Algebraic Concepts and Problem Solving

Algebraic Concepts and Problem Solving

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to solve a system of equations involving x^2 + y^2 = 25 and 2x + y = 10. The instructor first isolates y in the linear equation and substitutes it into the quadratic equation. After expanding and simplifying, the quadratic is factored to find possible x values. Corresponding y values are determined, and the possible values of x + y are evaluated. The solutions are also represented graphically, showing the intersection points of the equations.

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17 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the two equations given in the problem?

x^2 + y^2 = 20 and 2x + y = 15

x^2 + y^2 = 15 and 2x + y = 20

x^2 + y^2 = 10 and 2x + y = 25

x^2 + y^2 = 25 and 2x + y = 10

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving the equation 2x + y = 10?

Multiply both sides by 2

Subtract 2x from both sides

Add 2x to both sides

Divide both sides by 2

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

After isolating y, what expression do we substitute into x^2 + y^2 = 25?

2x + 10

2x - 10

10 - 2x

10 + 2x

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of expanding (10 - 2x)^2?

100 + 20x + 4x^2

100 - 20x + 4x^2

100 + 40x + 4x^2

100 - 40x + 4x^2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What do you get when you combine x^2 and 4x^2?

3x^2

5x^2

6x^2

7x^2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified form of the equation after dividing by 5?

x^2 + 8x - 15 = 0

x^2 - 8x - 15 = 0

x^2 + 8x + 15 = 0

x^2 - 8x + 15 = 0

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which pair of numbers adds to -8 and multiplies to 15?

3 and -5

-3 and -5

3 and 5

-3 and 5

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