TMAL Practice #1 (Very Hard)

Word Problems

100

Find the (quadratic) equation of the line which has a horizontal shift of 2 units to the right.

Assume the original equation is y = x²

What is

y = (x - 2)²

200

Imagine we have two numbers; the larger number is 4 more than twice the smaller number. 

Develop an equation for finding the larger number.

What is

2x + 4

300

Find the (quadratic) equation of the line which has a horizontal shift of 4 units to the left and 3 units downward.

Assume the original equation is y = x².

What is

y = (x+4)²-3

400

Find the (quadratic) equation of the line which has a horizontal shift of 2 units to the right and is reflected across the y-axis?

Assume the original equation is y = x²

What is

y = -(x - 2)²

500

The length of one leg of a right triangle is three times as large as the length of the other leg. If the hypotenuse has a length of 10 inches, what is the perimeter of the triangle in inches?

What is

10 + 4√10

Shapes/Radians

100

Convert to degrees:

4π

What is

360°

200

Convert to radians:

330°

What is

11π/3 

300

What is the Pythagorean Theorem IDENTITY?

sin²(θ) + cos²(θ)  = 1

400

Simplify the following:

2sin(x)cos(x)

What is sin(2x)?

(Double-Angle Identity)

500

Simplify the following:

cos(α) cos(b) – sin(α) sin(b)

What is cos(α + b)?

(Angle Sum/Difference Identity)

Imaginary Numbers

100

Evaluate the following (in radical form):

i³

What is -√-1?

200

Evaluate the following:

i²

What is -1?

300

Evaluate the following:

√-64x²

What is 8xi?

400

Evaluate the following:

√-121x³

What is

11x√-x

500

Evaluate the following:

√-200x⁵y²

What is 

10x²y√-2x

Algebra 2

100

Solve for all values of x: x3 - 3x2 + 4x - 12 = 0

x = 3, 2i, -2i

200

Factor Completely: x8 + 9x6 - x2 - 9

(x - 1)(x + 1)(x² + x + 1)(x² - x + 1)((x² + 9)

300

Solve the equation: |x + 3| = |2x - 3|

x = 0,6

400

Find all possible values for x. |2x - 5| < x + 1

4/3 < x < 6

500

Factor Completely: x⁴ + x² + 1

(x² + x + 1)(x² - x + 1)

Trivia

100

Who is the president of NSBE?

Izaiah Jackson 

200

In what year was NSBE established?

What is 1975?

300

What region of NSBE is our school chapter located in?

(Region I, II, III, IV, V, VI)

What is Region II?

(Pennsylvania, Maryland, DC, Delaware, Virginia, West Virginia, North Carolina, South Carolina)

400

What is the "Chicago Six"?

What is the original founders of NSBE?

Edward A. Coleman | Anthony Harris | Brian Harris | Stanley L. Kirtley | John W. Logan Jr. | George A. Smith

500

What is NSBE's official mission statement?

What is "to increase the number of culturally responsible black engineers who excel academically, succeed professionally, and positively impact the community"?