IM2 Review 1

IM2 Review 1

Information covered weeks 1 - 12

Part 1 Geometry

Area, Volume, Similar Triangles, Basic Trigonometric Functions

Important Formulas

• Area of a rectangle =  $\left(length\right)\left(width\right)$  

• Area of a triangle =   $\frac{1}{2}\left(base\right)\left(height\right)$  

• Volume of a sphere =  $\frac{4}{3}\pi r^3$ 

Important Triangle Information

• Triangles can be similar by AA, SAS, SSS

• Similar Triangles - angles are congruent, sides are proportional

•  $\cos\theta\ =\ \frac{adjacent}{hypotenuse}$  

•  $\sin\ \theta\ =\ \frac{opposite}{hypotenuse}$  

•  $\tan\ \theta\ =\ \frac{opposite}{adjacent}$  

Multiple Choice

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA

• SAS

• SSS

• Not Similar

Multiple Choice

Sarah is making a rectangular blanket. The length of the blanket is 5 inches greater than its width, w, in inches. Which function, f (w), describes the area, in square inches, of Sarah’s blanket as a function of the width, w.

• $f\left(w\right)=2w\ +\ 10$

• $f\left(w\right)\ =\ w\left(w\ -\ 10\right)$

• $f\left(w\right)=\left(w+10\right)w$

• $f\left(w\right)=\left(10w\right)\left(w\right)$

Multiple Choice

What is the length of side x?

• 6.57 cm

• 7 cm

• 7.44 cm

• 26.33 cm

Multiple Choice

In the figure shown, cos(w˚) = 0.40. What is sin(x˚)?

• 0.30

• 0.40

• 0.50

• 0.70

Multiple Choice

​ △ RST ∼ △ UVW . The dilation that maps △ RST to

△ UVW has a dilation factor of 1/2 . The measure of angle R is 30° and the measure of angle S is 100°.

What is the measure, in degrees, of angle W?​

• 20

• 30

• 50

• 70

Multiple Choice

Marcus is looking up at the top of a tree. He is standing 20 feet from the tree, and his line of sight is 35° from horizontal. His eyes are 5 feet above the ground.

To the nearest foot, how tall is the tree?

• 10 feet

• 12 feet

• 15 feet

• 19 feet

Multiple Choice

Find the Volume of the Sphere. ***Radius is half the diameter*** 

 $V=\frac{4}{3}\pi r^3$  

• 904.32 ft3

• 150.72 ft3

• 7,234.56 ft3

Polynomials

• Add like terms

• When subtracting change the signs in the second ( )

• Multiply by using the distributive property

Multiple Choice

Subtract the polynomial  $\left(4n^4-8n+4\right)-\left(8n^2+4n^4+1\right)$   

•  $-8n^2-8n+3$  

•  $-7n^2-8n+3$  

•  $-6n^2-8n+3$  

•  $-7n^2-4n+3$  

Multiple Choice

 $\left(x+7\right)\left(x+9\right)$  

Multiply the polynomial

•  $x^2+63x+16$  

•  $x^2+16x+63$  

•  $x^2+79$  

•  $x^2+16x+2$  

Multiple Choice

​ Factor the polynomial: 

 $s^2+12s+32$  

• (s+4)(s-8)

• (s-2)(s+16)

• (s+16)(s+2)

• (s+4)(s+8)

Quadratic Functions

• Polynomials with a highest exponent of 2

• Shape is a parabola

• Standard form   $f\left(x\right)=\ ax^2+bx+c$   

  
  

• Vertex Form  $f\left(x\right)=a\left(x-h\right)^2+k$  

Multiple Choice

Here is a pattern of squares. represents the number of small squares in the pattern as a function of , the step number.

Which expression could define ?

• $3n$

• $n+3$

• $n^2+2$

• $n^2+3$

Multiple Select

Consider the equation 3(x – 5)² + 6 = 54. What value(s) of x makes the equation true?

• x = 0

• x = 1

• x = 5

• x = 9

Multiple Choice

Consider the equation  $x^2-12x+27=0$ .  Which equation has the same solution(s) as the given equation?​

•  $\left(x-6\right)^2-9=0$  

•  $\left(x-7\right)^2-22=0$  

•  $\left(x-7\right)^2-4.7=0$  

•  $\left(x-12\right)^2-27=0$