FTCE Mathematics 6-12 Practice Version 2 Day 2

​FTCE Mathematics 6-12 Practice Test Version 2 Day 2

Multiple Choice

Two lines that are parallel will have ...#76

• negative reciprocal slopes

• No slope

• equal slopes

• none of the above

Multiple Choice

What is the equation of a line parallel to the following line that passes through the given point?

y = -4x + 6 (2, -1) #71

• y = 1/4x + 6

• y = -4x + 7

• y = -4x + 2

• y = 1/4x -1

Multiple Choice

y = -2/3x + 2

y = 3/2x + 9

These lines are...#72

• Parallel

• Perpendicular

• Neither

Multiple Choice

Write an equation for a line perpendicular to

y = -5x + 3 through (-5, -4). #73

• y = -3x + 1/5

• y = -3x - 1/5

• y = 1/5x - 3

• y = -1/5x - 3

Multiple Choice

Write an equation of a line that passes through the point (-9,2) and is perpendicular to the line y = 3x - 12. #74

• y = (-1/3)x - 1

• y = (1/3)x - 2

• y = -3x + 12

• y = 3x - 1

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Multiple Choice

What is the measure of x? #81

• 12

• 15

• 6

• 9

Multiple Choice

#82

• 10 ft

• 5 ft

• 8 ft

• 15 ft

Multiple Choice

 Find the scale factor of  $$\Delta RPQ\ to\ \Delta UST$$ .

Assume the small to large ratio. #83

• $$\frac{2}{3}$$  

• $$2$$  

• $$\frac{3}{2}$$  

• $$\frac{12}{8}$$  

Multiple Choice

What can we conclude about MN and KL? #85

• They are parallel by Triangle Proportionality Theorem

• They are parallel by the Converse of the Triangle Proportionality Theorem

• They are congruent by SSS

• They will intersect 10 units down from N

Multiple Choice

Which proportion could be used to prove that $$HJ\parallel KL$$  ? #86

• $$\frac{KL}{HJ}=\frac{KG}{LG}$$  

• $$\frac{KH}{KG}=\frac{LG}{LJ}$$  

• $$\frac{HK}{JL}=\frac{LG}{GK}$$  

• $$\frac{GK}{HK}=\frac{GL}{LJ}$$  

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Multiple Choice

Find the interior angle on a regular polygon with 5 sides... #87

• 72^o

• 108^o

• 60^o

• 120^o

Multiple Choice

Find the interior angle on a regular polygon with 12 sides...#88

• 36^o

• 144^o

• 30^o

• 150^o

Today we are going to be looking at the AREA SCALE FACTOR.

Think about this question, the lengths have been multipled by 2, but what happens to the area?

Here is another example, look at the length scale factor compared to the area scale factor.

Have you spotted the rule!?

Multiple Choice

The manufacturer of an ice cream company wants to change the design of its ice cream cones. The measurements of the ice cream cone are shown. If the manufacturer doubles the radius of the ice cream cone, what will be the resulting effect of the volume of the new ice cream cone? #89

• It will increase by a factor of 2.

• It will increase by a factor of 4.

• It will increase by a factor of 8.

• It will increase by a factor of 16.

Multiple Choice

If this circle is dilated by the scale factor of 2, what would be the new area in cm²? #90

• 48 cm²

• 24 cm²

• 6 cm²

• 36 cm²

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Multiple Select

Which statements are true regarding the area of circle D? Select two options. #93

• The area of the circle depends on the square of the radius.

• The area of circle D is $$36\pi\ cm^2$$ .

• The area of circle D is $$324\pi\ cm^2$$ .

• The area of the circle depends on the square of pi.

• The area of the circle depends on the central angle.

Multiple Choice

The area of circle Z is.

$$64\pi\ ft^2$$ .  What is the value of r? #94

• r = 4 ft

• r = 8 ft

• r = 16 ft

• r = 32 ft

Multiple Choice

The diagram shows one way to develop the formula for the area of a circle. Pieces of a circle with radius r are rearranged to create a shape that resembles a parallelogram.

Since the circumference of the circle can be represented by 2πr, and the area of a parallelogram is determined using A = bh, which represents the approximate area of the parallelogram-like figure? #95

• A = (2πr)(r)

• A = (2πr)(2r)

• $$A=\frac{1}{2}\left(2\pi r^{ }\right)r$$

• $$A=\frac{1}{2}\left(2\pi r\right)r^2$$

Multiple Choice

If the circumference of a circle is 10π inches, what is the area, in square inches, of the circle? #96

HINT: SOLVE FOR THE RADIUS AND USE THE RADIUS TO FIND THE AREA OF THE CIRCLE

• 10π

• 25π

• 50π

• 100π

Multiple Choice

A circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet.

What is the approximate area of the path alone? Use 3.14 for π. #97

• 172.70 ft²

• 178.98 ft²

• 200.96 ft²

• 379.94 ft²

Arc Length (COPY NOTES)

Arc Length is the length of a portion of the circumference.

To find this we multiply the circumference by the fraction of the circle the arc subtends.

The fraction of the circle is determined by dividing the central angle by 360.

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Multiple Choice

Find the arc length. Leave your answer in terms of π. $$S=\frac{\theta2\pi r}{360\degree}\ leave\ the\ \pi\ in\ the\ answer.$$  #99

• (7/4)π

• (7/2)π

• (1/8)π

• 45π

Multiple Choice

Find the arc length of the bold arc.  Leave π  in your answer. $$S=\frac{\theta2\pi r}{360\degree}$$  leave π in your answer. #100

• 5688π ft

• 15.8π ft

• 150.4π ft

• 54,150 ft

Multiple Choice

Find the arc length of the bolded arc in the picture. (Use 3.14 for $$\pi$$  )

$$S=\frac{\theta\cdot2\cdot\pi\cdot r}{360}$$  #98

• A

• B

• C

• D

Multiple Choice

What is the area of the shaded sector? #105

• 69.78 ft²

• 2791.11 ft²

• 558.22 ft²

• 697.78 ft²

Multiple Choice

$$USE\ S=\frac{\theta2\pi r}{360\degree}\ to\ find\ \ \theta first$$  Find the area of the dark blue sector shown at the left. The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units. Express answer to the nearest tenth of a square unit. #106

• 0.3 square units

• 15.7 square units

• 19.7 square units

• 50.3 square units

Multiple Choice

Find the value of x. #107

• A

• B

• C

• D

Multiple Choice

What is the value of x? #108

• A

• B

• C

• D

Multiple Choice

What is the value of x? #109

• A

• B

• C

• D

Multiple Choice

What is the measure of angle A? #115

• 34°

• 180°

• 112°

• 79°

Multiple Choice

Solve for x and y. #116

• x=85⁰ y = 150⁰

• x = 85⁰ y = 50⁰

• x = 95⁰ y = 150⁰

• x = 95⁰ y = 50⁰

Multiple Choice

Find m∠R. #117

• 24⁰

• 41⁰

• 67⁰

• 139⁰

Multiple Choice

Jenny used a compass and a straight edge to make this construction. Which statement best describes her construction? #119

• She is constructing a parallel line to PQ.

• She is copying line segment PQ.

• She is constructing the perpendicular bisector to PQ.

• She is constructing an angle bisector.

Multiple Choice

Name the construction. #120

• Corresponding angles

• Parallel line to a point not on the line

• Perpendicular line to a point not on the line

• Angle bisector

Multiple Choice

Find the volume of the figure. Round to the nearest tenth. #123

• 80 cm³

• 40 cm²

• 80 cm²

• 40 cm³

Multiple Choice

What is the volume(L*W*H) of this rectangular prism with a width of 2 and a length of 7 and a height of 4? #125

• 56 cm^3

• 28 cm³

• 14 cm³

• 8 cm³

Multiple Choice

Find the volume of the cylinder. $$V=\pi r^2h\ where\ r\ is\ the\ radius\ and\ h\ is\ the\ height.$$  #129

• 4239

• 1696

• 1130

• 565

Multiple Choice

Find the volume of the figure. $$V=\frac{\left(length\right)\left(width\right)\left(height\right)}{3}$$  #130

• 126 cm³

• 907.5 cm³

• 605 cm³

• 55 cm³

Multiple Choice

Find the volume of the composite figure.

$$V_{total}=V_{pyramid}+V_{prism}$$  Length and width of the pyramid is 12 ft. #131

• 2400 ft³

• 1920 ft³

• 4128 ft³

• 2112 ft³

Multiple Choice

A right square pyramid has a height of 15 cm. and a slant height of 25 cm.

What is the volume of the pyramid? #132

• 2400 square cm.

• 6000 square cm.

• 8000 square cm.

• 24000 square cm.

Multiple Choice

Find the volume of the Sphere. Use 3.14 for pi. $$V=\frac{4\pi r^3}{3}$$  #136

• 337.3 ft³

• 137.2 ft³

• 274.4 ft³

• 205.8 ft³

Multiple Choice

Change the following equation to standard form

x²+y²-4x+12y-8=0. #138

• (x-2)²+(y-6)²=48

• (x-2)²+(y+6)²=48

• (x-6)²+(y-2)²=48

• (x+2)²+(y-6)²=48

Multiple Choice

What is the equation of the circle, with center (-2,-7) and radius 3 units? #139

• (x + 2)² + (y + 7)² = 3

• (x - 2)² + (y - 7)² = 9

• (x + 2)² + (y + 7)² = 9

• (x - 2)² + (y - 7)² = 3

Multiple Choice

The endpoints of a diameter of a circle are (3,1) and (9,5).Find the equation of the circle? Hint: In this problem, we are not given the center or radius however we can find the length of the diameter using the distance formula and then divide it by 2. The center is simply the midpoint of the given points. $$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$$   $$Use\ Midpoint\ Formula\ to\ find\ the\ center\ \ \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$   #140

• (x−6)²+(y−3)²=13

• (x−3)²+(y−6)²=13²

• (x−5)²+(y−9)²=13

• (x−9)²+(y−5)²=169/4

Multiple Choice

Convert 150⁰ to radians. #144

MULTIPLY BY (π/180)

• 5π/6

• 3π/4

• 7π/6

• 2π/3

Match

Match the following angles measured in radians to degrees. #146

• $$90\degree$$  

•    $$180\degree$$

• $$30\degree$$

• $$45\degree$$

• $$60\degree$$

 

• $$\frac{\pi}{2}$$  

• $$\pi$$

• $$\frac{\pi}{6}$$

• $$\frac{\pi}{4}$$

• $$\frac{\pi}{3}$$

Multiple Choice

Point P(7, -24) is a point on the terminal side of the angle $$\theta$$ . Find the exact value of sine $$\theta$$ .

#149

• $$-\frac{24}{25}$$  

• $$\frac{7}{25}$$  

• $$-\frac{24}{7}$$  

• $$\frac{24}{25}$$  

Multiple Choice

Point R(3, 4) is a point on the terminal side of the angle $$\theta$$ . Find the exact value of tangent $$\theta$$ . #150

• $$\frac{3}{4}$$  

• $$-\frac{4}{3}$$  

• $$\frac{4}{5}$$  

• $$\frac{4}{3}$$  

Multiple Choice

Which of the following formulas shows the Law of Cosines? #151

• c² = a² + b² - 4ac + cosA

• c² = a² - b² - 2abcosC

• c² = a² + b² - 2abcosC

• (cos A)/a = (cos B)/b

Multiple Choice

What is the correct set up to find angle H?

 #152

•   $$\cos\ H\ =\ \frac{11^2-13^2-15^2}{4\left(11\right)\left(15\right)}$$  

• $$\cos\ H\ =\ \frac{11^2+13^2+15^2}{2\left(13\right)\left(15\right)}$$   

•   $$\cos\ H\ =\ \frac{11^2-13^2-15^2}{-2\left(13\right)\left(15\right)}$$  

• $$H^2\ =\ 11^2+13^2+15^2-2\left(13\right)\left(15\right)\cos11$$   

Multiple Choice

#153

• 60

• 66

• 76

• 96

Multiple Choice

Identify the Law of Sines. #155

• $$\sin^2x+\cos^2x=1$$

• $$\frac{\sin\left(A\right)}{a}=\frac{\sin\left(B\right)}{b}=\frac{\sin\left(C\right)}{c}$$

• $$\sin\left(A\right)\sin\left(B\right)\sin\left(C\right)=1$$

• Soh Cah Toa

Multiple Choice

Use the Law of Sines to solve for BC. #156

• 33

• 24

• 12

• 29

Multiple Select

Solve for 0≤x≤2π

2sin²x - sinx = 0 #158

• 0, π, 2π

• π/2, 3π/2

• π/6, 5π/6

• π/3, 2π/3

Multiple Choice

Solve for 0≤x≤2π

3sin²x + sinx - 4 = 0 #159

• 0, π

• π/2

• π/6, 5π/6

• 3π/2

Multiple Choice

Solve for 0≤x≤2π

tanx = 1 #161

• π/2, π

• π/4, 3π/4

• π/4, 5π/4

• 3π/4, 7π/4