UMHS Geometry - Summer Review
Summer Math assignments for current and incoming students
Geometry
All Geometry students are required to have a
TI 84-Plus Graphing Calculator for this course.
The calculator will be used throughout this course, and in future math courses.
Please keep your eyes open for sales and purchase one before school begins.
Show All Work
Area and Perimeter
Area is the number of square units in a flat region. The formulas to calculate the areas of several kinds of quadrilaterals or triangles are:
Perimeter is the number of units needed to surround a region. To calculate the perimeter of a quadrilateral or triangle, add the lengths of the sides. The circumference of a circle is the same as the perimeter of a circle.
Find the area and perimeter (when appropriate) of each figure below. SHOW YOUR WORK.
Area =
Perimeter =
Area =
Perimeter = (Circumference?)
Area =
Perimeter = (Circumference?)
Writing the Equation of a Line
To find the equation of a line:
- Find the slope
- Substitute one point and the slope into the equation of the line and solve for b.
- Rewrite the equation, only substituting in the slope and the y-intercept.
WRITING THE EQUATION OF A LINE. Find the equation of each line described/shown. SHOW YOUR WORK.
9. Write the equation of the line with a slope of 3/4, passing through the point (8, 5).
Equation:
10. Write the equation of the line with a slope of -4, passing through the point (-3, 2).
Equation:
11. Write the equation of the line passing through the points (6, 9) and (2, 7).
Equation:
Write the equation of the line passing through the points (3, -1) and (-2, -6).
Equation:
Multiplying Polynomials
Multiplying Polynomials
In Algebra 1, you learned two methods for multiplying polynomials:
Distributive Property (used to multiply ONE term times a polynomial)
Generic Rectangle (used to multiply a polynomial times a polynomial)
Multiply by using the distributive property or by using a generic rectangle. SHOW ALL WORK.
Factoring Polynomials
In Algebra 1, you learned two methods for factoring.
GCF ➡️ Take out the greatest common factor
Diamond and Rectangle ➡️ Expression must look like the image on the right. Find the outside of the generic rectangle.
Step 1: Take Out the GCF
Factor using the diamond and rectangle.
Step 2: Multiply ax squared and c. Put them in top of the diamond. Put bx in the bottom of the diamond. Find the two missing terms for the diamond.
Step 3: Put the terms from the diamond into the generic rectangle. Find the outside numbers.
Step 4: Write the factored form.
3(x+2) (x+1)
Solving Proportions
Solving Proportions A proportion is two equal fractions. To solve a proportion, simply cross multiply and the products will be equal. Lastly, isolate the variable.
Solve each equation. SHOW ALL WORK.
Solving Systems of Equations
A system of equations is two or more equations with two or more variables. There are four methods for solving systems of equations:
Graphing
Equal Values
Substitution
Elimination
There are many YouTube videos on all of these methods. If you need a refresher on one or more of these methods, please find a video or two to watch.
Solve each system of equations below using any method you choose. SHOW ALL WORK
Simplifying Radicals
Simplifying a radical DOES NOT mean to turn it into a decimal.
STEP 1: Create a factor tree for the number inside the radical. (Cross out any numbers that you break down).
STEP 2: Circle numbers in PAIRS.
STEP 3: The numbers that you circle go in front of the radical (1 number per circle). The numbers that aren’t crossed out or circled, stay inside the radical.
STEP 4: Multiply the outside numbers. Multiply the inside numbers.
Simplify each radical. SHOW ALL WORK.