Math3 Sem1 Review Short

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Math 3 Sem 1 Review

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Four bowls with the same height are constructed using quadratic equations as their shapes. Which bowl has the narrowest opening?

A Bowl 1:1₈x2 _C _{Bowl 3:5x}2

B Bowl 2:1 4x

2 _D _{Bowl 4:7x}2

____ 2. Which function is NOT a translation of f x  x2__17?

A f x   x4217 C f x   x2_₁₇

B f x  x2_₄

D f x  x 1₂

  



  

2

____ 3. Which is the average rate of change over the interval [0, 4]?

Equation A

Equation B f(x)2x1

A A: 4, B: 2 C A: 8, B: 16

B A: 4, B: 4 D A: 8, B: 4

____ 4. Which is the average rate of change over the interval [2,3]?

Equation A

Equation B f(x) x2

A A: 7, B: 1 C A: 3, B:1

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Name: ________________________ ID: A

____ 5. The table shows the height of a sassafras tree at each of two ages. What was the tree’s average rate of growth during this time period?

Age (years) Height (meters)

4 2

10 5

A 0.4 meter per year B 0.5 meter per year C 2 meters per year D 2.5 meters per year

____ 6. The graph shows the height h, in feet, of a football at time t, in seconds, from the moment it was kicked at ground level. Estimate the average rate of change in height from t1.5 seconds to t1.75 seconds.

A 20 feet per second B 12 feet per second C 12 feet per second D 20 feet per second

____ 7. On which of the following intervals is the average rate of change of the function f x  x3__4x_{the greatest?}

A From x  3 to x  1 B From x  1 to x 1 C From x 1 to x 3 D From x 3 to x 5

____ 8. The table shows the sizes of an artist’s paintings and the price of each painting. Painting Size (in.2₎ ₄₈ ₆₄ ₁₄₄ ₄₈ ₁₀₀

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____ 9. Without using graphing technology, sketch the parent graph and translate it to obtain a graph of y4 x5.

A C

B D

____ 10. Solve (13x7)2_{= 110.}

A 7 110

26 ,

7 110

26 C

7 110

13 ,

7 110

13

B 7 110

13 ,

7 110

13 D

7 110

26 ,

7 110 26

____ 11. What are the solutions of the equation x2 _₂₃__2x_?

A x  12 6 C x 1 22

B x 12 6 D x1 22

____ 12. Which of the following is equivalent to 121?

A 11 B 11 C 11i D 121i

____ 13. The graph of which equation would be a circle with a center at (9, 9) and a radius of 13? A x92_y9_2 13 C x92_y9_2 169

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Name: ________________________ ID: A

____ 14. Which is the equation of a circle that has a diameter with endpoints _1,3_ and _3,1_?

A x12_y2_2 10 C x12_y2_2 5

B x12_y2_2 20 D x12_y2_2 5

____ 15. Solve the system. y x25x4 y 8x8

    

A (4, 0), (1, 16) C (1, 0), (4, 40) B (1, 0), (4, 0) D (1, 16), (4, 40)

____ 16. Which ordered pair is a solution of the system formed by the equations below? 2x2__12x__y2_₅₄_₀

y3x5

A (0, 5) C (1, 8)

B (0, 54) D (1, 8)

____ 17. What is the distance between the points of intersection of the graphs of y x2_{and y} _₆__x_?

A 26

B 5 2

C 2 37

D 170

____ 18. How many times do the graphs of y  x2__5x__{6 and 2x}__y__{16 intersect?}

A 0

B 1

C 2

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____ 19. Which is the graph of the polynomial function p x  x1x1x4?

A C

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Name: ________________________ ID: A

____ 20. Which of the following polynomial functions could have the graph shown?

A p(x)(x1)(x2)(x5) B p(x)(x1)2_(x__2)(x_₅₎ C p(x)(x1)(x2)(x5) D p(x)(x1)2_(x__2)(x_₅₎

____ 21. Which of the following is a true statement about the graph of p(x) x4x23x2__6x



 _?

A The graph crosses the x-axis four times and is never tangent to the x-axis. B The graph crosses the x-axis three times and is never tangent to the x-axis. C The graph crosses the x-axis two times and is tangent to the x-axis once. D The graph crosses the x-axis three times and is tangent to the x-axis once.

____ 22. Multiply (2x)(2x).

A 4x2 _C ₄__4x__x2

B 42x D 44xx2

____ 23. Subtract. x3__2x_₃

 

 _ – 3x2 __4x_₃



 _

A 2x3__6x_₆ _C _x3__3x2__2x

B x3__3x2__6x_₆ _D _x3__3x2__6x_₆

____ 24. Find the product. x2__2x_₃

 

 _3x2__4x_₁



 _

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____ 25. Which expression represents the perimeter of the triangle below?

A 34m C 5  4m

B 3  6m D 5  6m

____ 26. A farmer has kept careful track of his orange grove’s output over the years. The number of oranges produced can be modeled by the polynomial t2100t200. The average weight of the oranges over this same time can be modeled by the polynomial 0.0001t20.02t0.5. Which polynomial below models the total weight of oranges produced by this grove?

A 0.0001t40.02t30.5t24t50 C 0.0001t40.03t31.48t254t100 B 0.0001t40.01t31.98t24t50 D 0.0001t40.02t31.50t24t100

____ 27. Carlita has a rectangular swimming pool in her back yard that has a length of 24 feet and a width of 12 feet. She wants to install a concrete walkway of width c around the pool. Surrounding the walkway, she wants to have a wood deck that extends w feet on all sides. Find an expression for the perimeter of the wood deck.

A 36 + 4c + 4w C 72 + 8c + 8w

B 64 + 8c + 8w D 288 + 6c + 2w

____ 28. A rectangular garden has a length of 5a + 17 feet and a width of 4a feet. Which expression represents the area of the garden in square feet?

A 20a + 68 C 20a2_{+ 17}

B 20a2_{+ 68a} _D _25a2_{+ 64a}

____ 29. Write an equivalent expression for x2__2xy__y2_.

A (xy)2 _C _(x__y)(x__y)

B (xy)2 _D _x2__y2

____ 30. Write an equivalent expression for (xy)(xy).

A x2 __2xy__y2 _C _(x__y)2

B x2 __2xy__y2 _D _x2__y2

____ 31. Completely factor 3x415x318x2. A x2 3x 22



 _1x9 C 3x2x1x6

B 3x21



 _x26



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ID: A

Math 3 Sem 1 Review

Answer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: DOK 1 NAT: F-BF.B.3

STA: F-BF.3

2. ANS: C PTS: 1 DIF: DOK 1 NAT: F-BF.B.3

STA: F-BF.3

3. ANS: A PTS: 1 DIF: DOK 2 NAT: F-IF.B.6

STA: F-IF.6

4. ANS: B PTS: 1 DIF: DOK 2 NAT: F-IF.B.6

STA: F-IF.6 5. ANS: B

average rate of growth change in height_{change in age}  ₁₀5_2₄  3₆ 0.5 meter per year

Feedback

A You need to find the rate of change in height to change in age. B That’s correct!

C You found the rate of change in age to change in height. You need to find the rate of change in height to change in age.

D You need to find the rate of change in height to change in age.

PTS: 1 DIF: DOK 1 NAT: F-IF.B.6* | MP.4

STA: F-IF.6* | MP.4 KEY: average rate of change from a table | modeling NOT: Data taken from height-versus-age graph of sassafras tree number 2 at

http://www.yale.edu/fes519b/totoket/allom/allom.htm 6. ANS: A

average rate of change h1.75_1.75_h_1.51.5  7_0.2512  _0.255  20 feet per second

Feedback A That’s correct!

B You found the average rate of change from t1.25 seconds to t1.5 seconds. C You found the average rate of change from t0.5 seconds to t0.75 seconds.

D Remember to subtract the values associated with t1.5 from the values associated with

t1.75.

PTS: 1 DIF: DOK 2 NAT: F-IF.B.6* | MP.4

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7. ANS: D

From x 3 to x 1: average rate of change f(_₁1)_{ }f ₃3

  

3  15

2 

18 2 9

From x 1 to x1: average rate of change f(1)₁_{ }f ₁1

  

3 3

2 

6 2  3

From x1 to x3: average rate of change f(3)₃_f₁ 1  15 ₂ 3  18₂ 9

From x3 to x5: average rate of change f(5)₅_f₃ 3  105₂15  90₂ 45

So, the average rate of change is greatest on the interval from x 3 to x 5.

Feedback

A Compare the average rate of change on this interval with the average rate of change on

an interval even farther from 0.

B Compare the average rate of change on this interval with the average rate of change on

an interval far from 0.

C Compare the average rate of change on this interval with the average rate of change on

an interval even farther from 0.

D That’s correct!

PTS: 1 DIF: DOK 1 NAT: F-IF.B.6* STA: F-IF.6* KEY: average rate of change from a function rule | polynomial functions

8. ANS: A PTS: 1 DIF: DOK 2 NAT: S-ID.B.6

STA: S-ID.6

9. ANS: B PTS: 1 DIF: Level B REF: MAL20308

TOP: Lesson 2.7 Use Absolute Value Functions and Transformations

KEY: translate | graph | absolute value | equation | parent MSC: Comprehension NOT: 978-0-618-65615-8

10. ANS: B PTS: 1 DIF: DOK 2 NAT: A-REI.B.4a

STA: A-REI.4a TOP: Complete the Square KEY: square | solve | complex | quadratic

11. ANS: B PTS: 1 DIF: DOK 2 NAT: A-REI.B.4b

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ID: A

12. ANS: C

121  (121)(1)  121 1 11i

Feedback

A Factor 121 as 121(1) and then apply the rule ab  a  b.

B That’s correct!

C Factor 121 as 121(1) and then apply the rule ab  a  b. D Factor 121 as 121(1) and then apply the rule ab  a  b.

PTS: 1 DIF: DOK 1 NAT: N-CN.A.1 STA: N-CN.1

KEY: imaginary numbers

13. ANS: C PTS: 1 DIF: DOK 1 NAT: G-GPE.A.1

STA: G-GPE.1

14. ANS: C PTS: 1 DIF: DOK 2 NAT: G-GPE.A.1

STA: G-GPE.1

15. ANS: C PTS: 1 DIF: DOK 1 NAT: A-REI.C.7

STA: A-REI.7

16. ANS: D PTS: 1 DIF: DOK 1 NAT: A-REI.C.7

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17. ANS: B

To find the points of intersection, set the expressions x2_{and 6}__{x equal to each other and solve for x.}

x2 _₆__x x2__x_₆_₀ x3

 x20 x  3 or 2

Substitute each x-value into one of the equations and solve for y.

y 6  3

63

9

y 62

4

The points of intersection are _2, 4_ and _3, 9_. Now use the distance formula,

D _x2x1_ 2

_y2y1_ 2

.

D 322942

  5 252

 50

5 2

Feedback

A It seems you added the x-coordinates instead of subtracting them in the distance

formula.

B That’s correct!

C Remember that the distance formula uses the differences between the x-values and the

y-values, not the difference between each x-value and its corresponding y-value.

D Remember that the pairs of coordinates are subtracted in the distance formula, not

added.

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ID: A

18. ANS: C

Solve 2xy 16 for y. 2xy 16

y  2x16

Substitute 2x16 for y in y x2__5x__6.

2x16 x2__5x_₆ 0 x2__7x_₁₀

  x5x2

x 2 or 5

There are two distinct solutions, so there are two points of intersection.

Feedback

A The parabola and the line have at least one point of intersection.

B Find the number of solutions by solving the system of equations. C That’s correct!

D A parabola and a line cannot have three points of intersection.

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19. ANS: B

The zeros of the function are x 1, x1, and x4, and these are the x-intercepts of the function’s graph. The result of expanding x1x1x4 is x3__4x2 __x__{4. The leading term, x}3_{, has a positive} coefficient and an odd exponent, so p x  approaches  as x approaches , and p x  approaches  as x approaches . Of the four given graphs, only the one shown below has these characteristics.

Feedback

A Check the zeros of p x .

B That’s correct!

C Check the end behavior of p x_{ }.

D Check the zeros and end behavior of p x .

PTS: 1 DIF: DOK 1 NAT: F-IF.C.7c* STA: F-IF.7c* KEY: graphs of polynomial functions | zeros | end behavior

20. ANS: D

The function p(x)(x1)2_(x__2)(x__{5) has 3 zeros,}__{1, 2, and 5. Since x}__{1 is a factor twice,}__{1 is a zero} twice, so the function’s graph would be tangent to the x-axis at x 1. Since x2 and x5 are factors once, 2 and 5 are zeros once, so the function’s graph would cross the x-axis at x2 and x 5.

Feedback

A Make sure you have identified the zeros of the function correctly.

B Make sure you have identified the zeros of the function correctly.

C This function is cubic, so its end behavior will not be the same at both ends of the graph.

D That’s correct!

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ID: A

21. ANS: C

The number of unique real zeros that a polynomial function has is equal to the number of times the graph of the function intersects the x-axis.

p(x) x4x23x2__6x



 _ 3x x 4x2x2

This function has 3 unique real zeros, 0, 4, and 2, so the graph intersects the x-axis three times. Since two of those zeros, 0 and 4, each occur once, the graph crosses the x-axis at x 0 and x 4. Since one of those zeros, 2, occurs twice, the graph is tangent to the x-axis at x 2.

Feedback

A Identify all of the zeros of the function and how many times each zero occurs. B Identify all of the zeros of the function and how many times each zero occurs.

C That’s correct!

D Identify all of the zeros of the function and how many times each zero occurs.

PTS: 1 DIF: DOK 1 NAT: A-APR.B.3 STA: A-APR.3 KEY: zeros of polynomial functions | graphs of polynomial functions

22. ANS: A PTS: 1 DIF: DOK 1 NAT: A-APR.A.1

STA: A-APR.1

23. ANS: D PTS: 1 DIF: DOK 1 NAT: A-APR.A.1

STA: A-APR.1

26. ANS: C PTS: 1 DIF: DOK 2 NAT: A-APR.A.1

STA: A-APR.1

27. ANS: C PTS: 1 DIF: DOK 2 OBJ: Application

NAT: A-APR.A.1 STA: A-APR.1

LOC: MTH.C.10.05.08.004 | MTH.C.12.11.02.002 | MTH.C.10.05.08.03.001 TOP: Adding Polynomials KEY: polynomial | addition

28. ANS: B PTS: 1 DIF: DOK 2 NAT: A-APR.A.1

STA: A-APR.1

LOC: MTH.C.10.05.08.03.02.002 | MTH.C.10.05.08.004 | MTH.C.10.02.03.002 | MTH.C.12.12.02.002 TOP: Multiplying Polynomials by Monomials

KEY: polynomial | monomial | multiplication

29. ANS: A PTS: 1 DIF: DOK 1 NAT: A-APR.C.4

STA: A-APR.4 KEY: polynomial identities

30. ANS: D PTS: 1 DIF: DOK 1 NAT: A-APR.C.4

STA: A-APR.4 KEY: polynomial identities

31. ANS: C PTS: 1 DIF: DOK 1 NAT: A-SSE.A.2