Summer math packet
For Students Entering Honors Algebra 2
This summer math booklet was developed to provide
students an opportunity to review grade level math objectives
and to improve math performance.
Summer 2011
Student Name______
Dear Parents and Students,
In this booklet you will find math activities that will help to review and maintain math skills learned in algebra and geometry and prepare your child for Honors Algebra 2. These activities are varied and are meant to show how much fun and relevant math can be in everyday life. These are activities that should be done throughout vacation, at the pool, at a restaurant, on the beach, etc. They are not intended to be completed in the last 2 or 3 days before school begins.
All activities should be done on separate sheets of paper, organized, and placed into a pocket folder. Parents and students should discuss the activities, and parents should check to see if the activities have been completed correctly. An answer key is included. If you need resources to complete this booklet, please call the school and ask to s peak to the math resource teacher. You may also borrow a text from the school.
All work should be returned to your child’s Algebra 2 teacher at the beginning of the 2011-12 school year in a pocket folder with your child’s name on it. The packet will be counted in the 10% homework category for the first quarter of Algebra 2. It is a completion grade in the homework category.
The work the students complete will prepare them to start the year successfully in Algebra 2. By completing the packet, students will be ready to begin Algebra 2 without having to use class time in review of previously learned skills.
June 20 - 24
Solving Equations
Students should be able to solve 2 step equations with parentheses and variables on both sides. The order is to remove parentheses first, then combine like terms, and finally to place the variable on one side in order to solve the equation. Solve the equations below without a calculator. Then use the calculator to check your solutions.
1. 3 ( r + 1 ) – 5 = 3r – 2 2. -5 ( m + 2 ) – 4( m + 1) - 4 = 0
3. 4 (2r – 8 ) = ( 49r + 70 ) 4.
5. 5 - ( x - 6 ) = 4 6. 2 ( w - 3 ) + 5 = 3 ( w - 1 )
7. The rectangle and square shown below have the same perimeter. Find the dimensions of each.
Solving and Graphing Inequalities
Students should be able to solve and graph inequalities. Inequalities are solved just like equations except for when dividing or multiplying by a negative number when solving. The you reverse the direction of the inequality symbol.
Solve and graph the following inequalities:
1. 2. -7b + 19 < -16
3. One eighth of a number decreased 4. 7q - 1 + 2q 29
by five is at least thirty.
June 27 – July 1
Absolute Value Equations and Inequalities
An absolute value equation is solved for you. Use algebra or the number line to solve.
Examples
-1 3 7
x - 3 = 4 x - 3 = -4 -4 +4
solution set is
Solve these
1. 2.
3. 4.
Arithmetic and Geometric Sequences
· An arithmetic sequence is a numerical pattern that increases or decreases at a constant rate or constant difference.
· A geometric sequence is a sequence in which each term after the nonzero first term is found by multiplying the previous term by a constant called the common ratio.
1. Find the next three terms of the geometric sequences
A. 4, -8, 16, ______, ______, ______
B. ______, ______, ______
2. Find the next three terms in the arithmetic sequences.
A. 12, 23, 34, 45, ______, ______, ______
B. ______, ______, ______
July 4 – July 8
Tables and Finding Patterns
In Algebra 1, we studied these functions: linear, quadratic, exponential, and absolute value. Each of them could be identified by their tables. Once identified, you could find the rule or regression line equation for the function. A linear function table has a constant difference in the y values. A quadratic function has a constant second difference in the table values for y. An exponential function table has y values that are multiplied by the same value each time (the rate of change), and an absolute value table has only positive y values.
In the tables below, identify the table as linear, quadratic, exponential, or absolute value. Then put the values into L1 and L2 and find the function rule for the table. (linreg, quadreg, etc.)
Remember, a linear table has a constant difference in y. A quadratic table has a constant difference in the second difference. An exponential table has y values that are multiplied by the same constant. An absolute value table has only positive y values.
1.
x / -1 / 0 / 1 / 2 / 3y / 5 / 4 / 5 / 8 / 13
type______rule ______
2.
x / -2 / -1 / 0 / 1 / 2y / -8 / -6 / -4 / -2 / 0
type______rule ______
3.
x / -2 / -1 / 0 / 1 / 2y / 2 / 1 / 0 / 1 / 2
type ______rule ______
4.
x / 0 / 1 / 2 / 3 / 4y / 2 / 6 / 18 / 54 / 162
type ______rule ______
5.
x / 3 / 4 / 5 / 6 / 7y / 0 / 6 / 14 / 24 / 36
type ______rule ______
July 11 - 15
Linear Functions
1. Write the Slope Formula
2. What does a line look like that has a a) positive slope b) negative slope c) zero slope d) undefined slope?
3. Find the slope that passes through these pairs of points:
A. ( -4, -1) and ( -3, -3 ) C. ( 2, -6 ) and ( -2, 0 )
B. ( -2, 1 ) and ( -2, 3 ) D. ( 1, 2 ) and ( -1, 2 )
4. Write down the general equation for the slope-intercept form of a line.
5. On a grid in the back of this packet, draw these lines:
A. Slope of , y-intercept of 3
B. Slope of -2, y-intercept of C. Slope of , y-intercept of 0
6. Write an equation that passes through ( 1, 5 ) and has a slope of 2
7. Solve these equations for y
A. 2x + y = 6 B. x + 2y = -4 C. x - y = 6
Linear Inequalities
Linear inequalities are solved just as if they were equations, remembering to change the direction of the inequality symbol when multiplying or dividing by a negative number. The solutions, however, are half planes either above or below the line and either including the line or not. You must solve for y before you can graph the inequality. Use the grids at the back
1. y - 2x -4 2.
3. 2x - 3y > 6 4. 3y - 4x > 12
July 18 - 22
Systems of Linear Equations
Two equations in two unknowns are known as a system of equations. A solution of the equations is an ordered pair that satisfies both equations. The two equations can intersect in one point thus having one solution, be parallel and never intersect thus having no solution, or be the same line and have infinitely many solutions.
You may solve a system of equations by 1) graphing and finding the point of intersection, 2) using substitution, and 3) use elimination by addition, subtraction, and multiplication.
You may use your calculator to solve the system. You would:
A. Solve both equations for y, put them into Y1 and Y2 and look for the point of intersection, or
B. Place the coefficients of the x and y terms in a 2 x 2 matrix (matrix A) and place the constants in a 2 x 1 matrix (matrix B). Then perform A-1B and you will have the solution.
Solve these systems:
1. y = 3x - 4 2. x + y = 2 3. y = 5x
y = -3x - 4 2y - x = 10 2x + 3 y = 34
4. 3a + b = 5 5. 3x - 5y = 16 6. 9x - 8y = 42
2a + b = 10 -3x + 2y = -10 4x + 8y = -16
Polynomials
We can multiply and divide monomials. Please work the following problems.
1. 2. 3.
4. 5. 6.
We can put polynomials in standard form (highest power of x to lowest)
Put in standard form:
1. 2.
We can add and subtract polynomials. Please perform the indicated operations. (Only combine like terms)
1. 2.
July 25 – 29
We can multiply polynomials (the terms do not have to be alike) Perform the indicated operations.
1 2. 3.
We can multiply 2 binomials by the FOIL method or by the BOX method. Please multiply.
1. ( x + 2 ) ( -2x + 4) 2. ( x + 2 ) ( x - 2 )
3. ( 6x - 4 ) ( -8x + 6) 4. ( a + b )2
Take a common monomial factor out of these polynomials.
1. 21cd - 3d 2. 3.
Factor these polynomials into 2 binomials
1. 2. 3.
Factor the polynomials and solve for x. Check them with your calculator (x-intercepts of a parabola)
1. 2. 3.
Use the quadratic formula to solve for x in these quadratics that have irrational roots. Remember to identify a, b, and c in the quadratic. Leave your answer in radical form.
1. 2. = 0 3.
August 1 - 5
Transformations of a Quadratic
You will see quadratics in standard form and vertex form. Both are equivalent and have the same solutions. You go from standard to vertex form by completing the square. You go from vertex form to standard form algebraically. We will present both as you look at properties of a quadratic.
Enter the following quadratics into your calculator and fill in the properties. The first one is done for you.
1.
coordinates of vertex ( -1, -6 ) Remember that the standard
parabola is
is vertex a max. or min.? minimum
max or min value -6
y intercept -5
x intercept(s) -3.4, 1.4
axis of symmetry -1 (x coordinate of vertex)
opens? up
increasing x > -1
decreasing x < -1
dilation? yes/no no (there is no coefficient of x other then 1)
reflection yes/no no (to reflect, coefficient of x must be negative)
translation of vertex left one and down 6 (from 0,0)
2.
coordinates of vertex ______
is vertex a max. or min.? ______
max or min value ______
y intercept ______
x intercept(s) ______
axis of symmetry ______
opens? ______
increasing ______
decreasing ______
dilation? yes/no ______
reflection yes/no ______
translation of vertex ______
5a 5b 5c
1. 2. 3.
4.
9