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.  

To the incoming Math 9 students:


Summer Math Work Part 1: 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.  This is due on Wednesday, September 4, 2019.


- 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 


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?

Summer Math Work Part 2: MATH VOCABULARY

Summer Vocabulary Assignment – due Friday, September 6, 2019

Each student is to purchase a 3-subject notebook used solely for Math Vocabulary.

You will have numerous checkpoints throughout the year, where each given word is to be accompanied by an appropriate definition and a sound example.  Vertically fold the pages down the middle, so that two columns are formed.  The word and its definition are to be located in the left column, while the example is to be provided in the right column (next to the word/definition).  All is to be neatly handwritten and completed alphabetically.  Remember to use valid resources when researching.




Absolute value   

Absolute value function                   

Acute angle                         

Acute triangle                                    


Addition property of equality

Addition property of inequality

Additive identity

Additive identity property

Additive inverse

Additive inverse property                                               

Adjacent angles 

Algebraic equation           

Algebraic expression       

Algebraic inequality        

Alternate exterior angles

Alternate interior angles 





Arithmetic sequence                                         

Associative property of addition

Associative property of multiplication


Average rate of change

Axis of symmetry


Base of a geometric figure             

Base of a power




Boundary line

Box plot (Box-and-whisker plot)

Break in a graph


Causal relationship

Center of dilation

Center of rotation                             

Central angle                                     



Circle graph                       



Closure property                                               





Common denominator

Common difference

Common ratio                                                   

Commutative property of addition

Commutative property of multiplication                   

Complementary angles   

Completing the square     

Composite numbers                          

Compound interest





Consecutive integers                                        


Constant function

Continuous graph

Conversion factor

Coordinate plane



Correlation coefficient                    

Corresponding angles for lines

Corresponding angles for polygons

Corresponding sides

Cosine ratio


Cross products


Cubic function


Customary system of measurement




Degree for measurement

Degree of a polynomial


Density property               

Dependent events

Dependent variable                          





Direct variation

Discrete graph



Distributive property                       


Division property of equality

Division property of inequality                                                     


Domain of relations/functions

Dot plot

Double distribution



Elimination method for systems


Equilateral polygon                         




Even integer


Experimental probability               


Exponential decay

Exponential function       

Exponential growth


Extended distribution

Exterior angle



Face of a geometric shape                              




First quartile





Function notation

Fundamental counting principle



Geometric sequence

Graph of a function                          

Greatest common factor (GCF)    

Greatest integer function







Horizontal shift

Horizontal shrink

Horizontal stretch                                             



This concludes the 1st checkpoint.  More words will be announced in September.