· web viewthe circuit law, v=i∙z , is used in circuit analysis. if i=3i and z=7i , what is the...

Standards Based Review NC M3 Name: _____________________________N-RN.3

5. If P and S are rational numbers and R and Q are irrational numbers, which of these statements is true?A. The product of R and Q is always an irrational number.B. The product of P and S is always a rational number.C. The sum of R and Qis always an irrational number. D. The sum of P and Q is always a rational number.

6. Which statement about rational and irrational numbers is always true?A. Any irrational number added to any rational number is equal to a rational number.B. Any irrational number added to any irrational number is equal to a rational number.C. Any irrational number multiplied by any non-zero rational number is equal to a rational number.D. Any irrational number multiplied by any non-zero rational number is equal to an irrational number.

7. Which expression results in an irrational number when simplified?A. √121+√16 B. √6+ 1

2 C. ( 45 )√49 D. (√4 ) (√9 )

8. The length of a rectangular prism is 4 √3 units. The height is 3√6 units. If the volume is irrational, which could be the measure of the width of the rectangular prism?

A. 2√50 B. 4 √12 C. 5√8 D. 7√18

N-CN.2

1. Which expressions is equivalent to (8−3 i )−(2−9 i )?A. 6+6i B. 6−12i C. 11+78 i D. 18−6 i

2. The circuit law, V=I ∙Z, is used in circuit analysis. If I=3 i and Z=7 i, what is the voltage, V ?A. 21 B. 21 i C. −21 D. −21 i

3. What is the value of 8 i−2 i (3 i+4 )?A. −2+8 i B. 10+8 i C. −6 D. 6

4. Which of the following is equivalent to (3−2i )2?A. 5−12i B. 6−4 i C. 9+4 i D. 13−12i

5. Which of the following expressions is equivalent to 3 i (−5+2i )−2 (5−4 i )??A. −16−23 i B. −16−7 i C. −10−i D. 21−¿4i

6. Which value is equivalent to i57?A. −1 B. – i C. 1 D. i

Standards Based Review NC M3 Name: _____________________________

A-SSE.3

For 1-3: What value of h is needed to complete the square in order to find the vertex?1. x2−4 x+9=( x−h )2+5

2. x2+2x+7=(x−h)2+6

3. x2−2 x+4=( x−1 )2+3

A-APR.2

5. Given the function P ( x )=x3+4 x2+kx+15, for what value of k is (x+3) a factor of P(x )?A. -26 B. -8 C. 8 D. 26

6. When the polynomial 4 x4−13 x2−2 x+1 is divided by the polynomial (x−2), what is the remainder?A. -23 B. 1 C. 9 D. 17

7. If p ( x )=x4+3 x3−2x2+4 and q ( x )=x+1, then g(x ) is a polynomial that equals p (x)q(x ) . What is the

remainder of g(x ) when it is divided by (x−2)?A. -4 B. 6 C. 12 D. 22

8. What is the remainder when p ( x )=x3−7 x−6 is divided by (x−4)?A. -42 B. -18 C. 9 D. 30

A-APR.3

1. Which of the following functions has the same zeros as the function f ( x )=x2−6x+8?A. g ( x )=x−4B. g ( x )=x2−5 x+6

C. g ( x )=2 x2−12x+16D. g ( x )=x3−6 x2+8 x

Standards Based Review NC M3 Name: _____________________________2. Which function, when graphed, would have the same zero(s) as the function below?

A. f ( x )=x (x+6)B. f ( x )=x (x−6)C. f ( x )=(x+6)2

f ( x )=(x−6)23. What are the zeros of the polynomial function f ( x )=( x2−16 ) ( x+5 ) x?A. −5 ,−4 ,0 ,4 B. −4 ,0 ,4 ,5 C. −¿5, −4 ,4 D. −¿5, 0, 4

4. Which function has zeros −4 ,2,and 0?A. f ( x )=x3+2 x2−8 x B. f ( x )=x3−2x2−8 x C. f ( x )=x2+2 x−8 D. f ( x )=x2−2x−8

5. Let the function f ( x )=(x+4)(x2−36)( x2+25). What are all the x-intercepts for the graph of f (x)?A. −4 ,6 B. −6 ,−4 ,6 C. −¿6, 4 ,6 D. −¿6,

−5 ,4 ,5 ,6

6. Which function best represents the graph below? 7. Which function best represents the graph below?

A. f ( x )= (x+2 ) ( x−3 ) A. g ( x )=x ( x−2 )2(x+3)B. f ( x )= (x+3 ) ( x−2 ) B. g ( x )=( x−2 )2(x+3)C. f ( x )=x ( x+2 ) ( x−3 ) C. g ( x )=x ( x−2 ) ( x+3 )D. f ( x )=x ( x+3 ) (x−2 ) D. g ( x )=(x−2)¿

A-APR.6

3. Which fraction is equal to y2+5 y+4y2+19 y+18

in simplest form?

A.9

37 B.4

18 C.y+4y+18

4.5 y+4

19 y+18 What is 2x2−18

2x2+18 reduced to lowest terms?

Standards Based Review NC M3 Name: _____________________________A.

x−3x+3 B.

x+3x−3 C.

(x−3)(x−3)x2+9

D.

(x−3)(x+3)x2+9

5. What value must be substituted for k so that x+4

x2+7 x+k can be reduced to

1x+3 ?

A. 3 B. 4 C. 12 D. 28

6. Which of the following is equivalent to x3−7 x2

x−7?

A. x B. x2

C.x

x−1 D.−6 xx−7

A-REI.2

1. Solve 5

2x−2= 15x2−1

A. 1B. 5

C. 1, 5D. No solution

2. Solve y5

+ y2=7

A. 2B. 5C. 7D. 10


3. Solve x

x−5+ 3x+2

= 7 x(x−5)(x+2)

A. -3B. 5C. -3, 5

D. No solution

4. Solve √ x−3+5=xA. 4B. 7

C. 4, 7D. No solution

5. Solve √3 x+7=x−1A. -1B. 6C. -1, 6D. No solution

6. After an accident, police can determine how fast a car was traveling before the driver put on his brakes by using the equation s=√30 fd. s represents the speed in miles per hour, f represents the coefficient of friction, and d represents the length of the skid in feet. Suppose the coefficient of friction is 0.6, if you were driving 35 miles per hour, how many feet would it take for you to stop?A. 30 feet B. 47 feet C. 68 feet D. 81 feet

A-REI.4.a 1. What number should be added to both sides of the equation to complete the square? x2 + 10x = 3

A. 5 B. 25 C. 50 D. 100

2. For what value of p is the expression ( x− p )2+5 is equivalent to the expression x2−14 x+54?A. -49 B. -7 C. 7 D. 49

3. The equation 2 x2−5 x=−12 is rewritten in the form 2(x−p)2+q=0. What is the value of q?

A.16716 B.

718 C.

258 D.

2516

A-REI.4.b 1. Solve 5 x2−180=0A. x=−6B. x=6C. x=±6D. No real solution

2. What are the solutions of −4 x2−72=0?A. ±2i√3 B. ±3i √2 C. ±2√3 D. ±3√2

3. What are the values of x that satisfy the equation 3−27 x2=0?

A. x=±3 B. x=± 19 C. x=± 1

3 D. x=±2√6

4. What are the solutions of x2+10 x+40=5?A. 10±i√5 C. 5±i√10B. −10±i√5 D. −5±i√10

5. Which equation has −3±5i as its solutions?A. x2+6 x=−34 C. x2+6 x=−14B. x2+3x=4 D. x2+3x=2

A-REI.11 1. For what values of x does f ( x )=g (x) if f ( x )=x3+3 x2 and g ( x )=x+3?

A. −3 ,−1,1 B. −3 ,1 ,3 C. −1 ,1 ,3 D. −3 ,−1,3

2. For what values of x does f ( x )=g (x) if f ( x )=|2x−1|+5 and g ( x )=−12

x+9?

A. −2 ,10 B. −2 ,8 C. −2 ,2 D. 8 ,10

3. For what values of x does f ( x )=g (x) if f ( x )=2x and g ( x )=32x+1?

A. 2, 4 B. 0, 1 C. 4, 1 D. 2, 0

Standards Based Review NC M3 Name: _____________________________4. At approximately what point or points do the graphs of f ( x )=x2−3 x−8 and g ( x )=−6+ log4 x intersect?

A. (3.6949 ,−5.4324 )B. (3.7824 ,−5.0403)

C. (0.0093 ,−8.0280 )∧(3.6949 ,−5.4324)D. (0.0507 ,−8.1497 )∧(3.7824 ,−5.0403)

5. Since January 2010, a grape farmer has been growing red and green grapes. The number of red grape vines can be modeled by the function f ( x )=1,000 (1.03 ) x, where x is the number of years since January 2010. The number of green grape vines can be modeled by the function g(x )=20 x+1,125, where x is the number of years since January 2010. In what year will the number of each type of grape vine be approximately equal?A. 2013 B. 2015 C. 2017 D. 2019

F-IF.4

1. During which interval is the graph of f ( x )=−12

x2+3 x−2.5 positive?

A. 1<x<5 B. x<1 and x>5 C.1≤x ≤5 D. x≤1 and x≥5

2. During which of following intervals is the graph of f ( x )=3 x3+10 x2−x−12=0 positive?

A. x>0 B. x>1 C. −3<x←1 D. −2<x<0

3. During which of the following intervals is the graph of f ( x )=x3+x2−6 x negative?A. x←3 B. x<0 C. −3<x<0 D. x>2

4. What is the y-intercept of y=sin(θ+ π2)?

A. (0,0) B. (0 ,1) C. (π2,0) D. (0 ,

π2

)

5. During which of the following intervals is the graph of y=12

cos θ increasing?

A. 0<θ< π2 B.

π2<θ<π C.

π2<θ< 3 π

2D. π<θ<2 π

6. Which function has a period of 4 π and an amplitude of 8?

A. y=−8sin 8θ B. y=8 sin2θ C. y=−8 sin 12θ D. y=4 sin 8θ

7. Which of the following describes the end behavior of 2 x4−20 x2+18?A. x→−∞ f ( x )→+∞, x→+∞ f ( x )→+∞B. x→−∞ f ( x )→+∞ , x→+∞ f ( x )→−∞

C. x→−∞ f ( x )→−∞, x→+∞ f ( x )→+∞D. x→−∞ f ( x )→−∞, x→+∞ f ( x )→−∞

8. Which rational function is decreasing in the interval (−∞,1) and is symmetric over the line x=1?A. C.

B. D.


F-BF.3 1. The graph f ( x )=3x is translated 2 units to the right and down 6 units resulting in g(x ). Which of the

following functions represents g(x )?A. g ( x )=3(x−2)−6 B. g ( x )=3(x+2)−6 C. g ( x )=3(x−6)−2 D. g ( x )=3(x+6 )−2

2. The function f ( x )=3 (2)x models the growth of a bacteria culture. What is the change that occurs to the graph if f (x+k ) is graphed and k<0?

A. The graph moves up k units B. The graph moves down k unitsC. The graph moves left k units D .The graph moves right k units

3. Which function is a phase shift of y=sinθ by 5 units to the left?A. y=5sin θ B. y=sinθ+5C. y=sin(θ+5) D. y=sin5θ

4. Which function is a translation of y=cosθ by 5 units down?A. y=−5cosθ B. y=cos(−5θ) C. y=cos(θ−5) D. y=cosθ−5

5. Which function is a translation of y=sinθ that is π3 units up and

π2 units to the left?

A. y=sin(θ+ π3)+ π

2 B. y=sin(θ+ π2 )+ π3

C. y=sin(θ−π2 )+ π

3 D. y=sin(θ−π3 )−π

26. The figure below shows the graph of the function g(x ). If f ( x )=|2x|+3, how is g(x )

related tof (x)?

A. g ( x )=f ( x )−4B. g ( x )=f ( x )+4C. g ( x )=f ( x−4 )D. g ( x )=f (x+4)

7. The cubic function y=x3 is changed to y=−2x3−7. What effect will this have on the function?A. The graph will be reflected in the y-axis, shifted up 2 units and vertical stretch by a factor of 7.B. The graph will be reflected in the x-axis, shifted up 7 units and vertical stretch by a factor of 2.C. The graph will be reflected in the x-axis, shifted down 7 units and vertical stretch by a factor of 2.D. The graph will be reflected in the y=axis, shifted down 2 units and vertical stretch by a factor of 7.

F-BF.4


5. What is the inverse, f−1(x), of the function f ( x )=3 x−7?

A. f−1 (x )= x−73 B. f−1 (x )= x+7

3C. f−1 (x )=−3x+7 D. f−1 (x )=7x−3

6. Which of the following is the inverse function of y=√3 x−22

?

A. y= x2+23

B. y=2 x2+23

C. y= 4 x2+23

D. y= x2

3

7. Which expression represents the inverse of f ( x )=8x+13?

A.x8−13 B.

18x+13

C. log21 ( x ) D. log 8 ( x−13 )

8. Given that f−1 (x )=g (x) and f ( x )=2√ x, which expression correctly defines the function g(x ) and its domain?

A. x2

2 for all values of x≥0 B. x2

4 for all values of x≥0 C. x2

2 for all real values of

x

D. x2

4 for all real values of

x

9. What is the inverse of f ( x )=x3+5?A. f−1 (x )=−x3−5 B. f−1 (x )= 3√x−5 C. f−1 (x )= 3√x3−5 D. f−1 (x )=x−3√5

10. What is the inverse of the equation y=√3 x−4 , x≥ 43?

A. y= x2+43

, x≥0 B. y= 4−x3

, x ≤4 C. y=−x2+43

, x≥0 D. y=−x+43

, x≥−4

F-LE.3 1. For what positive integer value of x will the value of g ( x )=3x first exceed the value of f ( x )=2x+25?

A. 3 B. 4 C. 25 D. 26

2. Which statement is true about the functions f ( x )=2x2+ x+2 and g ( x )=2x+2, when x=0?A. The value of f (x) and the value of g(x ) are the same.B. The value of f (x) exceeds the value of g(x ) by 1.C. The value of g(x ) exceeds the value of f (x) by 1.D. The value of g(x ) exceeds the value of f (x) by 2.

3. f ( x )=1.02 x+100;g ( x )=50 (1.02 )x What is the smallest positive integer in which the value of g(x ) exceeds the value of f (x)?A. 60 B. 59 C. 55 D. 50

4. George is comparing the graphs of two function f ( x )=3x and g ( x )=3 x2+x−1 for different values of x. Which statement best compares the values of the function as the value of x increases?

Standards Based Review NC M3 Name: _____________________________A. f (x) will eventually exceed g(x ) for all real numbers greater than a certain x-value.B. g(x ) will eventually exceed f (x) for all real numbers greater than a certain x-value.C. f (x) is greater than g(x ) for all values of x.D. g(x ) is greater than f (x) for all values of x.

5. What is the largest integer value of x such that the value of f ( x )=x2−6x+40 exceeds the value of g ( x )=2 (1.5 )x?A. 6 B. 8 C. 10 D. 12

F-TF.1

1. The radius of a circle is 2 centimeters. A central angle of the circle intercepts an arc of 8 centimeters. What is the radian measure of the angle?A. 2 B. 3 C. 4 D. 8

2. A circle has a central angle whose radian measure is 2 and an arc length of 6 meters. What is the diameter of the circle in inches?A. 2 B. 3 C. 6 D. 12

3. In a circle, an arc of length 8 π is intercepted by a central angle of 2π3 radians. What is the radius of the

circle?

A.3π16 cm B.

16π3 cm C. 16π2

3 cm D. 12 cm

4. The circle shown below has a diameter of 18 centimeters (cm). If the dotted arc is 33 cm long, what is the measure of angle θ in radians?

Standards Based Review NC M3 Name: _____________________________A.

311 B.

611 C.

116 D.

113

F-TF.2 1. William put the tip of his pencil on the outer edge of a graph of the unit circle at the point (0, -1).

He moved this pencil tip through an angle of 4 π3 radians in the counterclockwise direction along the

edge of the circle. At what angle of the unit circle did William’s pencil tip stop?

A.π3 B.

5π6 C.

7π6 D.

5π3

2. Max put the tip of his pencil on the outer edge of a graph of the unit circle at the point (-1, 0). He

moved his pencil tip through an angle of π6 radians in the counterclockwise direction along the edge of

the circle. At what angle of the unit circle did Max’s pencil tip stop in radians?

A.7π6 B.

π6 C.

5π6 D.

11π6

3. A Ferris wheel has a diameter of 114 feet and is 5 feet off the ground. After a person gets on the bottom car, the Ferris wheel rotates 1700 counterclockwise before stopping. How high above the ground is the car when it has stopped?A. 56 feet B. 62 feet C. 80 feet D. 118 feet

4. How many radians are 1800o?A. 10 B. 10π C. 180 D. 180π

5. In the right triangle pictured below, the measure of angle A, in radians, is θ. The side adjacent to angle A measures 6 cm and the side opposite measures 5 cm. Which value is closest to sin (5θ )?

A. -0.3260 B. 0.6402 C. 0.9723 D. 3.2009F-TF.5

1. A mark of T is at the top of a small wheel. The graph shows h, the height in centimeters of the T above the ground as a function of x, the angle the wheel has turned.

Which function is best represented by the graph?

A. h ( x )=12 cos x

B. h ( x )=12 sin(x− x2 )

C. h ( x )=6 sin( x+ π2 )+6

D. h ( x )=6 cos (x+ π2 )+6

Standards Based Review NC M3 Name: _____________________________2. An automotive engineer recorded an antilock brake sensor wave with an amplitude of 0.8, a midline of

0.1, and a frequency of π4 . Which equation best represents this wave?

A. y=0.1sin (8 x )+0.8 B. y=0.8 sin ( 4 x )+0.1 C. y=0.8sin ( 8x )+0.1 D. y=0.1sin ( 4 x )+0.8

3. A transmitter sends a radio wave from the top of a 70-foot building. The amplitude of the wave is 1.5, the midline of the wave is 4, and the frequency of the wave is π. Which equation best represents this radio wave?

A. y=1.5 sin (2 x ) B. y=1.5 sin (2 x )+4 C. y=2sin (1.5 x )+4 D. y=2sin ( 4 x )+1.5

G-GO.10 1. In ∆ ABC , AD=DB and AE=EC . Which of the following can be proven?

A. Triangle ABC is isosceles.

B. DE is perpendicular to AC

C. The length of DE is half the length of BC.D. Triangle ABC is congruent to triangle ADC.

2. In triangle ABC ,m<x and m<B= y . Which of these can be proved using the triangle sum theorem?A. m<C= y B. m<C=x+ y C. m<C=180o−x+ y D. m<C=180o−(x+ y )

3. Find the measure of each angle in the triangle. 4. Find SR in the figure below

7. If CR=24, what is KR?

A. 6 B. 8 C. 12 D. 16

8. If TR=12, what is CP?

A. 16 B. 18 C. 24 D. 36G-GO.11

1. Which of these properties is enough to prove that a given parallelogram is also a rectangle?A. The diagonals bisect each other.B. The opposite angles are equal.C. The opposite sides are equal.D. The diagonals are congruent.

2. In the figure below, PO /¿MN and PM /¿ON .


Which would be a correct way to begin a proof that shows ¿O ≅<M ?A. Draw diagonal PN and show that a pair of corresponding angles formed by the transversal are congruent.B. Draw diagonal OM and show that a pair of adjacent interior angles formed by the transversal are congruent.C. Draw diagonal PN and show that a pair of alternate interior angles formed by the transversal are congruent.D. Draw diagonal OM and show that a pair of alternate interior angles formed by the transversal are

complementary.G-SRT.2For 1-2, determine if the triangles below are similar. If so, write the similarity statement.

1. 2.

G-SRT.5

Standards Based Review NC M3 Name: _____________________________1. What is the value of x in the triangle below?

A. 5√32

cm B. 5√3 cmC. 10cm

D. 15 cm

2. Which of the figures shown below are similar?

3. If the rectangular prisms are similar, what is the value of x?

A. 9 B. 10 C. 12 D. 18

4. Triangle MNP is a right triangle. Point X is on MP, Point Y is on PN , and MN is parallel to XY .Which statement must be true?A. ∆ PMN ≅ ∆PXYB. ∆ PMN ∆ PXYC. m<PMN−m<XPYD. m<PMN>m<PXY

5. Triangle ABC is similar to ∆≝¿, AB=12, DE=8, and AC=15. What is the length of DF?

A. 6.4 B. 10 C. 11 D. 22.5


G-C.5

4. Which measurement is closest to the area of the shaded sector in the circle shown below?A. 12.56 square inchesB. 25.12 square inchesC. 50.24 square inchesD. 75.36 square inches

5. The drawing shows a semicircular window separated into 3 sections of color glass.Approximately how many square inches of the tinted glass are red?

A. 15.7B. 70.7C. 141.3D. 282.6

Standards Based Review NC M3 Name: _____________________________6. The windshield wiper blade on Julia’s car is 21 inches long. Each swipe of the wiper makes an angle of 85 degrees as pictured below.

To the nearest inch, how far does the tip of the windshield wiper travel with each swipe of the blade?A. 21 inchesB. 30 inchesC. 31 inchesD. 33 inches

7. Sally is creating a flower bed that wraps around the corner of her house. She will put edging around the flower bed 10 feet from the corner of the house in all directions as shown below.

Which is the best estimate of the number of feet of edging that Sally will need?

A. 24B. 43C. 48D. 63

G-GPE.1

5. What is the equation of the circle that has a center at (−1 ,−3) and a radius of 4 units?A. ( x−1 )2+( y−3 )2=16B. ( x+1 )2+ ( y+3 )2=16

C. ( x−1 )2+( y−3 )2=2D. ( x+1 )2+ ( y+3 )2=2

6. A circle is graphed on the coordinate plane below.A. x2+ ( y−4 )2=9B. ( x+4 )2+ y2=9C. ( x−4 )2+ y2=3D. x2+ ( y+4 )2=3

7. Which equation represents a circle with the center at (−1 ,7 ) and a radius of √17?A. ( x−1 )2+( y+7 )2=17B. ( x+1 )2+ ( y−7 )2=17

C. ( x+1 )2+ ( y+7 )2=√17D. ( x+1 )2+ ( y−7 )2=√17

8. What is the center and the radius of a circle given by the equation x2+ y2+4 x−10 y+20=0?A. (−2 ,5 )∧r=√20 B. (2 ,−5 )∧r=√20

Standards Based Review NC M3 Name: _____________________________C. (−2 ,5 )∧r=3 D. (2 ,−5 )∧r=3

9. The equation x2+ y2−4 x−8 y−16=0 represents a circle in the standard xy-coordinate plane. What is the radius of the circle?A. 6 B. √20 C. 4 D. √2

S-IC.4 1. Of 400 teenagers surveyed, 62% do not plan to stay in their communities after finishing their education.

Find the margin of error for the sample.A. ±2 % B. ±4 % C. ±5 % D. ±6%

2. In a random survey of 1,000 high school students, 65% said that math is their favorite subject. Based on these survey results, which of these represents a 95% confidence interval for the percentage of all high school students who would choose math as their favorite subject?

A. 60% to 70% B. 62.04% to 67.96% C. 62.5% to 67.5% D. 63.52 to 66.48

5. A sample of 121 high school seniors were surveyed on their level of school spirit on a scale of 0-100. The sample mean of this survey is 86. The known population standard deviation is 14 for all seniors in the class. Which of these is a 95% confidence interval for the population mean?A. [82.72, 89.28] B. [83.51, 88.49] C. [83.91, 88.09] D. [85.92, 86.08]

6. An electrics company conducted a customer satisfaction survey. The survey results showed, with a 95% confidence level, that 62% to 68% of customers are satisfied with their service. What is the margin of error of this survey?A. 3% B. 6% C. 65% D. 95%

7. A state senator requested a survey of registered voters to determine public opinion of a new law. Of the 940 voters who responded to the survey, 61.7% were in favor of the new law, 35.% were opposed, and the rest were undecided. What is the margin of error of this survey with a 95% level of confidence?A. ±1.44 % B. ±1.51% C. ±2.98% D. ±3.11%

8. A random sampling of 500 adults showed that 203 preferred Brand A potato chips more than all other brands of potato chips in the survey. Which interval reflects a 95% likelihood of containing p, the population proportion?

A. 0.305≤ p≤0.508 B. 0.356≤ p≤0.456 C. 0.363≤ p≤0.449 D. 0.386≤ p≤0.426

· web viewthe circuit law, v=i∙z , is used in circuit analysis. if i=3i and z=7i , what is the...

Documents