ALGEBRA III/IV 2019-2020 Scope and Sequencefunctions. 6 weeks UNIT 6: Functions • Deadline:...

ALGEBRA III/IV 2019-2020 Scope and Sequence

Unit Outline Synopsis Projected Time

UNIT 1: Solving equations and inequalities.

• Deadline: 09/13/2019

Review solving linear equations and inequalities. Solve absolute value, radical and rational (enrichment) equations.

6 weeks

UNIT 2: Exponents, radicals and complex numbers

• Deadline: 11/01/2019

Simplify radical expressions with numbers and variables. Use the properties (rules) of exponents to simplify radical expressions. Simplify expressions with complex numbers.

6 weeks

UNIT 3: Solving and graphing Quadratic equations and systems.

• Deadline: 12/18/2019

Review the operations on polynomials. Review factoring polynomials using GCF, grouping, quadratic methods and sum/difference of two cubes (enrichment). Solve quadratic equations. Graph quadratic equations including systems.

6 weeks

UNIT 4: Statistics and probability

• Deadline: 02/13/2020

Calculate simple probability. Use the fundamental counting principal to solve problems in real world context. Calculate compound probability. Calculate measures of central tendency and introduce normal distribution

6 weeks

UNIT 5: Using trigonometry to find missing parts of right and non-right triangle.

• Deadline: 03/27/2020

Solve to find missing parts of right triangles and non-right triangles, including 45-45-90 and 30-60-90, using Pythagorean theorem and trigonometry. Convert between degree and radian measure. Generate the Unit Circle and use the Pythagorean Identity and the quadrant to find the other 5 trig functions.

6 weeks

UNIT 6: Functions

• Deadline: 05/21/2020

Define a function. Determine domain and range. Graph parent functions - linear, quadratic, cubic, radical, absolute value, rational (enrichment) and piecewise functions. Perform translations including f(x+c), f(x)+c. and -f(x). Find the inverse of a function and compose functions.

6 weeks

Total Weeks = 36

YUHSD ALGEBRA III/IV SCOPE AND SEQUENCE 2019 - 2020

Unit 1: Solving equations and inequalities

Learning Goal: The student will be able to solve linear, absolute value, radical and rational equations and inequalities.

Objectives: TLW

Notes and Examples Proj. Time

Resources AZCCRS

1.1 Solve linear equations. • Review solving linear equations (multiple steps, fractional coefficients and proportions)

o Ex: 3

𝑥+1=

4

𝑥−1

• Include no solution, one solution and many solutions.

• Include applications of real-world context.

7 days Intermediate Algebra

(Green spine)

2.1, 2.2, 2.3

A2.A-CED.A.1

A2.A-REI.B

1.2 Solve linear inequalities • Review solving linear inequalities

• Represent solutions to inequalities using interval notation and line graphs. Include compound inequalities

• Include applications of real-world context.


(Green spine)

2.4 and 2.5

A2.A-CED.A.1

A2.A-REI.B

1.3 Solve absolute value equations include utilizing problems with real-world context.

• Review concept of absolute value as distance from zero with two possible values (+/-)

• Solve absolute value equations that only have one absolute value.

• Include problems that have no solution.


(Green Spine)

2.6

A2.A-REI.B

A2.N-Q.A.2

1.4 Solve radical equations include utilizing problems with real-world context.

• Solve radical equations with only one radical.

• Radicals could be square root or cube root.

• Include equations that have no solution

o Ex:

▪ √𝑥 + 5 = 7

▪ √𝑥 + 23

= 3

▪ √𝑥 + 5 = −8

6 days Intermediate Algebra:

(Green Spine)

7.6

A2.A-REI.A.2

A2.N-Q.A.2


1.5 Solve rational equations include utilizing problems with real-world context. (Enrichment)

• Teach restrictions on the domain when x is in the denominator

• Solve rational equations.

• Include equations with solutions that contradict the restriction on the domain


(Green Spine)

6.6, 6.7

A2.A-REI.A.2

A2.N-Q.A.2

Days for review and assessment

Formative Assessments 5:

Summative Assessment 1:

7 days

Deadline: 09/13/2019

Total projected time to complete the unit 6 weeks


Unit 2: Properties of Exponents, radicals and complex numbers

Learning Goal: The student will be able to simplify numeric and variable expressions using the properties of exponents and

complex numbers.

Objectives: TLW


Resources AZCCRS

2.1 Simplify radical expressions

• Simplify radical expressions containing numbers and variables.

• Locate rational numbers on a number line (ACT N303)

• Rationalize denominators with radicals (No conjugates)


(Green Spine)

7.1

A2.N-RN.A.2

2.2 Simplify expressions using the product rule, the zero exponent rule, the quotient rule and the negative exponent rule.

• Use the product rule, the quotient rule, and the negative exponent rule to simplify exponential expressions

• Evaluate expressions raised to the 0 power

• Include expressions that contain more than one variable.


(Green Spine):

5.1

A2.N-RN.A.1

A2.N-RN.A.2

2.3 Simplify expressions using the power rules.

• Use the Power rule for exponents to simplify expressions

• Use the Power of a product rule to simplify expressions: (𝒂𝒃)𝒎 = 𝒂𝒎𝒃𝒎

• Use the power of a quotient rule to simplify

expressions: (𝒂

𝒃)

𝒏=

𝒂𝒏

𝒃𝒏 (𝒃 ≠ 𝟎)

• Include expressions that contain more than one variable.


(Green Spine):

5.2

A2.N-RN.A.1

A2.N-RN.A.2

2.4 Simplify expressions using the rules for rational exponents

(enrichment)

• Understand the meaning of 𝑎1 𝑛⁄ , 𝑎𝑚 𝑛⁄ , 𝑎−𝑚 𝑛⁄

• Use the rules for exponents to simplify expressions that contain rational exponents.

• Include expressions that use more than one rule to simplify.


(Green Spine):

7.2

A2.N-RN.A.1

A2.N-RN.A.2


2.5 Perform arithmetic operations with complex numbers

• Know and use the vocabulary of complex numbers (I, imaginary number, complex number, conjugate, rationalize).

• Apply the relation 𝑖2 = −1

• Apply the commutative, associative, and distributive properties to add, subtract, and multiply complex number.

• Write complex numbers in the form (𝑎 + 𝑏𝑖) with a and b real. Find the conjugates and their products.

• Rationalize denominator using conjugates


(Green Spine)

7.7

Beginning Algebra:

(Red Spine)

9.4

A2.N-CN.A.1




7 days




Unit 3: Quadratic equations and systems

Learning Goal: The student will be able to represent quadratic equations both algebraically and graphically (systems)

Objectives: TLW


Resources AZCCRS

3.1 Solve quadratic equations • Review factoring methods – GCF, square root method, ac method.

• Solve quadratic equations by square root method, factoring and completing the square (enrichment)

• Solve quadratic equations by evaluating the quadratic formula. Answers can be real or imaginary, exact or approximate.


(green spine)

5.5, 5.6, and 5.7

5.8, 8.1, and 8.2

8.3

A2.A-REI.B.4

A2.N-CN.C.7

3.2 Graph quadratic equations • Determine Domain and Range

• Identify and graph the following:

o The x and y intercepts

o The vertex

o Relative maximums and minimums

o The axis of symmetry

• Determine on which intervals (interval notation) a function is increasing or decreasing

• Determine on which intervals (interval notation) a function is positive or negative

• Determine end behavior

o 𝑎𝑠 𝑥 → ∞; 𝑓(𝑥) → _____

o 𝑎𝑠 𝑥 → −∞; 𝑓(𝑥) → _____

• Graph and label the quadratic equation

7 days Beginning Algebra

(red spine)

9.5

Intermediate Algebra

(green spine)

8.5, 8.6

A2.A-APR.B.3

A2.F-IF.B.4

A2.F-IF.C.7


3.3 Solve systems consisting of a linear and quadratic equations both algebraically and graphically.

• Review graphing linear equations

• Solve systems of equations algebraically

o With two linear equations (review)

o With one linear and one quadratic equation.

• Solve systems of equations graphically

o With two linear equations (review)

o With one linear and one quadratic equation

7 days Rayner

7.6 (limit to linear and quadratic)

A2.A-REI.C.7

A2.A-REI.D.11

3.4 Graph piecewise functions (enrichment)

• Introduce piecewise notation:

o 𝑓(𝑥) = {𝑥 + 2, 𝑥 < −2

𝑥2 − 1, 𝑥 ≥ −2

• Graph piecewise functions, limit to:

o Two linear equations

o One linear and one quadratic

• Special attention should be given to the end behavior of each piece

6 days A2.F-IF.C.7




6 days




Unit 4: Probability and Statistics

Learning Goal:

Objectives: TLW


Resources AZCCRS

4.1 Simple Probability • Intro to probability P(A)

o Vocabulary

o Features of Dice, cards, socks and marbles (fair and unfair)

o With replacement, without replacement

• Experimental versus theoretical

8 days Pemberton

3.24, 3.25, 3.26, 3.27

6.24, 6.25, 6.26

Rayner

10.4

P.S-MD.B.5

4.2 Fundamental Counting Principle

• Sample spaces for multi-stage

o Ex: tree diagrams

• Sample spaces for compound

o Set, union, intersection

4 days Rayner

10.6

A2.S-CP.B.6

A2.S-CP.B.7

A2.S-CP.B.8

4.3 Compound probability

• Sample spaces for independent and dependent

o “or” versus “and”

• Probability of compound events

o P(A∪B) and P(A∩B)

8 days Pemberton

9.13,

Rayner

10.5

A2.S-CP.B.6

A2.S-CP.B.7

A2.S-CP.B.8

A1.S-CP.A.1


4.4 Normal Distribution • Measures of central tendency: Mean, Median, Mode and Range

• Applications of Mean.

• Normal Distribution:

o Bell curve

o Empirical rule (68/95/99.7)

10 days Rayner

10.2,

A1.S-ID.A.2




6 days




Unit 5: trigonometry

Learning Goal:

Objectives: TLW


Resources AZCCRS

5.1 Solve right triangles using trigonometry including application problems

• Find missing sides using Pythagorean theorem:

o Pythagorean triples (3, 4, 5), (5, 12, 13) (8, 15, 17) and (7, 24, 25)

o Find missing sides or a 30-60-90 and a 45-45-90

• Find side lengths using sin, cos and tan

• Find angles using sin-1, cos-1 and tan-1

• Find missing parts of right triangle in real-world context.

8 days Geometry (Glencoe)

7.4 and 7.5

G.G-SRT.C.8

5.2 Solve triangles using the law of sines and law of cosines including application problems

• Law of Sines (ASA and SSA)

• Law of Cosines (SAS and SSS)

• Finding missing parts of non-right triangles in real-world context.

10 days Geometry (Glencoe)

7.6 and 7.7

Rayner:

6.5, 6.6

G.G-C.B.5

P.G-SRT.D.11

5.3 Introduction to radian measure

• Definition of radian measure

• Converting between radian measure and degree measure

6 days Swokowski/Cole

6.1

G.G-C.B.5


5.4 30-60-90 and 45-45-90 triangles and the unit circle

• Review 30-60-90 and 45-45-90 and their side relationships. Introduce Pythagorean

triples (1, 1, √2) and (1, √3, 2)

• Develop the unit circle.

o Sign rules for each quadrant (ASTC)

o Given the value of a trig function, find the other 5 trig values.

6 days Rayner

6.4

Swokowski/Cole 6.2

P.F-TF.A.3

P.F-TF.A.4




6 days




Unit 6: Building Functions

Learning Goal:

Objectives: TLW


Resources AZCCRS

6.1 Definition of a Function • Determine if given relations are functions both graphically and algebraically (algebraically do basic relations only).

• Use function notation to evaluate functions given an equation, graph, or table of values.

3 Intermediate Algebra

(green spine)

3.2

A2.F-IF.C.8

6.2 Domain and Range • Find the domain and range of relations given graphical representations with and without discontinuities or a set of points.

• Express domain and range of relations in interval notation

• Find the domain of polynomial (quadratic and cubic), rational, and radical functions algebraically.


(green spine)

3.2

A1.F-IF.A.1

6.3 Operations on Functions • Add, subtract, multiply, divide functions (note restrictions in domain)

• Compose functions using the notation both sets of notations:

o 𝑓(𝑔(𝑥)) and 𝑓 ∘ 𝑔(𝑥)

• Evaluate composite functions 𝑓(𝑔(2)) given equations and graphs


(green spine)

9.1

A2.A-SSE.A.2

6.4 Inverse Functions • Generate the inverse of a linear, cubic

(𝑓(𝑥) = 𝑥3 + 2) and a rational function where the numerator is a constant.

• Verify that two functions are inverses of each other algebraically.

• Generate the graph of the inverse of a function given f(x).


(green spine)

9.2

A2.F-BF.B.4


6.5 Graphing Parent functions and their translations

• Graph parents functions and their translations including 𝑓(𝑥 + 𝑐), 𝑓(𝑥) + 𝑐, and −𝑓(𝑥) where c is an integer. Include linear, quadratic, cubic, square root (radical), absolute value and exponential.

• Determine:

o the domain and range in interval notation

o Intervals for increasing and decreasing

o Intervals for which the function is increasing or decreasing.

o End behavior

• Describe the transformation made to a parent function

• Find the new location of a point on a transformed function given the point on a parent function.

o Ex: If point P(2,3) is on 𝑓(𝑥), where is

P on 𝑓(𝑥 − 5) + 3.

8 College Algebra

(Gustafson and Frisk)

3.4

A2.F-BF.B.3




7 days



YUHSD #70 Math Progression

2019-2020

MAT 099 Principles of IGCSE

Mathematics

MAT 100 IGCSE

Mathematics I

MAT 201 IGCSE

Mathematics II

MAT 305 Algebra III/IV

MAT 310 Math

Analysis

MAT 330 Calculus

MAT 085 Financial Algebra

*For seniors who

struggled in 11th

grade math class

MAT 500 AP Calculus

MAT 320 Pre-Calculus

MAT 315 Statistical reasoning

in Sports

Prerequisites:

MAT 100, 200, and

201

MAT 515 AP Statistics

Prerequisites:

MAT 305

Notes:

MAT 200 will be retired as of June30, 2019

ELP for MAT 200 will be offered for recovery during the 2019-2020 school year.

ELP for MAT 201 will be created during the 2019-2020 school year so it can be implemented during the summer extended learning of 2020.

Level 1 Level 2 Level 3 Level 4

Struggled

Got It! Got It!

Got It!

©f n2g0e1r9N PKLuTteaW dSjoofhtww[ahrNeh pLhLUCj.C E xAolplA JreikgJhctKs` trTepsfeIrtvyezdn.s M CMqaedKeu OwGiwtXhf _IZnJfViVnNiWtPeh IA^lqgnexbLrOaf b2R.

Worksheet by Kuta Software LLC

Math III/IV

Pre-test Version 1

Name___________________________________ ID: 1

Date________________ Period____©i M2G0l1n9S GKXu]tPaT QSaoDfntIw[a`rbep tLtLiCe.q u IAtl_lC mrpiOgshZt[sP IrTezs]eFrQvleGdK.

-1-

Solve each equation.

1) -6a - 35 = -8(-2 + 3a) + a

A) No solution. B) {12} C) {3} D) {16}

2) -8(8 - 5a) = -384

A) {-16} B) {-8} C) {-6} D) {16}

Solve each inequality.

3) 248 < -4(8x - 8) - 8

A) x < -20 B) x > -20 C) x < -7 D) x < -28

4) Write the slope-intercept form of the equation through: (4, -4) and (-4, 1)

A) y = -3

2x +

5

8B) y =

5

8x -

3

2C) y = -

5

8x -

3

2D) y =

3

2x +

5

8

5) Find the measure of the angles of a triangle if the measure of the first angle is three times themeasure of the second angle and the third angle is 20° more than the second angle.

A) 40° , 20° , 120° B) 60° , 20° , 100° C) 52° , 32° , 96° D) 69° , 23° , 88°

6) A ladder measuring 24 feet in length is leaning against the side of a house. The angle the laddermakes with the ground is 46°. What is the distance (to the nearest foot) from the base of theladder to the base of the house?

A) 13 feet B) 21 feet C) 17 feet D) 36 feet

©Y T2o0V1x9[ uKsuUt_aI ySgorfptqwPa\rsew tLJLPC[.F N qAvlKlC crviQgGhat\sa DrUegsEefrnvReqd`.F Z QMBa]dieG SwviEtCh[ pICnHfkidnziotbed dA\leg[evbKrKaT Q2r.


-2-

7) Tori, Monica and Gina are camping in their tents. The tents form a triangle at the campsite. If thedistance between Tori and Monica is 153 feet, the distance between Tori and Gina is 201 feet,and the distance between Monica and Gina is 175 feet, what is the measure of angle (to thenearest degree) at Monica’s tent?

A) 48° B) 75° C) 47° D) 76°

8) Solve the system of equations given by:2x + y = 217x - 8y = 16

A) (-8, 5) B) (-8, -5) C) (8, -5) D) (8, 5)

9) Simplify (-3 + 2i)2

A) 5 + 12i B) 21 - 20i C) 5 - 12i D) 12 - 16i

10) Simplify i

-1 - 3i

A) -i7

B) 1 - 3i

10C)

-1 + 3i10

D) -i - 3

10

11) Solve 3m2 = 1 - 2m for m

A) {-3

2, 1} B) {

3

2, 2} C) {-

3

2, -2} D) {

1

3, -1}

©e Z2h0V1C9n TKdu`t]aZ KSkoZfttUwgarr^eg fL[LbCd.Y ` nAZlGlG OrliIgMhEt^sn FrMepsneZr[vAexdS.o s zMJaKdFeB MwFiwtFhL BIynMfDifn`iTtle] GAVlZg_eGbNrSae W2m.


-3-

12) A bag contains seven red marbles and eight blue marbles. You randomly pick a marble and thenreturn it to the bag before picking another marble. Find the probability that the first marble is redand the second marble is blue.

A) 7

30 » 0.233 B)

4

15 » 0.267 C)

24

91 » 0.264 D)

56

225 » 0.249

13) There are four nickels, three dimes, and three quarters in your pocket. You randomly pick a coin. Find the probability that it is a nickel or a dime.

A) 8

11 » 0.727 B)

1

3 » 0.333 C)

6

11 » 0.545 D)

7

10 = 0.7

Sketch the graph of each function.

14) y = -x2 + 4x - 3

A)

x

y

-20 -15 -10 -5 5

-25

-20

-15

-10

-5

B)

x

y

1 2 3 4 5 6 7

-2

-1

1

2

3

4

5

6

C)

x

y

-7 -6 -5 -4 -3 -2 -1

-2

-1

1

2

3

4

5

6

D)

x

y

-1 1 2 3 4 5

-4

-3

-2

-1

1

2

©g N2d0F1^9K jKLuktzaL XSBoofXtEwmawrIej hL\LvCg.X h lA[lzlv `rfi\gih\tisH Rr^eZsYeJrHvderdt.h w ]MeaVdMej ywKiStThA qIHnNfpiMnmiQtfeI oASlpgremb\rYaU B2k.


-4-

15) f (x) = 2(x + 2)2 - 3

A)

x

y

-4 -2 2 4

-4

-2

2

4

6

B)

x

y

-6 -4 -2 2

-4

-2

2

4

C)

x

y-4 -3 -2 -1 1 2

-7

-6

-5

-4

-3

-2

-1

D)

x

y

-1 1 2 3 4 5

-2

-1

1

2

3

4

Find the distance between each pair of points.

16)

x

y

-4 -2 2 4

-4

-2

2

4

A) 4 3 B) 3 10 C) 2 3 D) 17

©c M2A0K1J9t vKquet]ak HSuo\fZtJw[a\rKeW cLULdC`._ b CAdlllT YrkikgkhGtTsG UrJeCsZerrJvYende.f B UMmafdfeI gwhiZtmhr pIUnBfaimnMift\eA OAElPghe_bCriac ]2J.


-5-

17) Find the inverse of g(n) = 1

2n + 1

A) g-1(n) = 3n + 2 B) g-1(n) = 2n - 2 C) g-1(n) = n + 3 D) g-1(n) = 2

5n +

3

5

18) f (x) = -3x2 + 5g(x) = 3x - 3Find ( f g)(x)

A) -27x2 + 54x - 22 B) -9x2 + 12 C) -16x2 + 36x - 20 D) 3x2

19) Solve n = 4n - 7 + 3 (remember to check for extraneous solutions)

A) {10, 8} B) {8, -2} C) {8} D) {7, 8}

20) Solve 9x - 4 - 6 = 25

A) {5

2, -3} B) {

39

5} C) {

35

9, -3} D) {

39

5, -5}

©J U2J0h1C9i cKsu]tqap \SVo`fhtQwRaRrdeL zLCLkCf.E Z jAclrln Nr\isg`hItDs_ lrZeVsQeIrdvzeGdR.X [ pMea_dseT _wWi\tFhf EIln^fSiPnOiZtUee gAAlsgGeTbSrDav Q2`.


-6-

21) Solve 10x2 + x - 12 = 0

A) {-1 + 481

20,

-1 - 481

20} B) {

7 + 3 41

16,

7 - 3 41

16}

C) {7 + 89

2,

7 - 89

2} D) {

-7 + 89

2,

-7 - 89

2}

Find each measurement indicated. Round your answers to the nearest tenth.

22) Find BC

14 miA

B

C59° 30°

A) 15 mi B) 9 mi C) 12 mi D) 11 mi

23) cos q

106

8

q

A) 25

7B)

4

5C)

4

3D)

5

3

©G w2g0O1^9k bKtu[tWaL cSqoUfktSw^alrDeY PL]LOC`.A F \AklMlA pr[iggQhvtfsD Jrme]sfe`r_vjeqdS.P V _Mea[dWeB hwAihtph_ XIkn_fSibnIi^tOeR yAilsgZeVbgrYaN ]2j.


-7-

Graph each function.

24) f (x) = -2

x - 3 - 2

A)

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

B)

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

C)

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

D)

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

25) Given the midpoint (6, 2) and one endpoint (8, 6) of a line segment, find the other endpoint.

A) (10, 10) B) (4, -2) C) (-7, -10) D) (7, 4)

©b L2l0t1t9v wKwuCtSaw tSzo_fFt[wwahrzen OLeLWCd.a O `Avlpli HroihgXhytZso brUejsTeDrWvoekdD.Y E `Mda[dWeu gwsi]tshK lIbnOfOiJnNiotAei eAxlrgIe^b^rpaR m2X.


Math III/IV

Pre-test Version 2

Name___________________________________ ID: 1

Date________________ Period____©A k2U0U1[9\ aKXu`tlaP vSeo`fDtAwGaxrSep eLPL\CJ.V o rAzlWl` lrjikgIhPtjs\ XrKeUsjexrbvGe_dU.

-1-

Solve each equation.

1) 24 - 6a = -2(3 + 8a)A) {9} B) {-3} C) {15} D) {-7}

2) -7(1 - 5x) = -112

A) {-3} B) {-1} C) {-11} D) {9}

Solve each inequality.

3) 7 + 3(-5n + 4) < 139

A) n > -10 B) No solution. C) n > -8 D) n > -24

4) through: (-4, 2) and (0, 1)

A) y = 1

4x -

1

4B) y = -

1

4x + 1 C) y = x -

1

4D) y = -

3

4x -

1

4

5) Find the measure of the angles of a triangle if the measure of the first angle is three times themeasure of the second angle and the third angle is 20° more than the second angle.

A) 60° , 20° , 100° B) 40° , 20° , 120° C) 52° , 32° , 96° D) 69° , 23° , 88°

6) A ladder measuring 24 feet in length is leaning against the side of a house. The angle the laddermakes with the ground is 46°. What is the distance (to the nearest foot) from the base of theladder to the base of the house?

A) 36 feet B) 17 feet C) 21 feet D) 13 feet

©^ z2H0T1\9^ JKMugtla\ dSYoJfqtBwDabrUeV mLqLOCz.g j [Azlzln GrhiegWhptwsP aroePsWeZrNvWesdT.d p iM`ardqev uwbivtzhx iIFnRfKitnNibtpe^ yAPlbgAeQbUrSad g2r.


-2-

7) Tori, Monica and Gina are camping in their tents. The tents form a triangle at the campsite. If thedistance between Tori and Monica is 153 feet, the distance between Tori and Gina is 201 feet,and the distance between Monica and Gina is 175 feet, what is the measure of angle (to thenearest degree) at Monica’s tent?

A) 48° B) 75° C) 76° D) 47°

8) -2x - 2y = 4x - y = -6

A) (-2, -4) B) (-1, -4) C) No solution D) (-4, 2)

9) (1 - 3i)(7 + i)A) -4 - 22i B) 10 - 20i C) -4 + 22i D) 4 - 22i

10) 7

-2 - 3i

A) -14 + 21i

13B)

-12 + 18i13

C) -28 + 21i

25D)

-7 + 21i10

11) 2k2 = 3 - k

A) {3

2,

1

2} B) {1

2, -

3

2} C) {- 3

2, 1} D) {- 3

2}

©j S2M0F1W9z cKquvtcaH cSqoSfCtGwZajrneI RLVLTCB.C ` KAolylS erGiTgwhgtRsW MrUebsseerkv_edds.W J gMeaYdaeV PwbiKtWhZ KI]nNfliGnUiPtieg pAJlug_eNbcrXau P2u.


-3-

12) A spinner has an equal chance of landingon each of its five numbered regions. Youspin twice. The first spin lands in regionfour and the second spin lands in regionone.

A) 1

25 = 0.04 B)

16

121 » 0.132 C)

1

5 = 0.2 D)

5

22 » 0.227

13) A basket contains five apples and fourpeaches. One of the apples and one of thepeaches are rotten. You randomly pick apiece of fruit. It is fresh or it is a peach.

A) 8

9 » 0.889 B)

3

5 = 0.6 C)

2

7 » 0.286 D)

2

3 » 0.667

Sketch the graph of each function.

14) y = -x2 - 8x - 15

A)

x

y

-15 -10 -5 5 10

-30

-25

-20

-15

-10

-5

B)

x

y

-7 -6 -5 -4 -3 -2 -1

-5

-4

-3

-2

-1

1

2

3

C)

x

y

-1 1 2 3 4 5

-1

1

2

3

4

5

D)

x

y

-1 1 2 3 4 5 6

-5

-4

-3

-2

-1

1

2

3

©i R2O0l1z9M eKpustsaU tSCocfnt^wMabrYeX ELBLjCp.A H CAtlrlG xrnizgahJtas_ ]rgexsieFrOvnesds.[ ] jMLaFdces aw`imt_ho GIVnNfpiIncietiei wAClkg`eXbwrla` M2p.


-4-

15) f (x) = -(x + 1)2 - 3

A)

x

y

-5 -4 -3 -2 -1 1 2 3

-8

-7

-6

-5

-4

-3

-2

-1

B)

x

y

2 4 6 8 10

-4

-2

2

4

6

C)

x

y

-2 -1 1 2 3 4

-6

-5

-4

-3

-2

-1

D)

x

y

-5 -4 -3 -2 -1 1 2 3

-8

-7

-6

-5

-4

-3

-2

-1

Find the distance between each pair of points.

16)

x

y

-4 -2 2 4

-4

-2

2

4

A) 4 3 B) 3 10 C) 2 3 D) 17

©f s2U0F1n9J _KJuUt_au ySwojfgtAwoayrReT pLmL`Ct.` i NAglBlz KrFijgyhftwsn arqeQsbeNr^voe_dI.O A sMHaFdcef LwuiZtjhz yIenlfVifnCiBtKeR gASlLgFeubcrvaN Q2M.


-5-

17) g(x) = -20 - 2x

5

A) g-1(x) = -5x - 20

2B) g-1(x) = -5x

C) g-1(x) = 5x + 5

3D) g-1(x) = -

2

3x -

4

3

18) f (a) = -2a2 + 5aFind ( f f )(a)

A) -4a - 2 B) -8a4 - 40a3 - 60a2 - 25aC) -8a4 + 40a3 - 60a2 + 25a D) -a - 8

19) 1 = 3v + 4

A) {-1} B) {-1, 1} C) {1} D) {-2}

20) 1 + 8n

10 = 3

A) {0, -2

5} B) {- 13

5, 1} C) {6, -4} D) {29

8, -

31

8 }

©f _2T0G1o9g iKluvtaa^ JStoZf\tYw]aZr]ee [LjLUCJ.z h tAvlOlN RrQi_gjhTtdsk BrheHsvevrJvAeXdA.` H IMTaVdpeP dwAiktshC \INn]fxignliHtHec nAIligVeabIrPaj [2B.


-6-

21) 10k2 + 2k - 20 = 0

A) {-1 + 21 , -1 - 21} B) {1 + 201

10,

1 - 201

10 }C) {-2 + 19

6,

-2 - 19

6 } D) {-1 + 201

10,

-1 - 201

10 }

Find each measurement indicated. Round your answers to the nearest tenth.

22) Find AC

28 mC

A

B

66°

36°

A) 18 m B) 20 m C) 15 m D) 16 m

23) cos q

25

20 15

q

A) 4

3B)

3

5C)

3

4D)

4

5

©S A2h0N1x9y zKguKtSaE tSUoGfUtZwTasrLer nLELDCq.a W ^Aelplo urni^goh`tgst qrjeJsDenrBvCerda.N Y fMRaxdHen BwEiItthF xIXngfRiwnSiDtcer SAbltgievbLrlau W2_.


-7-

Graph each function.

24) f (x) = -2

x + 2 + 3

A)

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

B)

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

C)

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

D)

x

y

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

25) Given the midpoint (6, 2) and one endpoint (8, 6) of a line segment, find the other endpoint.

A) (10, 10) B) (4, -2) C) (-7, -10) D) (7, 4)

GR Alg III/IV Name:_____________________

Period:_______ 1.1 Assessment Solve. Show all your work. Reduce any fractions to simplest terms. 1. 5x – 4 = 26

2. 6x = 4(5 + x)

3. 4(x - 5) = 2x - 14

4. !

"+ #

$= 5

5. Golf Carts at Desert Hills Golf Course cost $10.50 to rent and $1.25 for each hour you use it. How many hours could you rent a bike if you had $35?

GR Alg III/IV Name: ________________ Quiz 1.2 – Inequalities Hour: ______ Show all your work. Credit will be awarded for correct follow through. Include the inequality, graph your answer, and write it in interval notation. Problem Inequality Graph Interval Notation

2𝑥 − 8 < 20

8 ≤ 2 − 𝑥 ≤ 20

−1 ≤𝑥 + 24 < 2

2𝑥 + 1 < 3𝑥 − 4 < 4𝑥 + 2

GR Alg III/IV Name:_____________________

Period:_______ 1.3 Assessment Solve. Show all your work. Reduce any fractions to simplest terms. 1. |8𝑥 − 4| = 36

2.3|6𝑥 + 2| = 12𝑥

3.

|"#$%|&

= 4 4. −10|5𝑥 − 10| + 6 = −44

GR Alg III/IV Name:_____________________

Period:_______ 1.3 Assessment

GR Alg III/IV Name:_____________________

Period:_______ 1.4 Assessment Solve. Show all your work. Reduce any fractions to simplest terms. 1. √𝑥 − 11 = 4

2. √3𝑥 + 3 − 4 = 8

3. *3𝑦 + 6 = *7𝑦 − 6

4. √2𝑥 − 3! − 2 = −5

5. A wire is needed to support a vertical pole 19 feet high. The cable will be anchored to a stake 7 feet from the base of the pole. How much cable is needed?

ALGEBRA III/IV 2019-2020 Scope and Sequencefunctions. 6 weeks UNIT 6: Functions • Deadline:...

Documents

Transcript of ALGEBRA III/IV 2019-2020 Scope and Sequencefunctions. 6 weeks UNIT 6: Functions • Deadline:...