Midterm Review Answers

Name:

Lomas MB43 Testl

Lo arithms and Ex onents Test 1.

The function y (1) x

= 2x

is equivalent to

= y10g2

(3) Y

~~~Ogv

2.

What is the value of 2 -3 ?

= x10g2

(1) .!..

(4) y=10g2x

(3)-6

~

(4) -8

CD 3.

If logx 9 = -2, what is the valueofx? 3 (1) 81 1 1 (2) (4) 81 3

4'

tV

\

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l j

Find x to the nearest tenth.

5x="-'.6

X~~ [OJ

_ rz.

'f

5.

If log a = 2 and log b = 3, what is the numericalvalue I 6.

~

of log -rb ?

If loga

=x

(1) x+2y

~

o

r;

and 10gb = y, whatis loga.Jb? x+y (3)-

(3) 25 (4) -25 (2) 2x+2y

~~D

b3 L'

* (o~ ~ ~,~

7.

--

3109

In the equation logx 4 + logx 9 = 2, x is equalto (1) .J13 (3) 6.5

~

8.

Write in exponential fonn. 1.5 = 10~8

(4) 18

(0J ~

9.

b

~'S

Write in logarithmic fonn. 72 = 49

)b ~ ~

10. Find the value ofx.

log93 = x

11. Solve algebraically for x: 82x = 46

12. Find the value of x. log6X= 2

14. Solve for x to the nearest hundredth. log35 + log3X= log3(7 + X) .

[~h

SX

'£:11(7 +-IC

5X

15. Solve for x: 10gb3 + lo~ x

= 10gb 12

16.

)

.

~

::

7-r- X

Solve for m: 3m+1- 5 = 22

ft;. +'5'

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)X :::/J-

fY\.+(

3 ~

~J-I In +-1

-:2

:::- J

3

M~d-

t'Y\~ \

~

'3

17. The number of houses in Central Village, New York, 18. A population of wolves in a county is represented by grows every year according to the function the equation P(t) = 80(0.98)', where t is the H(t) = 540(1.039Y, where H representsthe number number of years since 1998. Predict.the number of of houses, and t represents the number of years since wolves in the population in the year 2008. January 1995. A civil engineering firm has suggested that anew, larger well must be built by the village to supply its water when the number of houses exceeds 1,000. During which year will this fIrst happen?

l000~5~DL).D)~'f [

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101 (

Lomas MB43

Name: Transformations 2.

1. Which transformation is not an isometry? (1) rotation (2) line reflection

(2) (2,-5)

serve orientation?

(I) translation (2) dilation

3. If point (5,2) is rotated counterclockwise 90° about the origin, its image will be p . (1) (2, 5)

Which transformation does n

~

(-2, 5)

~

(-5, -2)

~

4.

h \

5. Which transformation represents a dilation?

When the point (2,-5) is reflected in the x-axis, what are the coordinates of its image? (1) (-5,2) (2) (-2,5)

6.

(3) (2,3)-+(3,2) ) (2,3)-+(-4,-5)

(4) (5,2)

The image of the origin under a certain translation is the point (2,-6). The image of point (-3,-2) under the same translation is the point (1) (-6,12) (2) (-5,4)

7. The x-axis is not the line of reflection for which of the following pairs of points? [A] R'(l, 5) ~ R'(l, - 5)

~5)~

3 1 (3)(-2:'-)

~) <-1,-80

8. Which transfonnation of y = 2X results in the (1) 1'0,2 ~2'+2?

[B] n'

(2) 1'0.-2

---Gl R'(-9. 4

(3) ry-axis (4) rx-axis

t

[D]R'(3, - 2) ~ R'(3, 2)

10.

II Solve for x: lo&. 64 = 3

12. If the coordinates of point A are (-2,3), what is the image of A under rx-axis 0 D2 ?

13

What is the image of point (1,1) under

~,-2

0 ~Oo

?

14. Is the transfotmatiollan isometry? Do the figures have the same 01'opposite orientation?

o

4

D'

C'

D 15 Is the transformation an isometry? Do the figures have the same or opposite orientation?

B.

yes ,5wk!1 <'7L5P.. 0ppD j,'k l>r)eJ-J'hv

c

p~;J)

A1f b(~

16. Reflect the triangle with vertices: (-3,-1), (-5,4), & (-3,-3) over the line y ""x.

c' Explain how you know.

17

Draw the image produced when tJ,.ABC is

18.Find rx-axis(4,-2)

translated (3. 4).

. . . .. . . '.1 . I . "'......

.

. . .. .. 1\' A...1 - .{L'.. .. . ... . ,,}., . . . _. . . . .. .. .. .. .. .. .. .. ...-. . ~. ,. .. .. , . .. .r ..-

..

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-~y

::::

--

J d---

, Cif

10-

.,... I. . x. ..I'.. ... ... ...t.. .. ."'. . . . . . I . . . . . .I'. ..tt....., .....t.... . . . . t. . . . . . . . . . . . . , . , ,,..,,t..

. . .. ., . . . I , ..

. . . . .. ... ! . . . . .. .-1~~

.

.

19 On the accompanying grid, graph and label AB, where A is (0,5) and B is (2,0). Under - the transformation rx-axis 0ry-axis (AB), A maps to A", and B maps to B". Graph and label A" B". What single transformation would map AB to A"B" ?

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,
Lomas MB43

Name:

Conics Review 1.

What is the discriminant ofy = x2 - 4x + 7

bd,-~ll(,

(-~)J-- '1 (\)\J)

16; 3.

5.

7.

What shape is the equation x2

d.-
What shape is the equation x2 + y2

= 16 ?

What are the coordinates of the center of the circle represented =25?

Which equation, when graphed on a Cartesian coordinate plane, would best represent an elliptical racetrack?

+3(y

8)2 = 36?

(_ \J i)

@

- 2y2 = 16?

by the equation (X+3)2 +(y_4)2

9.

2. What is the center of the ellipse (x+li

4. When the point (2,-5) is reflected in the x-axis, what are the coordinates of its image?

6. Solve: 3 = logzx

8. What is the equation of a circle with center (-3,1) and radius 7?

I ( The accompanying diagram shows the graphs of a linear equation and a quadratic equation.

y

16)3x2 + 10y2 = 288.000":) (2) 3x + 10y = 288,000 (3) 3x2 -1 oi = 288,000 (4) 30xy = 288,000

How many solutions are there to this system of equations? 11.

What is one solution of the accompanying system of equations?

y

y ~) (~

13.

= - x2 + 5

= -05x2

+3

1: The roots of a quadratic equation are real, rational, and equal when the discriminant is

~

(1) -2 (2) 2

(4) 4

Ci~~

The roots of the equation 2X2

- 8x - 4 = 0 are

1, The roots for the equation x2 (1) {1,-6} (2) {2,-3}

- 5x = 6

~6D

(4) {-2,3}

x~ -S')< -(, ~ (~-~ \(:'~,\,:;:()

are

\1

/

Find a)rootS,b)tUfI\ingpoint, and c)max

~\l)

y == ;+ 8x- 17

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\7.

On the accompanying grid, sketch the graphs of

3y

= 7x

- 3 ~ X ~ 3.

+ 3 over the interval

state the coordinates of all points of intersection.

Y

Identify

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18.

Graph: - -- - - -- - - - - -

try rot..

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------............-----------\ --- -- ---- --- -- --- ------- ------ -----'""--

(x_l)2 4

-c:--(y+l)2 = 1

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