = - 1 B) p = 3 and q = 1 C) p = 3 and q = - 1 D) p = - 3 and q = 1
9	Rahul and Rohan have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with.	A) x = - 36, x = - 9 B) x = 36, x = 9 C) x = 36, x = - 9 D) x = - 36, x = 9
10	Find the horizontal and vertical asymptotes of \$ f(x)= (3x^2-9x)/ (x^2-9) \$.	A) Horizontal Asymptote: y = 3 Vertical Asymptotes: x = ± 4 B) Horizontal Asymptote: y = 3 Vertical Asymptotes: x = 3 C) Horizontal Asymptote: y = 3 Vertical Asymptotes: x = ± 3 D) Horizontal Asymptote: y = 4 Vertical Asymptotes: x = ± 3

Problem Id

Problem

Options

Solve the equation
\$ (x^2 + 3x + 2)/(x + 2) \$ = 4.

A) x = 4 and x = - 3

B) x = 3 and x = 2

C) x = - 5 and x = 4

D) x = 3 and x = - 2

The equation \$e^4x + 8e^3x + 13e^2x - 8e^x + 1 = 0\$, x ∈ R has:

A) Two solutions and only one of them is negative.

B) Two solutions and both are negative.

C) Four solutions two of which are negative.

D) No solution.

Find the limit \$lim_(x->∞) ((x^2 + x + 1) / (3x + 2)^2)\$.

A) 0

B) \$1/9\$

C) 1

D) \$1/3\$

Let λ ≠ 0 be a real number. Let α, β be the roots of the equation \$14x^2 - 31x + 3λ\$ = 0 and α, γ be the roots of the equation \$35x^2 - 53x + 4λ\$ = 0. Then \$(3α) / β\$ and \$(4α) / γ\$ are the roots of the equation.

A) \$7x^2 - 245x + 250 = 0\$

B) \$49x^2 + 245x + 250 = 0\$

C) \$49x^2 - 245x + 250 = 0\$

D) \$7x^2 + 245x - 250 = 0\$

Which of the following could be the graph of \$y = k(x - 2 )^m (x + 1)^n\$, where k is a real number, m is an even integer, and n is an odd integer?

A) $5a$

B) $5b$

C) $5c$

D) $5d$

Find the x-values for which \$"f(x)" = 2/(sqrt(1 - x))\$ continuous.

A) (∞, 4)

B) (− ∞, 3)

C) (− ∞, 1)

D) (∞, 2)

Solve each of the inequalities \$x^6 - 4x^4 - 16x^2 + 64 ≥ 0\$.

A) \$ x ∈ (- ∞, - 2) ∪ (2, ∞)\$

B) \$ x ∈ (- ∞, - 1) ∪ (1, ∞)\$

C) \$ x ∈ (- ∞, - 2) \$

D) \$ x ∈ (2, ∞)\$

If the quadratic equation \$x^2 + px + q = 0\$ has roots α and 𝛽, \$α^2 + β ^2 = 7\$ and α + β =3 , find the values of p and q.

A) p = - 3 and q = - 1

B) p = 3 and q = 1

C) p = 3 and q = - 1

D) p = - 3 and q = 1

Rahul and Rohan have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with.

A) x = - 36, x = - 9

B) x = 36, x = 9

C) x = 36, x = - 9

D) x = - 36, x = 9

Find the horizontal and vertical asymptotes of \$ f(x)= (3x^2-9x)/ (x^2-9) \$.

A) Horizontal Asymptote: y = 3
Vertical Asymptotes: x = ± 4

B) Horizontal Asymptote: y = 3
Vertical Asymptotes: x = 3

C) Horizontal Asymptote: y = 3
Vertical Asymptotes: x = ± 3

D) Horizontal Asymptote: y = 4
Vertical Asymptotes: x = ± 3