College Prep Winter Break Math Packet

8/3/2019 College Prep Winter Break Math Packet

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Name__________________________________________ February Break Packet (honors Geometry) Due Mon, Feb. 27th

Answer all questions in the space provide. You must show all work to receive credit for all questions.

1. In the figure below, what is the value of ?

(A) 80

(B) 90

(C) 100

(D) 110

(E) 120

t u+

2. In the figure shown, line is parallel to line .

What is the value of ?

(A) 150

(B) 140

(C) 130

(D) 110

(E) 100

l m

x

3. If and bisects in the figure shown,

which of the following CANNOT be concluded?

(A)

(B)

(C)

(D)

(E)

AB BC BC AC

w x

w z

x y

AD DC

BD AC

=

=

=

=

=


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4. In the figure shown, if 30,

what is the value of ?

(A) 60

(B) 150

(C) 180

(D) 210(E) 330

z

x y

=

+

4. In the figure shown, and are each perpendicular to .

If , the length of is 4, and the length of is 8,

what is the length of ?

(A) 3 2

(B) 6 2(C) 8 2

(D) 10 2

(E) 12 2

AE CD CE

x y AB BD

CE

=

5. In the xy-plane, the center of a circle has coordinates (3, -7).

If one endpoint of a diamter of the circle is (-2, -7), what are the

coordinates of the other endpoint of this diameter?

(A) (-7, -7)

(B) (-2, -2)

(C) (3, -2)

(D) (8, -2)

(E) (8, -7)

6. A right circular cylinder with radius 5 and height 4 has volume .

In terms of v, what is the volume of a right circular cylinder

with radius 5 and height 8?

(A) 4

(B) 2

(C) 4

(D) 6

(E) 8

v

v

v

v

v

v

+


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7. The cube shown has edges of length 2,

and and are midpoints of two og the edges.

What is the length of (not shown)?

(A) 2

(B) 3

(C) 5

(D) 6

(E) 10

A B

AB

8. In the figure above, , and . If the lengths of

and are equal, what is the value of ?

KN JL LM JL

LN LM x

9. What is the value of ?x

10. On the number line shown, there are 9 equal intervals

between 0 and 1. What is the value of ?x


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11. Determine the value of x and y

12. Given points (-2, 3), (1,0), (7,6), (0,5)

a. Prove that quadrilateral is a trapezoid

b. If points , ( , ) and are collinear.

Find the values of and such that points

,

A B C D

ABCD

B E h k C

h k

A , , and are the vertices of a parallelogram.

c. Prove is a rectangle

B E D

ABED


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B

C

D

A

E

13.

: Rhombus

diagonal is extended through to

and are drawn

Prove:

Given ABCD

AC C E

BE DE

BE DE


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P

S T

WR

14.

: Isosceles trapezoid RSTW

Prove: RPW is isosceles

Given


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Name: ____________________________________________________ KIPP NYC College Prep

Geometry Midwinter Break Packet Due February 27th

1. In , , , and . What is the value ofx?1) 29

2) 313) 59

4) 61

2. Which expression best describes the transformation shown in the diagram below?

1) same orientation; reflection

2) opposite orientation; reflection

3) same orientation; translation

4) opposite orientation; translation

3. Which statement is logically equivalent to If a triangle is an isosceles triangle, then it has two congruen

sides?

(A) If a triangle does not have two congruent sides, then it is an isosceles triangle.(B) If a triangle does not have two congruent sides, then it is not an isosceles triangle.

(C) If a triangle is not an isosceles triangle, then it has two congruent sides.

(D) If a triangle is an isosceles triangle, then it does not have two congruent sides.

4. Which transformation is notalways an isometry?1) rotation

2) dilation

3) reflection

4) translation

5. In , . An altitude is drawn fromB to and intersects atD. Which conclusion is notalwaystrue?

1)

2)3)

4)

6. What is the negation of the statement "13 is prime"?

(A) 13 is odd. (B) 13 is not even. (C) 13 is composite. (D) 13 is not prime.


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7. Which equation represents a line parallel to the line whose equation is ?1)

2)

3)

4)

o o

o

o

8. ABC and DBE intersect at B. If m ABE= (2 +25) and m ( 50) , then

which of the following must be true?

I. 25

II. 75

III. = 85 .

(A) I o

x ABD x

x

m ABE

m ABD

= +

=

=

nly (B) II only (C) III only (D) I and II (E) II and III

9. In the diagram below of , , , and . What is the length of ?

1)

2)

3)

4)

10.What is an equation of the line that contains the point and is perpendicular to the line whose equation is?

1)2)

3)

4)


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11. In the diagram below, is shown with extended through pointD. If ,, and , what is the value ofx?

1) 12

2)

3) 164)

12.What is the image of point after the composition of transformations defined by ?1)

2)

3)

4)

13.What is the inverse of the statement If two triangles are not similar, their corresponding angles are notcongruent?

1) If two triangles are similar, their corresponding

angles are not congruent.

2) If corresponding angles of two triangles are not

congruent, the triangles are not similar.

3) If two triangles are similar, their corresponding

angles are congruent.4) If corresponding angles of two triangles are

congruent, the triangles are similar.

14. . In the accompanying diagram of rectangleABCD, mBAC= 3x + 4 and mACD =x + 28.

What is mCAD?

(A) 12 (B) 40 (C) 37 (D) 50


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15. Which is the slope of the line that passes through the points ( , ) and (2 , )a b a b ?2b -a

(A) (B) 0 (C) (D) undefined3a b

16. In the diagram below, under which transformation will be the image of ?1) rotation

2) dilation

3) translation4) glide reflection

17.After a composition of transformations, the coordinates , , and become ,, and , as shown on the set of axes below. Which composition of transformations was used?

1)

2)

3)

4)

18. In , , , and . Which expression correctly relates the lengths of the sides ofthis triangle?

1)

2)3)

4)

19.What is the contrapositive of the statement, If I am tall, then I will bump my head?1) If I bump my head, then I am tall.

2) If I do not bump my head, then I am tall.

3) If I am tall, then I will not bump my head.

4) If I do not bump my head, then I am not tall.


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20.SquareLMNO is shown in the diagram below. What are the coordinates of the midpoint of diagonal ?1)

2)

3)

4)

21.On the set of axes below, Geoff drew rectangleABCD. He will transform the rectangle by using the translationand then will reflect the translated rectangle over thex-axis. What will be the area of the

rectangle after these transformations?

1) exactly 28 square units

2) less than 28 square units

3) greater than 28 square units

4) It cannot be determined from the informationgiven.

22.What is the equation of a line that is parallel to the line whose equation is ?1)

2)

3)

4)

23.The endpoints of are and . What are the coordinates of the midpoint of ?1)

2)

3)

4)


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Part IIAnswer all questions in this part. Any questions with the correct answer with no work

shown will only receive 1 point. All questions in this part are 5 points. Be sure to write clearly and legibly. Show all your work. Clearly label any diagrams that you

use.

24. Write an equation of the line that passes through the point (2, 5) and is perpendicular to the line

6 3 12.x y =

25. QuadrilateralABCD has coordinates A (-3, -1), B (-1, 5), C (8, 2), D (6, -4).

Prove: QuadrilateralABCD is a rectangle


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x

(x-10)

30

B

A

E

C

F

D

26. In the figure below, what is the value of x?

27.

28.


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29.

0. On the set of axes below,

a. sketch the points that are 5 units from the originb. sketch the points that are 2 units from the linec. Label with an X all points that satisfy both conditions.


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Name:_________________________ KIPP NYC College Prep

Algebra Winter Break Packet Due February 27th

1. The solution set for the equation is1)

2)

3)

4)

2. What is the value ofm in the equation 2 1 0m m + =( ) ? (1) 1 (3)

1

3

(2) -1 (4) 0

3. In the equation 14

5 51

2n + = , n is equal to

(1) 8 (3)1

2

(2) 2 (4)1

8

4. What is the solution set of ?1)

2)

3)

4)

5. If 3 2 2 1 8( ) ( ) ,x x+ + = the value ofx is(1) 1 (3) 5

(2)1

5(4) 4

6. What is the solution set of the equation ?1)

2)

3)4)

7. If , thenx equals1)

2)

3) 1.254) 2.5


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8. The solution set for the equation is1)

2)

3)

4)

9. What is the solution of ?1)2)

3)

4)

10.If , the value ofx is1) 0

2) 53) 12

4) 20

11.Which value ofx is in the solution set of the inequality ?1)2) 2

3) 3

4)

12.If , then equals1)

2)3) 6

4) 18

13.What is the solution set of the equation ?1)

2)

3)

4)

14.What is the solution set of the equation ?1)

2) {2,8}

3)

4)


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15.What are the solutions of the equation ?1) 1 and 21

2)3) 3 and 7

4)

16.One of the roots of the equation is 3. What is the other root?1) 15

2) 6

3)

4)

17.Which equation has the solution set ?1)

2)

3)4)

18.For which equation is the solution set ?1)

2)

3)

4)

19.The greater solution of the equation is1)2)

3) 3

4) 4

20.What is the solution of ?1) 1 2)5

3) 6 4)14

21.Which value ofx is the solution of ?1)

2)

3)4) 4


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22.What is the value ofx in the equation ?1)

2)

3)

4) 8

23.Which value ofx is a solution of ?1) 2)-3

2) -10 4)-15

24.What is the solution set of ?1)2)

3)

4)

25.What is the value ofx in the equation ?1)

2)

3)

4) 4

26.Which number is in the solution set of the inequality ?1) 5

2) 63) 7

4) 8

27.What is the value of , if and ?1)

2) 23) 10

4) 14


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College Prep Winter Break Math Packet