Welcome to Common Core Algebra with Mr. Scapellati!

**Common Core Algebra is a rigorous high school level course which concludes with students sitting for the administration of the Algebra 1 Regents Examination in June. Placement in this course is based on the demonstration of strong math skills/potential in both sixth and seventh grades. Successful completion of this course results in appropriate high school credit.
**

*Summer Vacation Math Assignment
– due September 2018 (1 ^{st} day of school)*

PART 1: MATH VOCABULARY

Each student is to purchase two 5-subject spiral notebooks (one for classwork and one for homework) and one 3-subject spiral notebook.

The 3-subject notebook will be contain your math word compilation and should be labeled “Math Vocabulary.”

Vertically fold the pages down the middle, forming 2 columns.

Given the list below, write the word and give its definition in the left column and provide an example of such in the right column next to its meaning. This is to be handwritten (and as neatly as possible).

Please complete alphabetically.

**Abscissa **

**Absolute value **

**Acute triangle **

**Addend **

**Additive inverse property **

**Adjacent angles **

**Algebraic expression **

**Algebraic equation **

**Alternate exterior angles**

**Alternate interior angles **

**Angle **

**Arc **

**Area **

**Associative property of addition**

**Associate property of multiplication **

**Base of a geometric figure **

**Base of a power **

**Bias **

**Binomial **

**Box plot **

**Coordinate plane **

**Central angle in a circle **

**Chord **

**Circle **

**Circumference **

**Cluster **

**Coefficient **

**Commutative property of addition**

**Commutative property of multiplication **

**Complementary angles **

**Composite numbers **

**Compound event **

**Consecutive integers **

**Congruent **

**Constant **

**Corresponding angles **

**Cube root **

**Decagon **

**Degrees**

**Denominator **

**Dependent events **

**Dependent variable **

**Diagonal **

**Diameter **

**Difference **

**Direct variation**

**Distributive Property **

**Dividend **

**Divisor**

**Dot/Line plot **

**Equilateral **

**Equivalent fractions **

**Estimate **

**Evaluate **

**Experimental probability **

**Exponent **

**Factor **

**Fraction **

**Function **

**Gap **

**Greatest Common Factor (GCF) **

**Heptagon **

**Hexagon **

**Histogram **

**Horizontal **

**Hypotenuse **

**Improper fraction **

**Independent events**

**Independent variable **

**Index **

**Inequality **

**Integers **

**Inverse operations **

**Irrational numbers **

**Irregular polygon **

**Isosceles **

**Key/Legend **

**Least Common Multiple (LCM) **

**Legs **

**Line **

**Line segment **

**Linear function **

**Lower quartile **

**Maximum **

**Mean **

**Median **

**Midpoint **

**Minimum **

**Mixed number **

**Mode **

**Monomial **

**Multiple **

**Multiplicative inverse property **

**Natural numbers **

**Negative numbers**

**Non-linear function **

**Nonagon **

**Numerator **

**Obtuse triangle **

**Octagon **

**Order of operations **

**Ordered pair **

**Ordinate **

**Origin **

**Outlier **

**Parallel **

**Parallelogram **

**Pentagon **

**Percent **

**Perfect cube **

**Perfect square **

**Perimeter **

**Perpendicular **

**Pi **

**Plane **

**Point **

**Polygon **

**Polynomial **

**Positive numbers **

**Power **

**Prime numbers **

**Principal square root **

**Prisms **

**Probability **

**Product **

**Proper fraction **

**Proportion **

**Pythagorean Theorem **

**Quadrant **

**Quadrilateral **

**Quotient **

**Radical **

**Radicand **

**Radius **

**Range **

**Ratio **

**Rational numbers **

**Rate **

**Rate of change **

**Ray **

**Real numbers **

**Reciprocal **

**Rectangle **

**Regular polygon **

**Relation **

**Rhombus **

**Right triangle **

**Rounding **

**Same-side exterior angles **

**Same-side exterior angles **

**Scale **

**Scalene**

**Secant of a circle **

**Semicircle **

**Similar figures **

**Skew **

**Slope **

**Solution **

**Square **

**Square root **

**Statistical summary **

**Stem-and-leaf plot **

**Straight angle **

**Sum **

**Supplementary angles **

**Surface area **

**System of equations **

**Tangent to a circle **

**Terms **

**Transversal **

**Trapezoid **

**Triangle **

**Trinomial **

**Unit rate **

**Upper quartile **

**Variable **

**Vertex **

**Vertical **

**Vertical angles **

**Volume **

**Whole numbers **

**X-axis **

**X-intercept **

**Y-axis **

**Y-intercept **

**Zero**

**Zero property of multiplication**

**PART 2: MATH COMPUTATION
Please review the topics listed below and then complete the math exercises that follow, which should be done neatly on loose leaf and/or graph paper with ample work for every question.
TOPICS
- Operations with rational numbers
- Basic irrational numbers
- Extensive percent applications
- Order of operations
- Situations of proportionality
- Graphing points and lines in the coordinate plane
- Multi-step algebraic expressions, equations, and inequalities
- Systems of measurements
- Planar and spatial geometry
- Fundamental statistics and probability
- Radical concepts
- Relations and functions
- Analyzing graphs in detail
- Manipulating formulas
- Systems of equations
- Linear vs. non-linear situations
EXERCISES
1) What is four times the difference of 4/5 and -1/3?
2) Solve: 2w - 1.3 = 13.7 + 4w
3) If you purchase three shirts for $12.38 each and pay $2.81 in tax, how much change will you receive from the cashier if you give her a $50-bill?
4) Explain, in words, how to calculate the area of trapezoid.
5) Convert 13 miles into feet and then into inches.
6) If the area of a rectangle is 3/16 square meters and its length is 0.5 meter, what is the rectangle's width?
7) What is the GCF and LCM of 7, 28, and 35?
8) Explain, via absolute value, how to calculate the distance between the coordinates (14, -139) and (14, -581).
9) If the perimeter of a square is 48 cm, what is the area of this quadrilateral?
10) What is the solution set for -5(x + 2) < 30? Graph this on a # line.
11) If you plan to pay off a loan of $7,800 by submitting $250 per month, how many months will it take you to pay this debt off and how much will your final payment be?
12) Evaluate 10^3 - 12 + -20/4 - 14.4
13) How does one calculate the surface area of right circular cylinder? How does one find the volume of this same figure? Answer the same two questions for a cone too.
14) Convert 4/7 into a decimal and round this to the nearest thousandth.
15) Two angles of a triangle measures 43.95 degrees and 52.3 degrees. Calculate the measure of this polygon's third interior angle. Classify this triangle in two ways.
16) What is 40% of 3/5 of -800?
17) If a = -2/3 what is the value of the expression 8a^2 + 2?
18) Explain, in words, how to plot the point (-23, 12) on a coordinate plane.
19) Sketch a circle and draw one radius, one diameter, one central angle, and one inscribed angle, clearly labeling each of these.
20) Jody reads a book at a rate of 1 page every 3 minutes. If her reading rate remains the same, how long will it take her to read 18 pages?
21) What is the quotient of 724,821 and 15 written as a mixed number?
22) Calculate the mean, median, mode, and range for the test scores of 92, 65, 80, 75, and 80.
23) What is the probability of landing on tails two times if you flip a standard coin for three trials? Explain.
24) A hotel has a number of meeting rooms, m, available for events. Each meeting room has 325 chairs. Write an algebraic equation to represent c, the total number of chairs, in all of the meeting rooms at the hotel. Then, use your equation to determine the total number of chairs in the hotel if there are 8 meeting rooms.
25) If your total bill, after tax, comes to $112.80 and you wish to leave a 20% tip for your waiter, what will your new total be after you factor the tip in?
26) How much smaller is 32.913 than 32.9705?
27) What is the product of 5 radical 12 and 8 radical 3, expressed in simplest radical terms?
28) If you travel 240 miles over a period of 3.5 hours, what is your average speed for this trip?
29) Given the expression 5(4x + 2y) - 17, evaluate this if x = 2.3 and y = -3.
30) Algebraically, find the x-intercept and y-intercept of 5x = 10y + 12.
31) If a baker is making seven apple pies for every four cherry pies, how many cherry pies will he make if the baker makes 42 apple pies?
32) 60 is 90% of what #?
33) Solve: 7m + 8 + 5m = 8m + 24 + 4(m - 10)
34) Graph the function 3y - 8x = 12.
35) Construct a tree diagram for the compound event of rolling a standard number cube and then flipping a standard coin.
36) Solve 2(r - 8) - (r + 7) = 18 - (4r + 9)
37) What is 9.45 X 10^-4 written in standard form?
38) Explain, in detail, the quotient law of exponents.
39) What is the product of 11x^2 and -5x^7?
40) If the area of a circle is 441pi square feet, what is the exact circumference of this circle?
41) What monomial do you get when dividing 4x^6 into the product of 2x^3 and 8x^5?
42) Solve the system of linear equations given by 5x + 2y = 48 and 3x + 2y = 32.
43) Identify the statistical summary and then construct a box plot for the following data set: 5, 6, 7, 8, 19, 19, 18, 17, 9, 9, 9, 10, 17, 14, 12.
44) Jessie runs diagonally across a rectangular field with dimensions of 30 yards and 40 yards. What is the length of the diagonal, in feet, that Jessie runs?
45) A cylindrical can has a diameter of 1 foot and a height of 15 inches. Using 3.14 for pi, calculate the approximate volume for this cylinder.
46) Write an equation of line that passes through the points (2, 0) and (0, 3).
47) Give an example of situation outlined by bivariate date. Explain why such is bivariate.
48) What is the slope of the linear function containing the coordinates (3, 4) and (-6, 10)?
49) Rob's Print Stop just purchased a new printer for $27,000. Each year it depreciates at a rate of 5%. What will be the approximate value at the end of three years?
50) Make a table of values and then use this to graph y = x^2 + 1.
51) Solve -4x + 9 ≥ 45
52) What is the sum of r/2 and (2r)/3 in simplest terms?
53) Translate into algebra: Nine less than twice the difference of j cubed and one
54) What type of lines are not functions? Explain why.
55) Express 5 radical 72 in simplest radical terms.
56) Solve 3 + 2g = 5g - 9
57) Hannah took a trip to visit her cousin. She drove 120 miles to reach her cousin's house and the same distance back home. It took her 1.2 hours to get halfway to her cousin's house. What was her average speed for the first 1.2 hours of the trip? Hannah's average speed for the remainder of the trip was 40 mph. How long did it take her to drive the remaining distance?
58) Explain, in words, how to construct a frequency histogram after intervals have been set up for a set of data.
59) A prom ticket at a local high school costs $120. Zach is going to save money for the ticket by walking his neighbor's dog for $15 per week. If he has already saved $22, write an algebraic sentence that can be solved to determine the minimum number of weeks he must walk the dog to earn enough money for the ticket. Then solve accordingly.
60) Solve 11 - 4(c - 2) + 2c = 5(3c + 1) - 19 - c
**

**61) Solve: w – 1 = 5w + 3w – 8**

**62) Solve: -18 – 6k = 6(1 + 3k)**

**63) Solve: ½(12 – 4d) = 2d + 8 + 2d **

**64) Solve: 2n + 24 + 3n = -2(1 – 7n)**

**65) Solve: -3(4x + 3) + 4(6x + 1) = 43**

**66) Solve: 0.3h + 10 = 0.6h – 20 **

**67) Solve: 2(4v – 3) – 8 = 4 + 2v **

**68) Solve: -5(1 – 5c) + 5(-8c – 2) = -4c – 8c **

**69) Graph the line: y = 4x – 1 **

**70) If the volume of a cylinder is 160pi cubic feet and its height is 10 feet, what is the diameter of this cylinder? **

**
TEST CORRECTIONS
Students must follow this exact format to be eligible for earning points back:
For each exercise that was partially/completely wrong:
1) Write out the entire question.
2) Complete the exercise correctly with ample work.
3) Provide a brief reason as to why it was marked off the first time.
This should all be done neatly on loose leaf, stapled to the back of the signed test, and turned into the math bin within three days of class return. **

**â€‹Topics to review:
Fraction, decimal, and percent forms of rationals
Order of operations with real #s
Unit analysis
Algebraic translations
Solving equations and inequalities
Basic set theory
Function notation
Components of relations
Properties
Function equations in context
Writing linear equations
Rates of change
Literal equations
Manipulating formulas
Linear inequalities in two variables
Laws of exponents
Scientific notation
Systems of linear equations
Solving systems graphically
Solving systems algebraically
Systems of linear inequalities
Word problems using systems
Operations with functions
Basic transformations of functions
Functions and their inverses
Scatter plots
Trend lines and linear models
Data correlations
Residuals
Linear regression
Exponential functions
Exponential growth applications
Exponential decay applications
Solving basic exponential equations
Exponential regression
Comparing linear and exponential cases
Using piece-wise functions
Absolute value functions
Step functions
Quadratic functions
Graphing parabolas
Solving quadratic equations via square root method
Factoring techniques
Geometric transformations
Solving quadratic equations via factoring methods
The quadratic formula
Completing the square
Cumulative vocabulary**