Regents Common Core Algebra

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 (1st 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 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).

Abscissa

Absolute value

Acute triangle

Algebraic expression

Algebraic equation

Alternate exterior angles

Alternate interior angles

Angle

Arc

Area

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 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

Quotient

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
- 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.

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.