Geometry Summer Assignment
Dear Student and Parent,
These are the algebraic skills needed for success in Geometry. If you do not remember how to do some of the
problems, search the boldfaced topic on the internet and you will find multiple sites that will re-teach them to
you. It is suggested that you work on this worksheet one to two weeks prior to the school year in order to
refresh your memory and to get you into “math” mode.
For the following exercises, show all work on a separate sheet of paper and do not use a calculator. At Hagerty
High School, the work is extremely important and required. Answers alone will not be given any credit! All
work must be shown for each problem, neatly and in sequential order (even multiplication).
We look forward to helping you learn Geometry next year,
The Mathematics Department at Hagerty
Go Huskies!!!!
A. Solving for a variable:
Solve for the variable, give fractional answers and also write them as a decimal. Round to the fourth decimal place.
1. x + 91 = 146
3. x – 9 = 3x +11
4. 2(3x-4) = 8x + 2
b
3
2.
8
B. Quadratics
Solve the following quadratic functions for all possible values of x by using the quadratic formula.
2. x2 + 4x – 72 = 5x
1. x2 + 4x - 21 = 0
Solve the following quadratic functions for all possible values of x by completing the square.
3. x2 + 6x = 1
4. x2 - 14x = 11
C. Systems of Equations
Solve the following systems of equations (leave all answers in fractional form):
y = 2x – 5
y = 6x + 7
1.
2.
4x + 3y = 5
2x – 5y = -17
D. Simplifying Radicals:
Simplify each of the following radical expressions.
1.
64
4.
2  12
2.
40
5.
3 5  2 10
3.
72
6.
120
10
7.
8.
3 6 8 6
50
49
9. Find the distance between (8, -13) and (1, -7)
10. Find the midpoint between (8, -13) and (1, -7)
E. Slope
Find the slope the line that passes through each pair of points.
1. (7, 2) and (3, 5)
2. (-3, -2) and (4, -2)
F. Equations of Lines
Write the equation of a line with the given information in slope-intercept form: y = mx + b
1. m = 4, b = 8
2. m = -8, b = 11
Write the equation of a line with the given information in point-slope form: y – y1 = m(x – x1)
3. through point (-2, 3) and slope -½
4. through points (1, 2) and (3, 8)
G. Polynomials
Simplify the following:
1. 3x3 + x2 – 8x + 5 – 2x2 + x3 – 4
2. -2x4 + 5x – 7x + 4x9 – 5
Multiply the following:
3. (3v – 1) (4v + 3)
4. (9x – 2)(7x +20)
I. Factoring.
Factor the following equations:
1. x2 + 2x + 1
2. 2x2 + x – 6
3. 3y2 + 7y – 6
4. x2 – 25