honors geometry - trinity christian school

Approved: L. Byre Updated: 05.05.18

-

For students ENTERING:

Honors

Geometry

*Each page represents work for one week.

equals Week 1, Page 2 equals Week 2, etc.

2018 SUMMER ASSIGNMENT

HONORS GEOMETRY

Honors Geometry Summer Packet

1

*Each page represents work for one week. Page 1 equals Week 1, equals Week 2, etc.

1. Simplify: 12

1

4

2. Simplify: 29 ( 3 4)a a a

3. Simplify: 6 3 e e e

4. Simplify: 8 9

3 12

m

m

5. Solve: 7 6 36h

6. Solve: 13 8 0a a

7. Factor: 216 9s

8. Factor: 2 8 7k k

9. The sum of 37 and three times a number is

67. Find the number.

10. Find the slope of the line between (-1, 3)

and (2, 5).


2

1. Simplify: 2( 3)x

2. Simplify: 63

3. Simplify: 2 6

m mn

n

4. Simplify: 2

2

6

36

k k

k

5. Solve: 3 9 0w w

6. Solve: 2 9n

7. Factor: 235 12u u

8. Factor: 210 3d d

9. Martha has some nickels and dimes worth

$6.25. She has three times as many nickels

as dimes. How many nickels does she have?

10. Graph: 2 5y x


3

1. Simplify: 5 2 3 4(3 )(5 ) (7 )(2 )p p p p

2. Simplify: 2

2

3 17 20

3 10

x x

x x

3. Simplify: .36

4. Simplify: (5 3)(5 3)

5. Solve: 5

15 06

u

6. Solve: 2 7 6 0a a

7. Factor: 210 13 3a a

8. Factor: 281 f

9. Two buses leave a school at the same time

traveling opposite directions. One bus driver

is driving 15 mph faster than the other and

after 3 hrs the buses are 255 mi apart. What

are their speeds?

10. Write the equation of the line with slope

of 3 and containing the point (-3, -5).


4

1. Simplify: 24 ( 8) ( 4 6)

2. Simplify: 4

6

25

15

m n

mn

3. Simplify: 5 2( )w

4. Simplify: 2

5 3

y y

5. Solve: 2 16g

6. Solve: 63

x

7. Factor: 2 7 18n n

8. Factor: 4 4v w

9. If y is directly proportional to x and y =

300 when x = 5, find y when x = 15.

10. Write the equation in slope-intercept

form of the line containing the points (2, 1)

and

(6, 4).


5

1. Simplify: 5 15

3

m

m

2. Simplify: ( 5)( 3)x x

3. Simplify: 2

58x

4. Simplify: 6 9 12

3

x y

5. Solve: 8 5 4 11f f

6. Solve: 2

3 5

c

c

7. Factor: 210 24 8z z

8. Factor: 22 11 12x x

9. On a map, 1 cm represents 25 km. If Colo-

rado is represented by a rectangle 25.8 cm by

18.4 cm, find the approximate area of the

state.

10. Solve by graphing: 9

2

x y

y x


6

1. Simplify: 6 (6 )x x x

2. Simplify: 2

5 5 15

25 5

n

n n

3. Simplify: 9 3 5 3

4. Simplify: 5 2 3

5. Solve: 3 2 5z

6. Solve: 2 36 5c c

7. Factor: 2 7 30b b

8. Factor: 28 22 12a a

9. A camera that originally cost $150 is on

sale at 15% off the original price. Find the

sale price.

10. Write the equation of both lines in slope-

intercept form. y

x


7

1. Simplify: 2

2

5

25

a a

a a

2. Simplify: (6 4)(5 3)a a a

3. Simplify: 4125x

4. Simplify: 2 52

5. Simplify: 72

n

n

6. Simplify: 7 6 5

2 2 2x x x

7. Solve: 1 8 7 23m

8. Solve: 3 2 5

2 15

x y

x y

9. If a bag contains 3 red marbles, 4 blue

marbles, and 6 green marbles, what is the

probability of drawing a blue marble?

10. Determine whether or not the following

points are collinear: (2, 1), (0, -3), (4, 5), and

(-2, -7).


8

1. Simplify: 9

8

2. Simplify: 5

7

3. Simplify: 26

4. Simplify: 2 2 2(5 ) 3x y xy

5. Solve: 1 1 1

3 2x

6. Solve: (2 7)(3 4) 0m m m

7. Factor: 34 100n n

8. Factor: 6 ( 2) 4( 2)a a a

9. Write the following ratio in simplified

form. The ratio of wins to losses for a

baseball team that played 84 games and won

48 of them.

10. Find the slope of the line 3x – 2y = 8.


9

1. Simplify: 2(3 2 4)

2. Simplify:

23

4

x

3. Simplify: 2

4x

4. Simplify: 1

26

5. Solve: 4 7

4 9

x

6. Solve: 26 23 4 0z z

7. Factor: 22 7 4m m

8. Factor: 2 2 1a a

9. The Katchners invested $7500 at 8% and

$3500 at 5%. Find the total annual income

from the two investments.

10. Through the given point, draw a line with

the given slope. P(3, -1), slope 2.


10

1. Simplify: (4 3)(2 1)y y

2. Simplify: 3 54 2 6

3. Simplify: 1 8

3 3 3

c c

c c c

4. Simplify: 3 4 3

5. Solve: 2( 7) 9 19v

6. Solve: 23 9

a a

7. Factor: 2100 25d

8. Factor: 3 260 18 6y y y

9. The length of a rectangle is 5 cm less than

twice the width. If the area of the rectangle is

88 2cm , find the dimensions of the rectangle.

10. Write the equation of the line in

standard form of the line with slope 1/3 and

y-intercept of -2. (Ax + By = C)


11

1. Simplify:

23 5

33 1

2

8

a x

a x

2. Divide: 3 26 5 9

2 3

n n

n

(long division)

3. Simplify: 7 3 1

12 2

n

n n

4. Solve: 2 1a

5. Solve: 18 2 5x x

6. Solve: 1 3 2

2 3

x

x

(quadratic formula)


12

7. Solve: 34 4

x x

x x

8. Solve: 5 2 0

2 3 11

a b

a b

9. Solve by graphing: 3 4 0

2 6

x y

x y

10. Graph 2 1y x

11. Graph 2 2 5y x x and find the

vertex and the axis of symmetry.

Hint: 2

bx

a

12. Graph 1

31

yx


13

13. Find the range of the function

1 1 f x x x if the domain is

2,0, 2 .

14. If John can rake the leaves in 2 hours

and Jeff can rake them in 3, how long will it

take if they work together?

15. The length of one leg of a right triangle

is one centimeter less than twice the length of

the second leg. The hypotenuse is one

centimeter more than twice the length of the

second leg. Find the length of each leg.

16. In a math contest, each team is asked 50

questions. The teams earn 15 points for each

correct answer and lose 8 for each incorrect

answer. One team finished with a score of

566. How many questions did this team

answer correctly?

17. Betty earns a salary of $14,000 per year

plus 8% commission on all sales. How much

must her sales be if her annual income is to

be no less than $15,600?

18. Find the mean, median and mode of the

following set of data: 60, 81, 52, 75, 59, 81


14

19. Jenny has 6 different colored hair

ribbons and wants to wear 2 different colored

ribbons each day. From how many

combinations can she choose?

20. You flip a coin and roll a number cube.

What is the probability that the coin shows

tails and the number cube shows a 3?

Answers:

1) 7

32

x

a

2) 23 2 3n n 3)

22( 6 6)

( 2)( 2)

n n

n n

4) : 3 or 1a a a

5) 7

6) 2 22

6

7) 4 3 8) (2,5)

9) 10) Check on calculator

11) V( 1,4) ; x = 1 12) Check on calculator

13) 1,3 14) 1 .2 hours 15) 8cm 16) 42 questions 17) $20,000

18) mean: 68, median: 67.5, mode: 81 19) 15 20) 1

12


15

Answers

Week # 1

1) -48 2) 3 29 27 36a a a 3) 10e 4) 2 5) 6

6) 13, 8 7) (4 3)(4 3)s s 8) ( 7)( 1)k k 9) 10 10) 2/3

Week #2

1) 2 6 9x x 2) 3 7 3) 2

3

n 4)

6

k

k 5) 3,0,3

6) 83 7) (7 )(5 )u u 8) (5 3)(2 1)d d 9) 75 nickels 10)

Week #3

1) 729p 2) 4

2

x

x

3) .6 4) 22 5) 18 6) 6, 1

7) (5 1)(2 3)a a 8) (9 )(9 )f f 9) 35mph; 50mph 10) y = 3x + 4

Week #4

1) -14 2)3

5

5

3

m

n 3) 10w 4)

2

5 3y

y

5) 4,4 6) 108

7) ( 9)( 2)n n 8) 2 2( )( )( )v w v w v w 9) 900 10) 3 1

4 2y x

Week #5

1) 5 2) 2 2 15x x 3) 1064x 4) 2x -3y + 4 5) : 4f f

6) 2

7) 2(2 1)(2 5)z z 8) (2 3)( 4)x x 9) 296,700 2km 10) 3,6


16

Week #6

1) x 2) 1

( 5)( 3)n n 3) 4 3 4) 5 6 5) 3 6) 9,4

7) ( 10)( 3)b b 8) 2(4 3)( 2)a a 9) $127.50 10) 2y x ; y = 3

Week #7

1) 5

a

a 2) 3 230 38 12a a a 3) 25 5x 4) 4 13 5)

8 14

2

n

n

6)

4

x

7) : 1 2m m 8) (5,5) 9) 4

13 10) yes

Week #8

1) 3 2

4 2)

5 7

7 3)

1

36 4) 5 475x y 5) 6 6)

7 4,0,

2 3

7) 4 ( 5)( 5)n n n 8) 2(3 2)( 2)a a 9) 4 : 3 10) 3

2

Week #9

1) 34 24 2 2) 29

16

x 3) 2 8 16x x 4) 36 5)

64

9

6)

16,

4

7) (2 1)( 4)m m 8) 2( 1)a 9) $775 10)


17

Week #10

1) 28 10 3y y 2) 7 6 3) 2 7

3

c

c

4) 12 5) 7

6) 9 7) 25(2 1)(2 1)d d 8) 6 (5 1)(2 1)y y y 9) 8cm x 11cm 10) x – 3y = 6

honors geometry - trinity christian school

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