Geometry/Honors Geometry Summer Packet
Dear 2016-2017 Geometry and Honors Geometry Students:
Summer is a wonderful time for relaxing, reading, traveling and visiting
with family and friends. However, that wonderful time away from
school, as relaxing as it can be, is not good for academics. Since
mathematics is a skill like playing a sport or a musical instrument, lack
of practice can get in the way of mathematical success.
The enclosed problems will help you review the algebra skills that you
will continue to use in geometry. The packet will be collected on
Wednesday, August 17th, graded and will count as a homework
assignment for the first quarter of the upcoming school year. Also,
during the first week, there will be a 50-point Test on the same material.
I have included my email, if you have questions. Also, at the end, there
are some resources that can help you. If you have a lot of trouble
completing the problems in the packet, I highly recommend the Algebra
Brush-Up session the week before school begins.
The work is to be done on loose leaf paper and graph paper. Be sure to
read and follow the directions. I will collect this on Wednesday, August
17, 2016. No late work will be accepted.
Enjoy your summer and I look forward to meeting you in August.
Mrs. Joseph
[email protected]
Topics to Review
Order of Operations
Graph linear equation
Interpret slope and y-intercept of a graph
Write linear equation using slope and y-intercept, point and
slope, two points
Solve equations
Solve inequalities
Solve a system of linear equations algebraically and graphically
Factoring
Radicals – simplify, square
Verbalize processes
Supplies for Geometry and Honors Geometry
3-ring binder (1½ inch or 2-inch)
loose leaf paper
graph paper
a set of five notebook dividers
pencil pouch (several pencils, large eraser, black/blue pen, highlighters,
brightly colored pen/pencil-red, pink, purple)
TI-84 Plus CE graphing calculator
Use loose leaf paper. Copy the problem.
Show your work. Circle or box your answer.
Simplify:
1. 45/5 - (2•3)
2. (2 + 3) • (21 ÷ 3)
4. [6 – (15 ÷ 3)] • 13
5. 42 - 2•8
3. 39 – (7 + 4) • 2
Simplify completely (FOIL):
6. (x + 3)2
7. (a - √2)(a + √2)
9.
(3y + 4)2
10.
5(x – 3)2
15.
6√72
16.
√52
8. (2x – 5)2
Simplify: (Hint – use a factor tree)
11.
√49
12.
13.
14.
√81
√512
17.
2•11√5
√96
Write the equation for the line that…
18.
has a slope of -2 and a y-intercept of 3
19.
has a slope of 1/3 and goes through the point (-6, 2)
20.
goes through the points (-5, 7) and (3, 4)
21.
is horizontal and goes through the point (8, -3)
22.
is vertical and goes through the point (-3, 5)
Solve showing ALL steps:
𝑥
23.
= -13
4
27.
7(9 + m) = 84
24.
8n + 7 = 31
28.
8x – 2 = -9 + 7x
25.
-9a – 13 = -103
29.
14 = -(n – 8)
26.
8+
30.
12 = -4(-6x – 3)
34.
7n – 1 ≤ -169
35.
𝑥
38.
2n2 + 3n – 9
39.
16b2 – 40b + 25
𝑐
−4
=5
Solve and graph on a number line:
31.
-3 ≤ x – 4
32.
-168 > -12a
33.
-4c – 5 < -25
Factor completely:
36.
4a2 - 9
37.
2x2 – 18x – 72
3
>6
Factor and solve:
40.
y2 – 11y + 10
41.
x2 - 5x +6 = 0
42.
2n2 + 11n + 5 = 0
Solve the system by substitution or elimination:
45. 3x – 2y = 2
43.
-3x + 3y = 4
–x + y = 3
5x – 5y = 10
44.
–x – 7y = 14
-4x – 14y = 28
DO THESE PROBLEMS ON GRAPH PAPER!
Graph using the slope and y-intercept:
46.
y = 2x + 5
47.
y = -3x – 2
48.
2x – 3y = 12
Resources:
www.khanacademy.com
www.wolframalpha.com
www.321know.com
www.mathway.com
49.
y = ½x – 2
50.
-x + 4y = 2
FOR FUN!
SOME MORE FUN!
Brain Teasers
Here are some "math" problems that will put your logical and number sense skills to
work. Most of which do not require algebra to solve, but for some of them,
algebra can be helpful. Some are slightly tricky, in that you need to read the statement
of the problem very carefully. Have fun!
Brain Teasers 1
1. A man buys a seagull and a fish for a total of $1.05. The seagull costs a dollar more
than the fish. How much did each cost?
2. Half the employees in a firm went to lunch at noon. Since then, 25 have returned
and 7 others have gone out. At this point, there are twice as many people working as
there are people out to lunch. How many people are employed at the firm?
3. Arrange 8 pennies in a row. The object of the game is to move the pennies one at a
time into an arrangement of four "stacks" of two pennies each. The restriction is that
whenever you move a penny, you must jump two other pennies. To describe your
answer, number the pennies from 1 to 8, and describe a move, for example, by "move
#1 on top of #4".
4. A monk leaves at 6:00 A. M., climbs a trail to the top of a mountain at
a variable rate of speed, and arrives at the summit at 6:00 P. M. He sleeps until 6:00
A. M., and begins his descent along the same trail, arriving at the bottom at 6:00 P. M.
Show that there is at least one place on the trail that he crosses at the same time of day
going up and coming down. The answer is not "halfway up the mountain"!
5. Total the numbers from 1 to 100 by doing one addition and one multiplication. (The
famous mathematician Carl Friedrich Gauss solved this as a grade-school student).
6. Eric starts at 3:00 P. M. driving his car from New York to Philadelphia going 50
mph. Sixty minutes later Steve leaves in his car enroute from Philadelphia to New
York going 40 mph. When the two cars meet, which one is closer to New York?
7. A hunter left camp at 6:00 A. M. and traveled in a due south direction 5 miles,
where he saw a bear. The bear headed off due east, and the hunter tracked him for 5
miles, at which point he gave up, and then travelled due north 5 miles back to his
camp. What color was the bear?
8. If it takes 5 seconds for a clock to strike 6:00 (from the first "bong" to the last
"bong"), how many seconds will it take to strike 12:00?
9. Write an expression for 100 using only four 9's and any of the arithmetic operations
(addition, subtraction, multiplication, division).
10. Two doctors are walking down the street. If one doctor is the biological father of
the other doctor's biological son, how are the two doctors related?
11. How can two American coins equal 30 cents if one is not a nickel?
12. Obtain the next three items in the following sequences of items:
a. A, Z, C, X, E, V, G, ...
b. C, B, A, G, F, E, K, J, I, ...
c. O, T, T, F, F, S, S, E, N, T, E, ...
13. Consider the sequence 1, 4, 9, ... .
(a) Describe a rule that would yield 16 as the fourth term.
(b) What would the fifth term be?
(c) Describe a rule that would yield 22 as the fourth term.
(d) What would the fifth term be?
14. If 3 hens lay 3 eggs in 3 days, how many eggs will 300 hens lay in 300 days?
15. Five students are sitting in a circle. Two pairs of students have the same color hair.
Those with the same hair color are not sitting next to each other. Celeste is on the
right side of Theresa and on the left side of Jane. Celeste has the same color hair as
Ruth. Jane has the same color hair as Alice. Identify the positions of the girls in the
circle.
16. A farmer has 25 calves. All but 19 die. How many does he have left?
17. A rope is tied around the equator of the earth, at the surface. A second rope is also
tied around the equator, directly above the first one at a distance of one foot from it.
(a) How much longer is the second rope than the first?
(You do not need to know the diameter of the earth to solve this problem)
(b) Do you find the answer surprising?
(c) Why or why not?
18. A car made a round trip between two cities at 50 mph. The next day, it made the
same trip at 60 mph going and 40 mph coming back.
(a) Do both trips take the same amount of time?
(b) Do you find the answer surprising?
(c) Why or why not?
(d) How do you explain the apparent contradiction?
Brain Teasers 2
1. A college student sent a postcard home with the following message:
S E N D
M O R E
------------------------------
M O N E Y
If each letter represents a different digit, and the calculation represents a sum, how
much money did the student request?
2. Solve the coin game (Part 1 -- #3) starting with 12 coins.
3. Mr. Dithers is paid a salary of $1000 a week for 22 weeks. Dagwood earns 1 cent
the first week, 2 cents the second week, with his salary doubling every week for 22
weeks. Whose 22-week income is more?
4. What arithmetic symbol can be placed between 2 and 3 to make a number greater
than 2 but less than 3?
5. Why would a hair stylist rather cut the hair of two blondes than of one brunette?
6. My friend and I step onto an "up" escalator. I walk up the moving escalator, while
he enjoys the ride. As soon as I reach the top, the escalator stops. I look back, and he
is halfway down. He then walks up the remaining distance. If my friend and I climb at
the same rate, who has walked more steps to reach the top?
7. The mathematician Augustus de Morgan (who was born in the 19th century) once
said, "I was x years old in the year x2." When was he born?
8. A farmer has hens and rabbits. These animals have 50 heads and 140 feet. How
many of each are there?
9. A farmer's wife drove to town to sell a basket of eggs. To her first customer she
sold half her eggs plus half an egg. To her second customer, she sold half her
remaining eggs plus half an egg. The third customer bought half her remaining eggs
plus half an egg. After these transactions, three eggs were left. How many did she start
with?
10. What do the following words have in common?
OWE TOO FIX MEN SOUR DIVE PINE THREW SEVER LIGHT
11. A frog is at the bottom of a 30-foot well. Each hour he climbs up three feet, and
then slips back two. How many hours does it take him to get out?
12. On their way back to St. Ed's, Lindsey, Allison, and Monica took turns driving.
Lindsey drove 50 miles more than Allison. Allison drove twice as far as Monica.
Monica only drove 10 miles. How many miles was the trip back to St. Ed's?
13. Rafael buys only blue socks and brown socks. He keeps all his socks in one
drawer (unpaired) in which he has 8 blue socks and 6 brown socks. If he reaches into
the drawer without looking, what is the smallest number of socks he must take out to
be sure of getting two of the same color? If he wants a pair of blue? A pair of brown?
14. Solve:
= KISS (each letter represents a different digit.) This
is HARD, but it can be done without the aid of a computer. Please use a calculator,
though!
15. Please help Corey the Camel by creating a plan which gets as many bananas to
market as possible. Corey has 3000 bananas, and needs to take her bananas to market
which is 1000 miles away. The only problem is that Corey can carry only 1000
bananas at any given time, and must eat 1 banana for every mile she walks. Corey
only needs to get to the market and not return. How many bananas can Corey get to
market?