POMPTON LAKES PUBLIC SCHOOLS
Michael Yuhas
Math Departmental Chairperson
[email protected]
44 Lakeside Avenue
Pompton Lakes, NJ 07442
973-835-7100
June 2016
Dear Parent/Guardians:
In order for students to be ready for their mathematics program this fall, the Mathematics Department requires
that the incoming Academic Pre-Calculus and Honors Pre-Calculus students complete the appropriate Summer
Mathematics Review Assignment. These review activities were previously taught. Therefore students are not
expected to learn new material on their own.
We need your help to oversee the completion of the summer mathematics review questions. Attached is a copy
of the Summer Mathematics Review Assignment. The completed activities packet needs to be returned on
Monday, September 12, 2016. Students will be assessed on mastery of the material by Friday, September
16, 2016.
For those students who have IEPs, please contact your case manager for instructions.
With your help, this summer mathematics review program will be successful in helping your children be ready
for the new school year.
Sincerely,
Michael Yuhas
Math Departmental Chairperson
Summer Math Assignment
This assignment is for all students who are enrolled in Academic Pre-Calculus and Honors Pre-Calculus for the
upcoming school year.
The assignment is due on the first day of classes.
Review of each topic can be found on the following websites:
a.) www.khanacademy.com
b.) www.patrickjmt.com
Please show all work where applicable.
Part 1: Solving Equations Involving Absolute Value
Solve each of the following equations. Check your answers by substituting them back into the original equation.
1.) 3|x| + 7 = 28
2.) |3x – 10| = 5
3.) 4|4 – x| = 16
Part 2: Solving Multi-Step Equations
Solve each of the following equations. Check your answers by substituting them back into the original equation.
1.) 4(x – 3) – x = x – 6
4.) 7(m = 2) – 4m = 2(m + 10)
2.)
𝟔𝒙−𝟏
𝟐
=4
5.) -9 – 3(2x – 1) = -18
3.)
𝟕𝒙+𝟑
𝟑
𝟐
= 2x - 1
6.) n + 6 = 16
𝟑
Part 3: Graphing Linear Equations
Graph each of the following linear equations.
1.) y = 2x + 1
2.) y = -x - 3
3.) 2x + 3y = 6
Part 4: Slope of a Line
Find the slope of each line that passes through the given points.
1.) (2,3) and (5,4)
2.) (3,-2) and (5,1)
3.) (-7,-4) and (-3,-3)
Part 5: Slope-Intercept Equation of a Line
Find the equation of the line in slope-intercept form.
1.) Passes through (2,-3) with slope 4.
2.) Passes through (1,0) and (3,6)
Part 6: Solving and Graphing Inequalities.
Solve each inequality and graph the solution set on the number line.
1.) x + 7 < 𝟏𝟎
2.) -4x ≤ 16
3.) 2x + 6 < 12
4.) 5x +1 > 𝟒𝒙 − 𝟑
5.) - 7 ≤ x + 5 < 2
6.) |x – 2| ≤ 1
Part 7: Graphing Linear Inequalities
Graph each of the following linear inequalities.
1.) y > 3x - 1
2.) y ≥ - 3
3.) y – x ≤ 2
Part 8: Systems of Linear Systems
Solve each of the following using either the substitution or elimination method.
1.) x = y + 3
x + 7 = 2y
2.) 2x + y = 10
3x – y = 5
Part 9: Graphing Systems of Linear Inequalities
Graph each of the following systems of linear equalities.
1.) y < 3x + 1
y < -x - 4
2.) y ≤ x + 1
y ≥ -x + 2
Part 10: Multiplying Monomials
Multiply each of the following. Express your answer with positive exponents.
1.) a3 ∙ a4
2.) x2 ∙ 3x5
3.) (3x)(-2x4)
4.) (6x2y3)(-4x4y2)
5.) x3 ∙ x-5
6.) (x2)3
7.) (5x)2
8.) (2x)2(3y2)2
9.) (3x3)-2
Part 11: Dividing Monomials
Divide each of the following. Express your answer with positive exponents.
1.)
4.)
𝟔𝒂𝟑
𝒂𝟓
𝟗𝒙−𝟑
𝟖𝒙𝒚−𝟓
2.)
5.)
−𝟖𝒙𝟑
−𝟐𝒙𝟐
𝒙𝟓 𝒚 𝟐
𝒙𝒚𝟑
3.)
6.)
𝟐𝟒𝒙𝟐 𝒚𝟐
𝟖𝒙𝒚𝟒
𝟒𝟎
𝟐𝟐
Part 12: Multiplying Polynomials by Monomials
Perform each of the following
1.) 4c(2bc + 5 ab)
2.) 3x(2 – 5x + 5x2)
3.) 3x2y3(-4x2 + 2xy -2x)
Part 13: Multiplying Binomials
Multiply the following pairs of binomials.
1.) (x + 5)(x + 3)
2.) (x + 3)(x – 4)
3.) (x – 6)(2x – 1)
4.) (3x + 2)(x + 4)
5.) 5x – 3y)(2x – y)
6.) (-2x + 1)(2x + 2)
Part 14: Factoring Using Common Monomial Factors
Factor each of the following.
1.) 28x2 – 7x
2.) 20x2 – 80
3.) 21n2 – 14mn
4.) 6x2 + 12x + 24xy + 36
5.) x3 + x2 + 2x
6.) 2x2 + 8x + 4
7.) 16x3 + 25xy2
8.) 3x3 + 30x2 – 75x
9.) 4x5y3 + 4x3y3
Part 15: Trinomials and Differences of Two Squares and Solving.
Solve.
1.) x2 – 64=0
2.) x2 + 11x + 24=0
3.) x2 + 3x -40=0
4.) 4x2 – 1=0
5.) x2 + 24x + 63=0
6.) 16x2 – 25=0
7.) 2x2 + 5x + 2=0
8.) xy2 – xz2
9.) 2x2 – 200y2=0
10.) 7x2 – 9x + 2=0
11.) x2 – 5x + 6=0
12.) 121 – m2=0
13.) 2x2 – 3x – 9 =0
14.) 5x2 – 16x + 3=0
16.) 3x3 – 48x=0
Part 16: Solving Equations Involving Algebraic Fractions
Solve each of the following
1.)
𝟒𝒙
𝟑
=
𝒙
𝟑
+6
2.)
𝒙
𝟑
𝒙
+ = 40
𝟐
3.)
𝟐𝒙
𝟓
𝒙
- =3
𝟒
Part 17: Simplifying Radical Expressions
Simplify each radical expression
1.) √𝟒𝟎𝟎
2.) √𝟒𝟓
3.) √𝟐𝟓𝒙𝟐
4.) √𝟒𝟗𝒙𝟑
5.) √𝟑𝟐𝟎
6.) √𝒙𝟒
7.) √𝟕𝟐𝒚𝟔
8.) √𝟏𝟔𝒚𝟓
Part 18: Adding and Subtracting Radical Expressions
Add or Subtract each of the following. Express in simplest in simplest form.
1.) 9√𝟐 + 3√𝟐
2.) 7√𝟑 - 9√𝟑
3.) √𝟏𝟖 + 5√𝟐
4.) 3√𝟐 + 2√𝟑𝟐
5.) √𝟐𝟕 - √𝟑 - √𝟏𝟐
4.) √𝟑𝒙𝟐 + 3√𝟏𝟔𝒙𝟐
2.) √𝟏𝟒 ∙ √𝟐
3.) 𝟐√𝟐 ∙ √𝟐0
Part 19 Multiplying Radical Expressions
Multiply and simplify each of the following
1.) √𝟑𝟐 ∙ √𝟐
Part 20: Dividing Radical Expressions
Divide and simplify each of the following.
1.)
√𝟕𝟓
2.)
√𝟑
𝟖√𝟒𝟖
3.)
𝟐√𝟑
𝟏𝟐√𝟐𝟎
𝟑√𝟓
Part 21: Rationalizing the Denominator
Rationalize the denominator and simplify completely each of the following.
𝟑
1.) √𝟓
2.)
𝟗
3.)
√𝟑
𝟔
√𝟏𝟐
𝟒
𝒙
4.) √ 𝟐
Part 22: Solving Equations Involving Radicals
Solve each of the following.
1.) x2 = 81
2.) x2 + 5 = 21
3.) 2√𝒙 - 12 = 0
4.) √𝟐𝒙 − 𝟏 = 7
5.) x2 + 7 = 52
6.) 2√𝟓𝒙 = 20
Part 23: Simplifying Radical Expressions with Binomial Denominators
Simplify each of the following.
1.)
𝟏
𝟏+ √𝟑
2.)
√𝟔
𝟏− √𝟔
Part 24: Completing the Square
Solve each of the following by completing the square.
1.) x2 + 6x + 5 = 0
2.) x2 + 2x – 6 = 0
3.) x2 – 4x = 1
Part 25: The Quadratic Formula
Use the quadratic formula to solve each of the following: x =
1.) 2x2 + 3x + 1 = 0
2.) 5x2 + 7x + 2 = 0
Part 26: Composition of Functions
Let f(x) = x2 – 1 and g(x) = 3x.
1.) Find f ° 𝐠
−𝒃±√𝒃𝟐 −𝟒𝒂𝒄
2.) Find g ° f
𝟐𝒂
3.) 2x2 + 5x + 3 = 0
Part 27: Matrices
Find the product.
𝟑
𝟏 𝟓
1.) [
]∙[
−𝟑 𝟎 −𝟒
−𝟐
]
𝟔
𝟐
2.) [𝟎] ∙ [𝟏
𝟔
−𝟑 𝟒]