Keyport Public Schools
Summer Mathematics Packet for Students Entering
Geometry
Name:_________________
Teacher:_______________
Keyport School District
Summer Course Work
Review for Geometry
Congruence
Experiment with transformations in the plane
Understand congruence in terms of rigid motions
Prove geometric theorems
Make geometric constructions
Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations
Prove theorems involving similarity
Define trigonometric ratios and solve problems involving right triangles
Apply trigonometry to general triangles
Circles
Understand and apply theorems about circles
Find arc lengths and areas of sectors of circles
Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
Use coordinates to prove simple geometric theorems algebraically
Geometric Measurement and Dimension
Explain volume formulas and use them to solve problems
Visualize relationships between two-dimensional and three-dimensional objects
Modeling with Geometry
Apply geometric concepts in modeling situations
Mathematical Practices
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Reference Sheet
Geometry Summer Packet
Show all work for each question in order to receive full credit.
1. Evaluate the expression 43𝑤 , when 𝑤 = 5
2. Evaluate the expression 𝑟 2 , when 𝑟 = 17
2
1
5
6
3. Evaluate the expression 𝑥 , when 𝑥 =
4. Evaluate the expression 2𝑛 , when 𝑛 = 4
5. Evaluate the expression 12 − 2(13 − 9 + 3)
6. Evaluate the expression 130 ÷ (42 − 6)
7. Evaluate the expression
(4+62 )
5
8.
7
8
+
3
10
9. 5.3(−0.8)
10. −42.6 ÷ (−7.1)
11.
4
5
×
1
4
12. Express 30% percent as a fraction in simplest form.
13. Express 13.7% as a decimal.
14. 20 is what percent of 160?
15. 51 is 50% of what number?
16. What number is 75% of 600?
17. Translate the verbal phrase “the quotient of four and a number, minus seventeen” into
an expression.
18. Translate the verbal phrase “the quantity of twelve more than a number, times eight”
into an expression.
19. Translate the verbal phrase “six less than the product of five and a number is twentynine” into an equation, then solve.
20. Find the missing side using the Pythagorean Theorem.
21. The two shorter sides of a right triangle have measures of 3 inches and 4 inches
respectively. What is the measure of the hypotenuse? (hint: Use the Pythagorean
Theorem)
22. What is the volume of a rectangular prism with a length of 5 cm, a width of 8cm, and a
height of 10 cm?
23. What is the volume of a cylinder with a height of 10 in and a radius of 6 in? (Use 3.14
for 𝜋)
24. What is the volume of a cylinder with a height of 10 in and a diameter of 8 in? (Use 3.14
for 𝜋)
25. The volume of a cylinder is 3 times larger than a cone with the same height and radius.
What would the volume of a cone be if a cylinder with the same height and radius has a
volume of 240 𝑐𝑚3 ?
26. The area of a square is 100 square centimeters. Suppose the sides of the figure are
doubled. What will be the new area of the similar figure?
27. What is the sum of the measures of the interior angles of a nonagon? Use 180(n-2).
28. What is the measure of one angle in a regular octagon? Use
180(𝑛−2)
𝑛
.
29. A road sign in Spain gives the distance to Madrid as 80 kilometers. What is the distance
in meters?
30. Solve for the variable:
7𝑥 − 90 = 120 + 𝑥
31. Solve for the variable:
22 − 15𝑥 = −8 − 2𝑥 − 18𝑥
32. Solve for the variable:
4𝑦 + 5 + 5𝑦 + 40 = 180
33. Solve for the variable:
−2(14𝑥 + 5) = −8
34. Solve for the variable:
(𝑥 − 4)
=8
6
35. Use FOIL to multiply:
(𝑥 + 4)(𝑥 − 2)
36. Use FOIL to multiply:
(3𝑥 − 5)(6𝑥 + 2)
37. Calculate the slope of a line containing the following points: (3,8) and (0,4)
38. Calculate the slope of a line containing the following points: (4,2) and (-7,-8)
39. Solve the following proportion:
2
8
=
𝑥 + 1 12
40. Solve the following proportion:
𝑥+3 𝑥−1
=
16
8
41. If the area of the rectangle below is 48 square units, solve for x:
42. Give the coordinates of the image of point A(3,5) after it is translated 5 units up, and 4
units to the left.
43. Using the graph below, plot the following points: R(4,3) , S(6,8), T(-4,7), X(-2,-3), and
Y(6,-2)
44. What is the area of a circle with a diameter of 20 inches?
45. What is the circumference of a circle with a radius of 3cm?
46. What is the area of the trapezoid below?
47. What is the measure of angle BCD?
48. Angle X and Angle Y are supplementary angles. What is the measure of Angle X if Angle
Y is 30°?
49. What is the value of x in the diagram below?
50. Determine whether or not the two rectangles below are similar. Show your work.