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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Algebra

Grade: Best-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: at Home

Problem Id	Problem	Options
1	\$ - x^2 + bx - 676 = 0\$ In the given equation, b is a positive integer. The equation has no real solution. What is the greatest possible value of b?	A) 51 B) 50 C) 48 D) 41
2	If there is no solution to the linear equation system \$ (20 \times 2)m = 36 - dn\$, \$20m = 16 + 4n\$, then find the value of d + 12.	A) 1 B) 2 C) 3 D) 4
3	Find the values of x that make the following expressions equivalent: \$ -(x^2 - x - 2) / (x + 2) < 0 \$.	A) \$ − 1 < x < − 1 and x > 2 \$ B) \$ − 2 < x < −1 and x > 2 \$ C) \$ − 2 < x < − 4 and x > 2 \$ D) \$ − 2 < x < − 3 and x > - 2 \$
4	Analyze the following system to find the conditions under which it has infinite solutions: 2x − y + 3z = 7 4x − 2y + 6z = 14 6x − 3y + mz = 21	A) m = 7 B) m = 8 C) m = 9 D) m = 10
5	Two workers, C and D, can complete a painting job together in 8 hours. Worker C alone can complete the job in 12 hours. Write an expression for the time it takes worker D to complete the job alone, and solve for it.	A) 20 hrs B) 18 hrs C) 28 hrs D) 24 hrs
6	For what values of a and b does the following system of linear equations have infinitely many solutions? ax + by = 1 (a + b)x + (a + 2b)y = 2	A) a ≠ 1 and b ≠ 1 B) a = 0 and b ≠ 2 C) a = 0 and b ≠ 0 D) a = 1 and b ≠ 0
7	A gardener plants flowers in a rectangular garden. The total number of flowers planted is 300. If she plants 15 rows of daisies and 10 rows of tulips, she uses 300 flowers. If she plants 10 rows of daisies and 15 rows of tulips, she also uses 300 flowers. Find the number of daisies and tulips planted in each row.	A) 12 B) 21 C) 24 D) 18
8	If b and d are positive numbers, which of the following is equivalent to \$\sqrt((b + d)^2)\$. \$\sqrt((b + d))\$?	A) \$(b + d)^2\$ B) \$(b + d)^4\$ C) \$(b - d)^4\$ D) b + d
9	A mixture of sugar and flour contains 20% sugar. Another mixture contains 30% sugar. How much of each mixture should be combined to create 100 kg of a mixture that is 25% sugar ?	A) 40 kg of the 20% sugar mixture and 60 kg of the 30% sugar mixture. B) 70 kg of the 20% sugar mixture and 30 kg of the 30% sugar mixture. C) 50 kg of the 20% sugar mixture and 50 kg of the 30% sugar mixture. D) 60 kg of the 20% sugar mixture and 40 kg of the 30% sugar mixture.
10	Find all real solutions to \$\sqrt(x + 3) - \sqrt(x) = 1\$.	A) x = 1 B) x = 2 C) x = \$1/2\$ D) x = - 1

Problem Id

Problem

Options

\$ - x^2 + bx - 676 = 0\$

In the given equation, b is a positive integer. The equation has no real solution. What is the greatest possible value of b?

A) 51

B) 50

C) 48

D) 41

If there is no solution to the linear equation system
\$ (20 \times 2)m = 36 - dn\$,
\$20m = 16 + 4n\$, then find the value of d + 12.

A) 1

B) 2

C) 3

D) 4

Find the values of x that make the following expressions equivalent:
\$ -(x^2 - x - 2) / (x + 2) < 0 \$.

A) \$ − 1 < x < − 1 and x > 2 \$

B) \$ − 2 < x < −1 and x > 2 \$

C) \$ − 2 < x < − 4 and x > 2 \$

D) \$ − 2 < x < − 3 and x > - 2 \$

Analyze the following system to find the conditions under which it has infinite solutions:
2x − y + 3z = 7
4x − 2y + 6z = 14
6x − 3y + mz = 21

A) m = 7

B) m = 8

C) m = 9

D) m = 10

Two workers, C and D, can complete a painting job together in 8 hours. Worker C alone can complete the job in 12 hours. Write an expression for the time it takes worker D to complete the job alone, and solve for it.

A) 20 hrs

B) 18 hrs

C) 28 hrs

D) 24 hrs

For what values of a and b does the following system of linear equations have infinitely many solutions?
ax + by = 1
(a + b)x + (a + 2b)y = 2

A) a ≠ 1 and b ≠ 1

B) a = 0 and b ≠ 2

C) a = 0 and b ≠ 0

D) a = 1 and b ≠ 0

A gardener plants flowers in a rectangular garden. The total number of flowers planted is 300. If she plants 15 rows of daisies and 10 rows of tulips, she uses 300 flowers. If she plants 10 rows of daisies and 15 rows of tulips, she also uses 300 flowers. Find the number of daisies and tulips planted in each row.

A) 12

B) 21

C) 24

D) 18

If b and d are positive numbers, which of the following is equivalent to \$\sqrt((b + d)^2)\$. \$\sqrt((b + d))\$?

A) \$(b + d)^2\$

B) \$(b + d)^4\$

C) \$(b - d)^4\$

D) b + d

A mixture of sugar and flour contains 20% sugar. Another mixture contains 30% sugar. How much of each mixture should be combined to create 100 kg of a mixture that is 25% sugar ?

A) 40 kg of the 20% sugar mixture and 60 kg of the 30% sugar mixture.

B) 70 kg of the 20% sugar mixture and 30 kg of the 30% sugar mixture.

C) 50 kg of the 20% sugar mixture and 50 kg of the 30% sugar mixture.

D) 60 kg of the 20% sugar mixture and 40 kg of the 30% sugar mixture.

Find all real solutions to \$\sqrt(x + 3) - \sqrt(x) = 1\$.

A) x = 1

B) x = 2

C) x = \$1/2\$

D) x = - 1