Algebra II MATH 435 REVIEW for the Quarter 1 Common ...mrlevesquemath.weebly.com/uploads/7/0/0/8/7008589/... · REVIEW for Quarter 1 Common Assessment * REVIEW * Page 7 4

Algebra II Name:___________________________________ Date:______ REVIEW for Quarter 1 Common Assessment

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Algebra II MATH 435

REVIEW for the

Quarter 1 Common Assessment

PART I

True/False Circle T if the statement is TRUE; circle F if the statement is FALSE. ****** If FALSE, modify the underlined text to make the statement TRUE.

1. T F When simplified, the expression (7x −1)

2 will be a perfect square trinomial. 2. T F Given any angle θ, in standard position, the corresponding reference angle is greater than or equal to 0. 3. T F The radius of a unit circle is 2π units. 4. T F If a triangle has sides with measures 6, 8 , and 11, then the triangle is a right

triangle. 5. T F If z2 =100 , then z =10 .

6. T F If 22sin =θ , then θ could be

4π , or

43π , −π

4 or any other coterminal angle.


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Multiple Choice. On the scan sheet: Grid in the letter corresponding to the correct response.

1. Below are sketches of an angle, θ. Which diagram(s) show θ NOT drawn in standard position?

CIRCLE ALL THAT APPLY. A. B. C. D.

2. An angle, 411π

θ = , in standard position, is coterminal with which of the following angles?

A. °135 B. °− 220 C. °45 D. °− 45

3. Which equation could be used to find the measure of one acute angle in the right triangle shown below?

A. 54sin =A B.

45tan =A C.

45cos =B D.

45tan =B

4. Given angle °−= 300θ , the equivalent radian measure is

A. 6π

− B. 3π C.

35π

− D. 611π

−


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5. If tan θ = -1, and if θ is an angle in standard position, then the terminal ray of θ is in Quadrant(s)

A. II B. I, II C. II, III D. II, IV

6. An angle P, drawn in standard position, terminates in Quadrant III, if

A. 0cos <P and 0tan >P B. 0cos <P and 0tan <P C. 0cos >P and 0tan >P D. 0cos <P and 0tan <P

7. Given an angle 5.1=θ , the equivalent degree measure in exact form is

A. 85.5° B. π°270 C. 540° D. 270°

8. Given tan θ = 0, θ could be

A. 45° B. 90° C. 180° D. 270°

9. Which of the following IS a quadratic equation?

A. 932 =+ yx B. )541(310

43 2 +++−= xxxy C. 10)92( 2 =−x D. 10=x

10. In the diagram below shows unit circle O, with radius OB = 1. Which line segment has a length equivalent to cos θ?

A. OA B. AB C. OC D. Cannot be determined


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11. Which of the following is an expression written as a product of a greatest common factor and a binomial?

A. x(x2 − 9x) B. )96( 2 ++ xxx C. x(x2 − 9) D. )3()3( −−− xxxx

12. If completing the square 222 35 ggxx +=+− the value of g is

A. 5− B. 25

− C. 25 D.

425

13. In the accompanying diagram of a unit circle, the ordered pair (x,y) represents the locus of points forming a circle, Which ordered pair is equivalent to (x, y)? a) (sinθ , cosθ ) b) (cosθ , tanθ ) c) (tanθ , sinθ ) d) (cosθ , sinθ )

Fill in the Blank Leave all answers as exact answers, in most simplified form. Show all of your work in the space provided next to each question below.

1. Given an angle, θ, in standard position and °=∠ 75 θm ,then θ will be created by rotating the

terminal ray of θ counter clockwise. If the °−=∠ 75 θm , θ will be created by rotating the terminal ray of θ _____________.

2. Given an angle θ, in standard position, in Quadrant I with a reference angle θ’, then θ > < = θ ' . (Circle one)

3. Sketch the angle 38π

θ =


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4. What is the reference angle of an angle 38π

θ = ? ______________

5. What is the positive angle πθ 20 << coterminal with 38π

θ = ? ______________

6. What is the negative angle 02 <<− θπ coterminal with 38π

θ = ? ____________

7. sin !!

! is _____________.

8. cos !!!

is _____________.

9. tan !!!

is _____________.

10. i=−1 is a definition. i is called the __________________ _________ .

11. The real number system and the imaginary number system combine to form the ___________ number system.

12. A student is completing the square below, fill in the blanks.

_____10____ 72 +−=+− zz

13. A student is completing the square below, his teacher came by and indicated there is a mistake in the work. Help the student spot the error made, circle it and correct it.

10z2 + 90z = −1010z2 + 90z+ (45)2 = −10+ (45)2

(5z+ 45)2 = −10+ 2025

14. Fill in the table below.

Complex Number

Real Part

Imaginary Part

Conjugate Product of the complex number and its conjugate

i+−1 i525 −

bia +


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15. Fill in the table below.

Complex Number Opposite Sum of the complex number and its opposite

i+−1 i525 −

bia + Open Response On the answer sheet: Write your final answers. Leave all answers as exact answers, in most simplified form. Show all of your work in the space provided next to each question below. 1. Fill in the table. (1 point each – 8 points)

θ

cos θ

sin θ

tan θ

25π

45°

3π

−

-150°

2. Determine the exact point of intersection of the terminal ray of angle °= 37θ and the unit circle.

3. If angle θ is in Quadrant IV, and 54sin −=θ , what is θtan ?


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4. Give the measure of θ in standard position, πθπ 42 ≤≤ whose terminal ray intersects the unit circle at

⎟⎟⎠

⎞⎜⎜⎝

⎛

22,

22 .

5. Give the measure of θ in standard position, 0360 ≤≤°− θ whose terminal ray intersects the unit circle at ( )1,0 − . 6. Simplify 5 )60sin(3)60cos( °+°− 7. Simplify. Answers cannot include negative exponents. a) b)

b) )2()160(18

30

343

−zxzyx

7 4 3(3 )x y ( ) ( )3 5 59 2− −⋅ −x y x y


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REVIEW for Quarter 1 Common Assessment PART II

Open Response On the answer sheet: Write your final answers. Leave all answers as exact answers, in most simplified form. Show all of your work in the space provided next to each question below. 1. Simplify. Write all answers in standard form of a complex number.

a) −5i( )2 (3)(i)5 b) −4 −36 c) −16 48−2

d) )3()1(3)57( −++++ iii e) )5(2)24()35( −−+−−− iiii f) 2)8( i− g) )26)(54( ii +−

h) ii

921−

− i) ii5347

+

+

j) Find the values of a and b. ibabai )23(34515 +−+−=−


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2. Solve each equation for x.

a. 37 |32|25 −=+− x b. 312

24)5(

51 −

=+

−+xxx

c. 7543 2

−=−− x d. 093 2 =−− xx

e. 2(x −3)(x +3) = −6x2 f. 0)56)(4( =−− xx

You must clear fractions as part of the solution process.


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3. Solve the following inequalities for x and graph your answers on the number lines provided on the answer sheet.

a. 13)96(32

>−− x b. 5 AND 2 >−< xx

c. 279 ≤−x d. 279 >−x

4. Circle the products below that will result in a real number. a. )5)(5( ii +− b. )5)(5( ii +−− c. )5(4 i+− d. )5(4 ii +− e. )5)(4( ii f. 2)5( i+ g. )5( ii +− 5. An egg is dropped off a building from a height of 48ft. The height of the egg in relation to time is modeled by the equation 4816 2 +−= th .

a. How many seconds will it take for the egg to reach 24 ft?

b. When does the egg explode on the ground?


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6. The graph represents the average temperature (in degrees Fahrenheit) per week in in Central Park after

the spring equinox in 2013.

a.) Based on the graph, what was the temperature on the spring equinox 2013? b.) What was the maximum average temperature shown on the graph? c.) What was the minimum average temperature shown on the graph? d) Assuming this graph continues in a similar fashion, could you predict what the average temperature

would be 12 weeks after the next spring equinox? e) Why is the average temperature approximately the same 52 weeks after the spring equinox?

Weeks since Spring Equinox 2013


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7. A mother puts her child on a merry-go-round and stands at the fence directly next to the merry-go-round where her child is sitting. The distance in feet, d, the child will be away from her mother after time, t in minutes is modeled by the equation d = −10cos(2t)+15 .

a) Fill in the table. Time, t, (minutes) d = −10cos(2t)+15 Distance away from

Mom 0 d = −10cos(2(0))+15

d = −10(1)+15= 5

5 feet

π4

π2

3π4

π

5π4

6π4

7π4

b) Before the merry-go-round begins, (at time t=0) the mother is 5 feet from her child. How many minutes go by before the child is 5 feet away from the mother again? c) Using the table above, what is the maximum distance away that the child is from her mother?

Fence


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8. Which expression is a factor of 2458172 bcabcabc +− ? Select ALL that apply. A. 3 B. 9 C. 3a D. 3b E. 9b F. 9c G. 9ab H. 9bc I. 9abc J. 9bc2 K. 9ac2 L. 15 WHICH of the possible factors above is the GREATEST COMMON FACTOR? _________

9. A system of equations is ⎩⎨⎧

=−

−=

52433zx

z. What is the solution (x, y) of this system of equations?

10 The table shows two systems of linear equations. Indicate whether each system of equations has no solution, one solution, or infinitely many solutions.

a) ⎩⎨⎧

−=

−=

xyxy88

_____________________

b) ⎩⎨⎧

−=

+=

413

yxy

___________________

11. Select the point on the number line that best approximates the location of 60 , and − 5 .


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Vocabulary to Know and Understand Pythagorean triples (3,4,5) (6,8,10) Unit Circle Family of angles Angle in standard position Family of angles Reference angle Coterminal angle Degree measure Radian measure Imaginary unit Powers of i Complex Number System Complex Number Real part of a complex number Imaginary part of a complex number Property of equality of complex numbers Conjugate Perfect square trinomial Concepts Sketching angles Right triangle trigonometry Unit circle trigonometry Finding the sine, cosine, and tangent of special angles Given an angle measure, find the point of intersection of the terminal ray with the unit circle. Given the point of intersection of the terminal ray of an angle with the unit circle, what is the measure of the angle? Solving a quadratic equation by completing the square Solving a quadratic equation by extracting the root Solving a quadratic equation using the zero product property Factoring a polynomial using the GCF Spiral Review Fraction operations Simplifying monomials Solving systems of equations Solving a linear equation by clearing fractions Solving an absolute value equation or inequality Solving simple and compound inequalities and graphing Simplifying radical expressions

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Algebra II MATH 435 REVIEW for the Quarter 1 Common ...mrlevesquemath.weebly.com/uploads/7/0/0/8/7008589/... · REVIEW for Quarter 1 Common Assessment ***** REVIEW ***** Page 7 4

Algebra II MATH 435 REVIEW for the Quarter 1 Common ...mrlevesquemath.weebly.com/uploads/7/0/0/8/7008589/... · REVIEW for Quarter 1 Common Assessment * REVIEW * Page 7 4