Review 1

Multiple Choice

Probability is defined as...

• ...the likelihood that an event will occur.

• ...a game that involves coins.

• ...a guarantee.

Multiple Choice

A poll asked 25 people which gift was their favorite.

The gift of _____ had a probability of 4/25 of being picked.

• Flowers
• Perfume
• Jewelry
• Clothes

Multiple Choice

The spinner is spun 20 times. Predict how many times the spinner should land on blue.

• 0 times

• 5 times

• 10 times

• 20 times

Multiple Choice

A jar contains 2 pink, 6 red, and 4 blue marbles. If you pick one marble without looking, what is the probability that the marble you pick will be red or blue?

• 5/6
• 1/2
• 1/3
• 1/6

Multiple Choice

What determines if a quadratic will have complex solutions?

• The a-value

• The discriminant is a perfect square

• The discriminant is negative

• The x-intercepts are decimals

Multiple Choice

What are the solutions of the function f(x) = x² + 64?

• -8 and 8
• -8i and 8i
• $$-\sqrt[]{8}\ i$$ and $$\sqrt[]{8}\ i$$  

• $$-\ \sqrt[]{8}$$  and $$\sqrt[]{8}$$  

Multiple Choice

Find the solutions of the equation

$$-2x^2-3x-9$$  

• $$\left\{\frac{3+3i\sqrt{7}}{-4},\frac{3-3i\sqrt{7}}{-4}\right\}$$

• $$\left\{-3i\sqrt{7},3i\sqrt{7}\right\}$$

• $$\left\{-63,63\right\}$$

Multiple Choice

Solve for x: 

$$x^2-4x+5=0$$  

• x = $$\left\{-4,\ -1\right\}$$  

• x = $$2\pm2i$$  

• x = $$2\pm i$$  

• x = $$-2\pm i$$  

Multiple Choice

A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle? 

• 6
• 8
• 3
• 19

Example 3.

​The area of a rectangle is 40 cm². If the length is 3 cm longer than the width, find the dimension of the rectangle.

Solution:

​

Let A = the area of the rectangle

w = width of the rectangle​​

l = w + 3 = length of the rectangle

​

​

The area of a rectangle is 40 cm². If the length is 3 cm longer than the width, find the dimension of the rectangle.

Solution:

​

A = lw

A = (w + 3)w

40 = w² + 3w

w² + 3w - 40 = 0

(w + 8)(w - 5) = 0​

​

w + 8 = 0​

w = -8​

​

w - 5 = 0​

w = 5​

​

w + 8 = 0​

w = -8​

​

Thus, the width is 5 cm and the length is w + 3 = 5 + 3 = 8 cm.