Algebra EOC Review: Unit 3 Real Numbers & Unit 4 Quadratics

​Sum and Product of Rational and Irrational Numbers

​Use Desmos to check your
sum and product!

Multiple Choice

Which value is a rational number?

• $$\pi+18$$

• $$\sqrt[]{25}+1.75$$

• $$\sqrt[]{3}+5.5$$

• $$\pi+\sqrt[]{2}$$

Multiple Choice

Which value is an irrational number?

• $$\sqrt[]{2}\cdot\sqrt[]{50}$$

• $$\sqrt[]{64}\cdot\sqrt[]{4}$$

• $$\sqrt[]{9}\cdot\sqrt[]{49}$$

• $$\sqrt[]{10}\cdot\sqrt[]{8}$$

​Simplifying Radicals

​Operations with Radicals

Match

Match the equivalent radical expressions.

• $$2\sqrt[]{90}$$

• $$2\sqrt[]{2}\cdot\sqrt[]{3}$$

• $$2\sqrt[]{3}+2\sqrt[]{3}$$

• $$\sqrt[]{60}\cdot\sqrt[]{10}$$

• $$6\sqrt[]{10}$$

• $$2\sqrt[]{6}$$

• $$4\sqrt[]{3}$$

• $$10\sqrt[]{6}$$

Multiple Choice

$$The\ side\ lengths\ of\ a\ triangle\ are\ \sqrt{2},\ \sqrt{8},\ and\ \sqrt{18}.\ \ What\ is\ the\ perimeter\ of\ the\ triangle?\ \$$  

• $$\sqrt[]{28}$$

• $$6\sqrt[]{2}$$

• $$6\sqrt[]{6}$$

• $$5\sqrt[]{2}$$

Multiple Choice

In which expression is the coefficient of the n term –1?

• 3n² + 4n - 1

• -n² + 5n + 4

• -2n² - n + 5

• 4n² + n - 5

​1

​1

Multiple Choice

Which expression has the same value as the given expression? $$(8x^2+2x-6)-(5x^2-3x+2)$$  

• $$3x^2-x-4$$  

• $$3x^2+5x-8$$  

• $$13x^2-x-8$$  

• $$13x^2-5x-4$$  

Multiple Choice

What is the perimeter of the rectangle?

• x²+8x-5

• 2x²+16x-10

• 2x²+10x-8

• 6x-2

Multiple Choice

The length of a rectangle is (4x + 9) and the width is (5x - 7).

What is the area of the rectangle? (A = L x W)

• 9x + 2

• 20x - 63

•  20x² + 17x - 63

•  20x² + 73x + 63

Multiple Choice

The area of a rectangle is x² + 4x. Which could be the length and width of the rectangle? (A = L x W) 

• Length: x; Width: x + 4

• Length: x; Width: x² + 4

• Length: x²; Width: 4x

• Length: x; Width: 4x

Drag and Drop

Move an expression into each box to show the factored form of the given quadratic expression. 5x² - 6x - 8 =

Placeholder

​

Placeholder

Drag these tiles and drop them in the correct blank above

(5x - 4)

(x + 2)

(x - 2)

(5x + 4)

​points on the x-axis

Multiple Choice

What is the factored form of f(x) that reveals the zeros of the function?

$$f(x)=x^2+6x+8$$  

• f(x) = (x + 2)(x + 3)

• f(x) = (x + 2)(x + 4)

• f(x) = (x + 3)(x + 5)

• f(x) = (x + 1)(x + 8)

Multiple Choice

What is the equivalent form of f(x) that reveals the minimum value of the function?

$$f(x)=x^2+6x+8$$  

• $$f(x)=(x+3)^2-1$$  

• $$f\left(x\right)=(x+3)^2$$  

• $$f(x)=(x-1)^2+3$$  

• $$f(x)=(x-3)^2-1$$  

​Key Features of Quadratic Function

Multiple Choice

What is the vertex of the graph of $$f(x)=x^2+10x-9$$  ?

• (5, 66)

• (5, -9)

• (-5, -9)

• (-5, -34)

Multiple Choice

What are the solutions of the quadratic equation x² + 4x + 1 = 0?

• $$x=-2\pm\sqrt{3}$$

• $$x=-3\pm\sqrt{2}$$

• $$x=2\pm\sqrt{3}$$

• $$x=2\pm\sqrt{2}$$

Multiple Choice

The expression $$-x^2+70x-600$$   represents a company’s profit for selling x items. For which number(s) of items sold is the company’s profit equal to $0?

• 0 items

• 35 items

• 10 items and 60 items

• 20 items and 30 items

Labelling

Label each part of the graph.

Drag labels to their correct position on the image

Y-INTERCEPT

AXIS OF SYMMETRY

X-INTERCEPT

VERTEX

Multiple Choice

A soccer ball kicked off the ground has height modeled by the function $$H\left(t\right)=-t^2+6t$$ , where t is the number of seconds since the ball was kicked and H(t) is the height in meters. What is the maximum height reached by the ball?

• 3 meters

• 6 meters

• 9 meters

• 27 meters

Multiple Choice

Which function is shown on the graph?

• $$f\left(x\right)=x^2-3x-10$$  

• $$f\left(x\right)=x^2+3x-10$$  

• $$f\left(x\right)=x^2+x-12$$  

• $$f\left(x\right)=x^2-5x-8$$  

Multiple Choice

Which of the following is the equation for g(x) after a transformation of the parent function f(x)?

• g(x) = (x + 3)²
• g(x) = (x - 3)²
• g(x) = x² + 3
• g(x) = x² - 2

Multiple Choice

Describe the transformation of f(x) = x² to g(x) = -3x².

• reflection across the x-axis and vertical shift down

• reflection across the x-axis and vertical stretch

• horizontal stretch
• reflection across the x-axis and vertical compression