  Science Mathematics Technology
Education For Building America's Future!

# January 27, 1998

This exam measures your knowledge of Mathematics Course 2. Only part one of the exam is presented here. When you are finished filling out the test press the "Submit" button and you will be able to see how you did.

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1) If a binary operation is defined as

 a * b= 2a+b b
evaluate 6 * 3

(Please note the * represents a dot)

2) In the accompanying diagram, rectangle ABCD is similar to rectangle EFGH, AD = 3, AB= 5, EF = 8 and FG = x. Find the value of x. 3) In the accompanying diagram

 <--> <--> ALB || CJD
and
 <--> LJ
is a transversal.

If m of angle JLB = 6x - 7 and m of angle LJD = 7x +5, find the value of x. 4) Factor completely 2x2 - 18

5) In the accompanying diagram, m of angle ECB = 6x, m of angle ECD = 3x - 11 , and m of angle DCB = 74 . What is the value of x? 6) In triangle MEC, and exterior angle at C measures 1150 and the measure of of angle M is 600. Which is the shortest side of triangle MEC?

7) In the accompanying diagram of rhombus ABCD, m of angle CAB = 35. Find m of angle CDA. 8) Find the positive root of

 1 x+2 x-1 = 4

x "` 1

9) The length of a side of a square is 5. In simplest radical form, find the length of a diagonal of the square.

10) In which quadrant does the image of (4,-7) lie after the translation that shifts (x,y) to (x-6,y+3)?

11) If the endpoints of the diameter of a circle are A(5,2) and B(-3,4). Find the coordinates of the center of the circle.

12) Solve for x:

 2 4 14 x + 3 = 3x

13) In rigth triangle ABC, m of angle C = 90 and altitude

 ___ ___ CD is drawn to hypotenuse AB.

If AD = 4 and DB = 5, find AC. 14) Find the slope of a line that passes through points (-6,8) and (2,-4).

Directions for questions 15 -34. Enter only the number for the answer you choose.

15) If the statements s-->t and t-->u are true, then what is a logically valid conclusion?

1. ~u --> ~s
2. ~u --> t
3. u --> ~t
4. t --> ~u

16) What is the image of (-4,-5) when reflected in the x-axis?

1. (5,-4)
2. (-5,-4)
3. (-4,5)
4. (4,-5)

17) In the accompanying diagram of triangle CDE, m of angle D = 90, m of angle C = 28 and ED = 15. Which equation can be used to find CD?

1.  15 sin 280 = CD
2.  CD sin 280 = 15
3.  15 tan 280 = CD
4.  CD tan 280 = 15

 12! 18) The expression 8!4! is equivalent to

1. 1
2. 495
3. 2970
4. 3960

19) What is the locus of points at a given distance from a line?

1. 1 point
2. 2 points
3. 1 circle
4. 2 parallel lines

20) Which statment is false about the line whose equation is y = -2x-5?

1. Its slope is -2
2. It is parallel to the line whose equation is y = 2x +5
3. Its intercept is -5
4. It is perpendicular to the line whose equation is y = 1/2 x-5.

21) What is the total number of different six-letter permutations that can be formed from the letters in the word "MUUMUU"?

1. 6
2. 15
3. 120
4. 180

22) In the accompanying diagram

 ____ ____ __ __ ACE, BCD, AB, and DE,
angle A is congruent to angle E and C is the midpoint of
 ___ AE. Which theorem justifies triangle ABC is congruent to triangle EDC?

1. SSS is congruent to SSS
2. SAS is congruent to SAS
3. ASA is congruent to ASA
4. SSA is congruent to SSA

23) What is the value (P S) (L U)in the system defined below? PLUS P L U S USPL SPLU PLUS LUSP
1. P
2. L
3. U
4. S

24) In right triangle ABC, angle C is the right angle.If the coordinates of A are (-1,1) and the coordinates of B are (4,-2), the cordinates of C may be

1. (-1,-2)
2. (-1,2)
3. (1,2)
4. (1,-2)

25) In the accompanying diagram, parallel lines

 <--> <--> <--> AB and CD are cut by transverse EF

at P and Q respectively. Which statement must always be true?

1. m of angle APE = m of angle CQF
2. m of angle APE< m of angle CQF
3. m of angle APE + m of angle CQF = 90
4. m of angle APE + m of angle CQF = 180

26) What is the distance between points (6,-9) and (-3,4)?

1. " 34
2. " 106
3. " 178
4. " 250

( Please note " represent the square root symbol)

27) Which equation represents the axis of symmetry of the graph of the equation y = x2 - 6x +5?

1. y = 3
2. y = -3
3. x = 3
4. x = -3

28) If the statements ~(n ^ ~c) and n are true, then which statement is a logical conclusion?

1. c
2. ~c
3. ~n ^ c
4. ~n v c

29) Which set of numbers may be the measure of the sides of a triangle?

1. {10,10,20}
2. {4,6,12}
3. {2,4,6}
4. {8,10,12}

 ___ 30) In the accompanying diagram, altitude EH

is drawn in trapezoid DEFG, DE = 10, EF = 9, FG = 8, and GD = 15 What is m of angle D to the nearest degree?

1. 37
2. 53
3. 60
4. 80

31) Which set is closed under the operation of subtraction?

1. odd numbers
2. counting numbers
3. integers
4. prime numbers

32) What are the roots of the equation x2 - 2x - 1 = 0?

1. x = -1 ± " 2
2. x = 1 ± "
3. x = -1 ± 2 " 2
4. x = 1 ± 2 " 2

( Please note " represent the square root symbol)

33) What are the coordinates of the image of point (-1,2) under a dilation of 3 with respect to the origin?

1. (-6,3)
2. (6,-3)
3. (3,6)
4. (-3,6)

34) The number of degrees in the measure of one exterior angle of a regular pentagon is

1. 72
2. 108
3. 360
4. 540  