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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Algebra

Grade: Top-SAT3 Lesson: S5-P2

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	\$2/(x - 2) + 3/ (x + 5) = (rx + t) /((x -2) (x - 5)) \$ The equation above is true for all x > 2, where r and t are positive constants. What is the value of rt?	A) 89 B) 26 C) 48 D) 60
2	\$(ax + b) (5x^2 - bx + 4) = 20x^3 - 9x^2 - 2x + 12\$ The equation above is true for all x, where a and b are constants. What is the value of ab?	A) 19 B) 24 C) 35 D) 31
3	\$57x^2 + (57b + a)x + ab = 0\$ In the given equation, a and b are positive constants. The product of the solutions to the given equation is kab , where is k a constant. What is the value of k?	A) 19 B) \$1/(57)\$ C) 57 D) \$1/(19)\$
4	\$x^2 - 2x - 9 = 0\$ One solution to the given equation can be written as \$1 + \sqrt(k)\$, where k is a constant. What is the value of k?	A) 25 B) 20 C) 10 D) 30
5	A 3D object is represented by the system of equations: x + 2y + z = 5 The system has infinitely many solutions. Which of the following equations could describe another line/plane that is part of the same 3D object?	A) x + 2y + 2z = 7 B) 2x + 4y + 2z = 10 C) 3x + 6y + 3z = 12 D) x - y + z = 0
6	In the system of equations below, a and c are constants. \$ (1/2)x + (1/3)y = (1/6) \$ \$ ax + y = c\$ If the system of equations has an infinite number of solutions(x,y), what is the value of a?	A)\$ - 1/2 \$ B) 0 C) \$ 3/2 \$ D) \$ 1/2 \$
7	One of the two equations in a linear system is 2x + 6y = 10. The system has no solution. Which of the following could be the other equation in the system?	A) x + 3y = -20 B) 6x + 2y = 10 C) 6x - 2y = 0 D) x + 3y = 5
8	The two linear equations sx - 5y = 2 and 6x + 2y = 7, which have no solution, and we have to find the value of s which is the coefficient of x?	A) - 30 B) 15 C) 30 D) - 15
9	\$f(x) = x^3 - 9x\$, \$g(x) = x^2 - 2x - 3\$ Which of the following expressions is equivalent to \$f(x)/g(x)\$, for x > 3?	A) \$(x - 3)/ (x - 1)\$ B) \$(x(x + 3))/ (x + 1)\$ C) \$(x + 3)/ (x - 1)\$ D) \$(x(x - 3))/ (x + 1)\$
10	\$1/(x^2 + 10x + 25) = 4\$ If x is a solution to the given equation, which of the following is a possible value of x + 5?	A) \$5/2\$ B) \$11/2\$ C) \$1/2\$ D) \$9/2\$

Problem Id

Problem

Options

\$2/(x - 2) + 3/ (x + 5) = (rx + t) /((x -2) (x - 5)) \$
The equation above is true for all x > 2, where r and t are positive constants. What is the value of rt?

A) 89

B) 26

C) 48

D) 60

\$(ax + b) (5x^2 - bx + 4) = 20x^3 - 9x^2 - 2x + 12\$
The equation above is true for all x, where a and b are constants. What is the value of ab?

A) 19

B) 24

C) 35

D) 31

\$57x^2 + (57b + a)x + ab = 0\$
In the given equation, a and b are positive constants. The product of the solutions to the given equation is kab , where is k a constant. What is the value of k?

A) 19

B) \$1/(57)\$

C) 57

D) \$1/(19)\$

\$x^2 - 2x - 9 = 0\$
One solution to the given equation can be written as \$1 + \sqrt(k)\$, where k is a constant. What is the value of k?

A) 25

B) 20

C) 10

D) 30

A 3D object is represented by the system of equations: x + 2y + z = 5
The system has infinitely many solutions. Which of the following equations could describe another line/plane that is part of the same 3D object?

A) x + 2y + 2z = 7

B) 2x + 4y + 2z = 10

C) 3x + 6y + 3z = 12

D) x - y + z = 0

In the system of equations below, a and c are constants.
\$ (1/2)x + (1/3)y = (1/6) \$
\$ ax + y = c\$
If the system of equations has an infinite number of solutions(x,y), what is the value of a?

A)\$ - 1/2 \$

B) 0

C) \$ 3/2 \$

D) \$ 1/2 \$

One of the two equations in a linear system is 2x + 6y = 10. The system has no solution. Which of the following could be the other equation in the system?

A) x + 3y = -20

B) 6x + 2y = 10

C) 6x - 2y = 0

D) x + 3y = 5

The two linear equations sx - 5y = 2 and 6x + 2y = 7, which have no solution, and we have to find the value of s which is the coefficient of x?

A) - 30

B) 15

C) 30

D) - 15

\$f(x) = x^3 - 9x\$, \$g(x) = x^2 - 2x - 3\$
Which of the following expressions is equivalent to \$f(x)/g(x)\$, for x > 3?

A) \$(x - 3)/ (x - 1)\$

B) \$(x(x + 3))/ (x + 1)\$

C) \$(x + 3)/ (x - 1)\$

D) \$(x(x - 3))/ (x + 1)\$

\$1/(x^2 + 10x + 25) = 4\$
If x is a solution to the given equation, which of the following is a possible value of x + 5?

A) \$5/2\$

B) \$11/2\$

C) \$1/2\$

D) \$9/2\$