3' a (0,6) b (0,-6) c (6,0) d (-6,0) 1. d 2. f 6 g 10 h 13...

MP v i i a p t c i t 9 I r u i I I I I

W r i t e t h e l e t t e r f o r t h e c o r r e c t a n s w e r i n t h e b l a n k a t t h e r i g h t o f e a c h q u e s t i o n .

1 . W h e r e d o e s t h e g r a p h o f 3' = — 3 x — 1 8 i n t e r s e c t t h e x - a x i s ? A ( 0 , 6 ) B ( 0 , - 6 ) C ( 6 , 0 ) D ( - 6 , 0 )

2. T i c k e t s t o s e e a m o v i e c o s t $ 5 f o r c h i l d r e n a n d $ 8 f o r a d u l t s . T h e e q u a t i o n 5 x + 8 j = 8 0 r e p r e s e n t s t h e n u m b e r o f c h i l d r e n ( x ) c m d a d u l t s ( y ) w h o c a n s e e t h e m o v i e w i t h $ 8 0 . I f n o a d u l t s s e e t h e m o v i e , h o w m a n y c h i l d r e n c a n s e e t h e m o v i e w i t h $ 8 0 ? F 6 G 1 0 H 1 3 J 1 6

1.

2.

D

i

f

3.

F o r Questions 3 -5 , find the slope of each line described.

3. t h e l i n e t h r o u g h ( 3 , 7 ) a n d ( - 1 , 4 ) A 1 B ^

4 . t h e l i n e t h r o u g h ( - 3 , 2 ) a n d ( 6 , 2 )

11 D 11

^ 1 5. a v e r t i c a l l i n e

A 1 B O

6. W h i c h g r a p h h a s a s l o p e o f — 3 ? G

H 0

C - 1

J u n d e f i n e d

D u n d e f i n e d

H

3.

4 .

5.

6.

7. COMMUNICATION I n 1 9 9 6 , t h e r e w e r e 1 7 1 a r e a c o d e s i n t h e U n i t e d S t a t e s . I n 2 0 0 7 , t h e r e w e r e 2 1 5 . F i n d t h e r a t e o f c h a n g e f r o m 1 9 9 6 t o 2 0 0 7 .

A 4 4 B 4 C 4 D - 4 4

F o r Questions 8 and 9, use the arithmetic sequence 12,15, 18, 21,

7.

8. W h i c h i s a n e q u a t i o n f o r t h e n t h t e r m o f t h e s e q u e n c e ? F a = 3 n + 9 H a = 1 2 n + 3

n n

G a = 9 ? i + 3 J a = n + 3

9. W h a t i s t h e 1 2 t h t e r m i n t h e s e q u e n c e ? A 3 8 B 4 2 C 4 5 D 4 8

8.

9.

B

H

B

Chapter 3 49 G l e n c o e A l g e b r a 1

NAME DATE

3 Chapter 3 Test, Form 1 (continued)

PERIOD

J 2 1 1 . 2 5

10 . S u p p o s e y v a r i e s d i r e c t l y a s x, a n d y — 26 w h e n x = 8. F i n d X w h e n y — 65.

F 3 . 2 5 G 2 0 H 4 7

F o r Questions 1 1 and 1 2 , use the graph shown. 1 1 . W h i c h l i n e h a s a n j - i n t e r c e p t o f - 2 ?

A e. c t

Bp D b o t h ^ a u d i

1 2 . W h i c h l i n e i s t h e g r a p h ofy = 2x + 4? F i H t h e j c - a x i s G p J t

1 3 . W h i c h a r i t h m e t i c s e q u e n c e h a s a p r o p o r t i o n a l r e l a t e d f u n c t i o n ? A - 4 , - 1 , 2 , . . . B 0 , - 2 , - 4 , . . . C 1 , 2 , 3 , . . . D - | , 0 , ̂ , . . .

14. W r i t e 3' + l = — 2 j c - 3 i n s t a n d a r d f o r m . F 2 J C + 3 ' = - 4 G y = -2x - 4 H -2x - y =^ 4 J x + ^ y = -2

y i

f 1 X

0 £\

P

1 5 . F i n d U i e r o o t o f 5a. - 2 0 - 0 .

A - 2 0 B O C 4 D 5

16 . D e t e r m i n e w h i c h s e q u e n c e i s a n a r i t h m e t i c s e q u e n c e . F 3 , 6 , 1 2 , 2 4 , . . . H - 7 , - 3 , 1 , 5 , . . .

J - 1 0 , 5 , - ^ , 4 - . - -A 4 r i i i - 1 -

5- 7' 9- 1 1 '

1 7 . F i n d t h e n e x t t h r e e t e r m s o f t h e s i r i t h m e t i c s e q u e n c e 5, 9 , 13 , 1 7 , . A 2 1 , 2 3 , 2 5 B 2 1 , 2 5 , 2 9 C 4 1 , 4 5 , 4 9 D 2 1 , 4 1 , 6 1

18 . F i n d t h e f u n c t i o n t h a t r e p r e s e n t s t h e r e l a t i o n s h i p . F 3/ = S x H >' - 14A; + 8

G 3 ' - = 8 x + 1 4 J 3 ' = 1 4 x ; + 1 4

1 9 . W h i c h e q u a t i o n i s a l i n e a r e q u a t i o n ? A 4 m 2 = 6

X 0 1 2 3 y 1 4 2 2 3 0 3 8 4 6

B 3 a + 5 6 = 3

C \ x y - \ y = ^

D a;2 + y = 0

20. W r i t e a n e q u a t i o n i n f u n c t i o n n o t a t i o n f o r t h e r e l a t i o n a t t h e r i g h t . F fix) ^2x n f{x)=^\-x G fix^ = X + 1 J fix) = ~x

Bonus G r a p h y = x - 3hy u s i n g t h e x- a n d ^ / - i n t e r c e p t s .

Chapter 3 50

M

10.

1 1 .

1 2 .

13.

1 4 .

1 5 .

16 .

1 7 .

1 8 .

1 9 .

B

B

H

B

G

B

B :

2 0 .

See students' work; x: 3, y i - 3

G l e n c o e A l g e b r a 1

NAME

3 DATE PERIOD

Chapter 3 Test, Form 2A S C O R E

W r i t e t h e l e t t e r f o r t h e c o r r e c t a n s w e r i n t h e b l a n k a t t h e r i g h t o f e a c h q u e s t i o n .

1. LANDSCAPING T h e e q u a t i o n 3x + 7y = 1 0 5 r e p r e s e n t s t h e n u m b e r o f b a g s o f s a n d x a n d b a g s o f m u l c h y t h a t c a n b e b o u g h t w i t h $ 1 0 5 . I f n o b a g s o f s a n d a r e b o u g h t , h o w m a n y b a g s o f m u l c h c a n b e b o u g h t w i t h $ 1 0 5 ?

A 3 5 B 1 7 C 1 5 D 1 0 1 - 9 .

2. I f (a, — 5 ) i s a s o l u t i o n t o t h e e q u a t i o n 3 a = —2b — 7 , w h a t i s a ? F - 1 G O H I J 4

3. W h a t i s t h e s l o p e o f t h e l i n e t h r o u g h ( 1 , 9 ) a n d ( - 3 , 1 6 ) ? c -

25 D 2 25

4. W h i c h e q u a t i o n i s not a l i n e a r e q u a t i o n ? F - 4 0 + 2 u ; = 7 G I = 3 ^ H a; = - 5 J

5. W h a t i s t h e s l o p e o f t h e l i n e t h r o u g h ( - 4 , 3 ) a n d ( 5 , 3 ) ? A O B u n d e f i n e d C 9 D

2 . 3 _ ^

6. I n 2 0 0 5 , t h e r e w e r e 1 2 , 0 0 0 s t u d e n t s a t B e a c o n H i g h . I n 2 0 1 0 , t h e r e w e r e 1 2 , 2 5 0 . W h a t i s t h e r a t e o f c h a n g e i n t h e n u m b e r o f s t u d e n t s ? F 2 5 0 / y r G 5 0 / y r

7. W h i c h i s t h e g r a p h o f y = |^x?

B

H 4 2 / y r

C

X

J 2 0 0 / y r

D

2.

3.

4.

5 .

6.

8. I f y v a r i e s d i r e c t l y a s T a n d y = 3 w h e n . r = 1 0 , find . r w h e n y = 8 , 8 0 G 1 2 H 15 J n o n e o f t h e s e

3 5 4 9. DRIVING A d r i v e r ' s d i s t a n c e v a r i e s d i r e c t l y a s t h e a m o u n t o f t i m e t r a v e l e d .

A f t e r 6 h o u r s , a d r i v e r h a d t r a v e l e d 3 9 0 m i l e s . H o w f a r h a d t h e d r i v e r t r a v e l e d a f t e r 4 h o u r s ? A 1 3 0 m i l e s B 2 2 0 m i l e s C 2 6 0 m i l e s D 6 5 0 m i l e s

F o r Questions 1 0 and 1 1 , use the following information.

T h e n u m b e r o f s e a t s i n e a c h r o w o f a t h e a t e r f o r m a n a r i t h m e t i c s e q u e n c e , a s s h o w n i n t h e t a b l e . 1 0 . H o w m a n y s e a t s a r e i n t h e 1 2 t h r o w ?

F 6 8 G 7 4 H 9 6 1 1 . W h i c h f o r m u l a c a n b e u s e d t o find t h e n u m b e r o f s e a t s i n E i n y g i v e n r o w ?

A a = 6^1 + 2 B a = 2 n + 6 C a = n + 6 D a 5n + 3

Row 1 2 3 4 Number of Seats 8 1 4 2 0 2 6

7.

8.

9.

J 1 1 4 1 0 .

H

1 1 .


NAME DATE

3 Chapter 3 Test, Form 2A (continued)

PERIOD

12. F i n d t h e f u n c t i o n t h a t r e p r e s e n t s t h e r e l a t i o n s h i p .

G y - 3 x - 3 J y = 6x

X 0 1 2 3 4 y - 3 3 9 1 5 2 1 12.

F o r Questions 13 and 14, use the relation shown i n the table.

13. W h i c h e q u a t i o n d e s c r i b e s t h i s r e l a t i o n s h i p ? A f\x)^3x C f{x)=x + 2 B f\x)=4x-l D / T x ) = 2 x + 1

X y 1 3

2 5 3 7 4 9 5 11

y i

m

0 t P

i k

14.

14. W h a t i s t h e v a l u e oiy w h e n x = 4 3 ? F 8 7 H 4 9 G 8 5 J 4 5

15. W h i c h l i n e s h o w n a t t h e r i g h t i s t h e g r a p h o f X - 23/ = 4 ? A I C p B m a t

16. W h i c h e q u a t i o n h a s a g r a p h t h a t i s a v e r t i c a l l i n e ? F 2x=y H 3 x - 2 = 0 G J + 5 = 3 J x-y =0

1 7 . W h a t i s t h e s t a n d a r d f o r m o f j - 7 = - - | ( x + 1 ) ? O

A - 2 x + 3 y = 2 3 B - 3 x + 2y = n C 2 x + 3 y = 1 9 B 3x + 2y = 11 17.

18. D e t e r m i n e w h i c h s e q u e n c e i s not a n a r i t h m e t i c s e q u e n c e .

F - 7 , 0 , 7 , 1 4 , . . . H 1 0 , 6 , 2 , - 2 , . . .

G 0 , i 1 , | , . . . J 2 , 4 , 8 , 1 6 , . . .

19. W h i c h e q u a t i o n d e s c r i b e s t h e n t h t e r m o f t h e a r i t h m e t i c s e q t i e n c e 7 , 1 0 , 1 3 , 1 6 , . . .? A a = 3 n + 4 B a = 7 + 3 n C a = - 4 n + 3 D a = 3 n - 4

15.

16.

18.

19.

20. W r i t e a n e q u a t i o n i n f u n c t i o n n o t a t i o n f o r t h e r e l a t i o n s h o w n a t t h e r i g h t . F f i x ) = - 2 x H f i x ) - X - 2 G / " ( x ) = 2 x + 2 J f i x ) = - X + 2

H

13.

H

20. H

Bonus T h e t a b l e s h o w s t h e s c h e d u l e f o r a t h e m e p a r k r o l l e r c o a s t e r .

Run Number 1 2 3 4 Time 9 : 3 0 A.M. 9 : 3 7 AM. 9 : 4 4 A.M. 9 : 5 1 A.M.

A t w h a t t i m e w i l l t h e r o l l e r c o a s t e r m a k e i t s 1 5 t h r u n ?

Chapter 3 52

B : 11:08 A.M.


NAME DATE PERIOD

Chapter 3 Test, Form 2C S C O R E

1. T i c k e t s for a s p a g h e t t i d i n n e r c o s t $ 4 for c l i i l d r e n a n d $ 6 for a d u l t s . T h e e q u a t i o n 4x + 6y =^ 3 6 r e p r e s e n t s t h e n u m b e r o f c h i l d r e n x a n d a d u l t s y w h o c a n e a t a t t h e d i n n e r f o r $ 3 6 . I f n o c h i l d r e n a r e e a t i n g a t t h e d i n n e r , h o w m a n y a d u l t s c a n e a t f o r $ 3 6 ? 1.

2. I f ( a , 9 ) i s a s o l u t i o n t o t h e e q u a t i o n - 4 a = 6 - 2 1 , w h a t i s a ? 2,

3. F i n d t h e x - i n t e r c e p t ofx — 2y = 9. 3.

4. S o l v e — 3 = — 2 x + 1 b y g r a p h i n g . 4. r r

x = 2

5. F i n d t h e r o o t o f 9 x - 3 6 = 0 . 5.

F o r Questions 6 -8 , find the slope of the line passing through each pair of points. I f the slope is undefined, write undefined.

6. ( 2 , 5 ) a n d ( 3 , 6 )

7. ( 6 , - 4 ) a n d ( - 3 , 7 )

8. ( - 1 , 3 ) a n d ( 6 , 3 )

9. I n 1 9 7 2 , f e d e r a l v e h i c l e e m i s s i o n s t a n d a r d s a l l o w e d 3 . 4 h y d r o c a r b o n s r e l e a s e d p e r m i l e d r i v e n . B y 2 0 0 7 , t h e s t a n d a r d s a l l o w e d o n l y 0 . 8 h y d r o c a r b o n s p e r m i l e d r i v e n . W h a t w a s t h e r a t e o f c h a n g e f r o m 1 9 7 2 t o 2 0 0 7 ?

10. I f a s h a r k c a n s w i m 2 7 m i l e s i n 9 h o u r s , h o w m a n y m i l e s w i l l i t s w i m i n 1 2 h o u r s ?

F o r Questions 11 and 12, determine whether each equation is a linear equation. I f so, write the equation in standard form.

l l . x y = 6 12. 2 x + 3 y + 7 = 3

13. G r a p h t h e e q u a t i o n x - 4 y = 2 .

6.

7.

8.

9.

10.

11.

12.

13.

0

about — 0.07/yr

36 mi

n o

yes ; 2x + 3 y = - 4


NAME DATE PERIOD

3 Chapter 3 Test, Form 2C (continued)

x = 3

1 6 . D e t e r m i n e w h e t h e r t h e s e q u e n c e - 1 0 , - 7 , - 4 , - 1 , . . . i s a n a r i t h m e t i c s e q u e n c e . W r i t e y e s o r no. I f s o , s t a t e t h e c o m m o n d i f f e r e n c e .

1 7 . F i n d t h e n e x t t h r e e t e r m s o f t h e a r i t h m e t i c s e q u e n c e 8 , 1 5 , 2 2 , 2 9 , . . ..

1 8 . W r i t e a n e q u a t i o n f o r t h e nth t e r m o f t h e s e q u e n c e 1 2 , 5 , - 2 , - 9 , . . ..

1 6 . yes; 3

1 7 36. 43, 50

i« an = -7n + 19

F o r Questions 1 9 and 20, use the table below that shows the amount of gasoline a c a r consumes for different distances driven.

Distance (ml) 1 2 3 4 5 Gasoline (gal) 0.04 0.08 0.12 0.16 0.20

1 9 . W r i t e a n e q u a t i o n i n f u n c t i o n n o t a t i o n f o r t h e r e l a t i o n s h i p b e t w e e n d i s t a n c e a n d g a s o l i n e u s e d . 1 9 .

20. H o w m a n y g a l l o n s w i l l t h e c a r c o n s u m e a f t e r d r i v i n g f o r 1 5 0 m i l e s ? 20.

Sample answer: f(d) = 0.04d

Bonus G r a p h x = 3 , y = - 1 , a n d 2 x - 2 y = 0 o n a c o o r d i n a t e p l a n e . /g _-\G i v e t h e v e r t i c e s o f t h e figure f o r m e d b y t h e ' ' ' t h r e e l i n e s . B : ^ ' '

Ciiapter 3 56 G l e n c o e A l g e b r a 1

NAME DATE PERIOD

Chapter 3 Test, Form 3 S C O R E

1. D e t e r m i n e w h e t h e r 3 x - 4 ^ + 7 = 3 y + 1 i s a h n e a r e q u a t i o n . W r i t e yes o r no. I f s o , w r i t e t h e e q u a t i o n i n s t a n d a r d f o r m . J yes; 3x - 7y = - (

2. T h e e q u a t i o n 3 0 0 r c + 5 0 y = 6 0 0 r e p r e s e n t s t h e n u m b e r o f p r e m i u m t i c k e t s x a n d t h e n u m b e r o f d i s c o u n t t i c k e t s y f o r a h o r s e r a c e t h a t c a n b e b o u g h t w i t h $ 6 0 0 . I f n o p r e m i u m t i c k e t s a r e p u r c h a s e d , h o w m a n y d i s c o u n t t i c k e t s c a n b e p u r c h a s e d w i t h $ 6 0 0 ?

3. K ( a , - 7 ) i s a s o l u t i o n t o t h e e q u a t i o n 5 a - 7 6 = 2 8 , w h a t i s a ?

2.

3.

12

-4.2

4. F i n d t h e j c - i n t e r c e p t o f 4 x - 5 y = 1 5 .

5 . S o l v e - - f x + 7 = ^ b y g r a p h i n g .

6. F i n d t h e r o o t o f 1 4 c + 5 = 6 1 .

4.

5 .

6.

3.75

5

T . G r a p h f = | - 1 .

F o r Questions 8 and 9, find the slope of the line passing through each p a i r of points. I f the slope is undefined, write u n d e f i n e d .

8. ( - 8 , 7 ) a n d ( 5 , - 2 )

9. ( 5 , 9 ) a n d ( 5 , - 3 )

10. F i v e y e a r s a g o t h e r e w e r e a p p r o x i m a t e l y 3 5 , 0 0 0 p e o p l e l i v i n g i n L a n c a s t e r . N o w t h e p o p u l a t i o n i s 3 8 , 4 5 2 . F i n d t h e r a t e o f c h a n g e i n t h e p o p u l a t i o n .

7.

8.

9.

10.

13

undef ined

690.4/yr

1 1 . I f a n o s t r i c h c a n r u n 1 5 k i l o m e t e r s i n 1 5 m i n u t e s , h o w m a n y k i l o m e t e r s c a n i t r u n i n a n h o u r ? 11. 60


NAME DATE PERIOD

I Chapter 3 Test, Form 3 (continued)

1 2 . G r a p h y = -^x. 1 2 . 1

1 3 . F i n d t h e v a l u e o f /- s o t h a t t h e l i n e t l i r o u g h ( - 4 , 3 ) a n d ( r , - 3 ) o

h a s a s l o p e o f —. 1 3 . 3

1 4 . F i n d t h e v a l u e o f r s o t h a t t h e l i n e t h r o u g h (r, 5 ) a n d ( 6 , r ) h a s a s l o p e o f 1 4 . 8

1 5 . D e t e r m i n e w h e t h e r t h e s e q u e n c e 0 , ^ , 1 , |, . . . i s a n a r i t h m e t i c s e q u e n c e . I f i t i s , s t a t e t h e c o m m o n d i f f e r e n c e . 1 5 .

1 6 . F i n d t h e v a l u e o f y t h a t m a k e s 9 , 4 , y, - 6 , . . . a n a r i t h m e t i c s e q u e n c e . 1 6 .

1 7 . W r i t e a n e q u a t i o n f o r t h e n t h t e r m o f t h e a r i t h m e t i c 1 7 . s e q u e n c e - 1 5 , - 1 1 , — 7 , - 3 , . . .. T h e n g r a p h t h e first five t e r m s o f t h e s e q u e n c e .

F o r Questions 1 8 and 1 9 , use the table below that shows the value of a vending machine over the first five years of use.

-13

70 13

K = - 1

1

n t t ! ) f

c. A

-Q

-- t y -

i n - 1 V

1 9 - }£.--

Number of Years 0 1 2 3 1 4 5

Value (dollars) 2000 1810 1620 1430 1 1240 1050 a = 4 n - 1 9

1 8 . W r i t e a n e q u a t i o n i n f u n c t i o n n o t a t i o n f o r t h e r e l a t i o n s h i p b e t w e e n y e a r s o f u s e t a n d v a l u e v(t).

1 9 . W h e n w i l l t h e v a l u e o f t h e v e n d i n g m a c h i n e r e a c h 0 ?

2 0 . B r i a n c o l l e c t s b a s e b a l l c a r d s . H i s f a t h e r g a v e h i m 2 0 c a r d s t o s t a r t h i s c o l l e c t i o n o n h i s t e n t h b i r t h d a j ^ E a c h y e a r B r i a n a d d s a b o u t 1 5 c a r d s t o h i s c o l l e c t i o n . A b o u t h o w m a n y y e a r s w i l l i t t a k e t o fill h i s c o l l e c t i o n b i n d e r i f i t h o l d s 2 0 0 c a r d s ?

Bonus A g y m m e m b e r s h i p c o s t s $ 2 9 . 9 9 p e r m o n t h . W r i t e a d i r e c t v a r i a t i o n e q u a t i o n t o find t h e t o t a l c o s t c t o o w n a g y m m e m b e r s h i p f o r y y e a r s .

1 8 = 2000 - 190t

1 9 .

2 0 .

B :

about l O ^ y r s

12 yrs

c = 359.88y


NAME DATE

4 Chapter 4 Test, Form 2A PERIOD

Write t h e l e t t e r for t h e c o r r e c t a n s w e r i n t h e b l a n k at t h e r i g h t of e a c h q u e s t i o n .

1. W h a t i s t h e s l o p e - i n t e r c e p t f o r m o f t h e e q u a t i o n o f a l i n e w i t h a s l o p e o f 5 a n d a y - i n t e r c e p t o f — 8 ? A 3/ = - 8 x 4 - 5 B j = 8 x - 5 C 5 x - y = - 8 B y = 5x - 8

2. W h i c h e q u a t i o n i s g r a p h e d a t t h e r i g h t ? F 2 y - x = 1 0 H 2x-y = 5 G 2 x + 3 ' = - 5 J 23 ' + x = - 5

3. W h i c h i s a n e q u a t i o n o f t h e l i n e t h a t p a s s e s t h r o u g h ( 2 , - 5 ) a n d ( 6 , 3 ) ?

B y ^ i x

C v = 2 x + 1 2

D y = 2 x - 9

4. W h a t i s a n e q u a t i o n o f t h e l i n e t h r o u g h ( 0 , — 3 ) w i t h s l o p e — ? o

F - 5 x + 2 y = 1 5 G - 5 x — 2y = — 1 5

H 2 x - 5 y = 1 5 J - 2 x + 5 y = 1 5

5. W h i c h i s a n e q u a t i o n o f t h e l i n e w i t h s l o p e - 3 a n d a y - i n t e r c e p t o f 5 ? A y = - 3 ( x + 5 ) B y - 5 = - 3 x C - 3 x + ^ = 5 D > ' = 5 x - 3

6. What i s t h e e q u a t i o n o f t h e l i n e t h r o u g h ( - 2 , - 3 ) w i t h a s l o p e o f 0 ? F x = - 2 G y ^ - y H - 2 x - 3 y = U J - 3 x + 2 y = 0

7. F i n d t h e s l o p e - i n t e r c e p t f o r m o f t h e e q u a t i o n o f t h e l i n e t h a t p a s s e s t h r o u g h ( - 5 , 3 ) a n d i s p a r a l l e l t o 1 2 x - 33- = 1 0 . A y^-4x~n B y = 4x-13 C y = - 4 x + 1 3 D > ' = 4 x + 2 3

o 8. I f l i n e q h a s a s l o p e o f — w h a t i s t h e s l o p e o f a n j ' l i n e p e r p e n d i c u l a r t o q?

8 F - I G i 8 " 8

9 . A l i n e o f fit m i g h t b e d e f i n e d a s A a l i n e t h a t c o n n e c t s a l l t h e d a t a p o i n t s . B a l i n e t h a t m i g h t b e s t e s t i m a t e t h e d a t a a n d b e u s e d f o r p r e d i c t i n g v a l u e s . C a v e r t i c a l l i n e h a l f w a y t h r o u g h t h e d a t a . D a l i n e t h a t h a s a s l o p e g r e a t e r t h a n 1 .

10. A s c a t t e r p l o t o f d a t a c o m p a r i n g t h e n u m b e r o f y e a r s s i n c e H o l b r o o k H i g h S c h o o l i n t r o d u c e d a m a t h c l u b a n d t h e n u m b e r o f s t u d e n t s p a r t i c i p a t i n g c o n t a i n s t h e o r d e r e d p a i r s ( 3 , 1 9 ) a n d ( 8 , 4 2 ) . W h i c h i s t h e s l o p e - i n t e r c e p t f o r m o f a n e q u a t i o n f o r t h e l i n e o f fit? F y = 4 . 6 x + 5 . 2 G y = 3 x + 1

H y = 5 . 2 x + 4 . 6 J y = 0 . 2 2 x - 1 . 1 3

11. U s e t h e e q u a t i o n f r o m Q u e s t i o n 1 0 t o e s t i m a t e t h e n u m b e r o f s t u d e n t s w h o w i l l b e i n t h e m a t h c l u b d u r i n g t h e 1 5 t h y e a r . A 5 3 B 6 1 C 6 5 D 7 4

1.

2.

3.

4 .

5.

6.

7.

8 .

9.

10.

Chapter 4 57

X I . .

H

H

B

H

B


NAME DATE PERIOD

4 Chapter 4 Test, Form 2A (continued)

•

•95 '00 '05

F o r Questions 12-14, use the scatter plot shown. 12. W h i c h d a t a a r e s h o w n b y t h e s c a t t e r p l o t ?

F ( 1 9 9 5 , 5 . 5 ) , ( 1 9 9 7 , 6 . 1 ) , ( 2 0 0 4 , 7 . 6 ) G ( 1 9 9 5 , 5 . 5 ) , ( 2 0 0 0 , 6 . 1 ) , ( 2 0 0 4 , 7 . 6 ) H ( 1 9 9 5 , 5 . 5 ) , ( 2 0 0 0 , 6 . 6 ) , ( 2 0 0 5 , 8 . 0 ) J ( 1 9 9 5 , 5 . 5 ) , ( 1 9 9 7 , 6 . 6 ) , ( 2 0 0 5 , 8 . 0 )

13. W h i c h i s t r u e a b o u t t h e d a t a ? A T h e s l o p e o f a b e s t - f i t l i n e w o u l d b e n e g a t i v e . B T h e r e i s a p o s i t i v e c o r r e l a t i o n . C T h e r e i s n o c o r r e l a t i o n . D T h e r e i s a n e g a t i v e c o r r e l a t i o n .

14. B a s e d o n t h e d a t a i n t h e s c a t t e r p l o t , w h a t w o u l d y o u e x p e c t t h e y - v a l u e t o b e f o r X = 2 0 1 0 ? F b e t w e e n 7 a n d 8 H b e t w e e n 5 a n d 7 G h i g h e r t h a n 8 J i m p o s s i b l e t o t e l l

15. T o c a l c u l a t e t h e c h a r g e f o r a l o a d o f b r i c k s , i n c l u d i n g d e l i v e r y , t h e R e d s t o n e B r i c k C o . u s e s t h e e q u a t i o n C = 0 . 4 2 b + 2 5 , w h e r e C i s t h e c h a r g e a n d b i s t h e n u m b e r o f b r i c k s . W h a t i s t h e d e l i v e r y f e e p e r l o a d ? A $ 4 2 C $ 2 5 B $ 6 7 D I t d e p e n d s o n t h e n u m b e r o f b r i c k s

F o r Questions 16 and 17, use the table shown. Shots on Goal 22 25 28 29 33

Points Scored 5 7 7 9 8

16. F i n d t h e s l o p e o f t h e b e s t - f i t l i n e . F - 0 . 5 6 1 G 0 . 2 8 3 H 0 . 6 3 1 J 0 . 7 9 4

17. E s t i m a t e h o w m a n y p o i n t s w o u l d b e s c o r e d i f 8 0 s h o t s w e r e t a k e n o n t h e g o a l u s i n g t h e b e s t - f i t l i n e . A 1 8 B 1 9 C 2 2 D 2 4

18. F i n d t h e i n v e r s e o f { ( 4 , - 1 ) , ( 3 , - 2 ) , ( 6 , 9 ) , ( 8 , 5 ) } . F { ( 8 , 5 ) , ( 6 , 9 ) , ( 3 , - 2 ) , ( 4 , - 1 ) } G ( ( - 4 , 1 ) , ( - 3 , 2 ) , ( - 6 , - 9 ) , ( - 8 , - 5 ) }

19. If fix) = 3 x - 4 , find fHx).

A f-\x) = 4x-3 B f-Kx) =

20. If fix) = 8 ( 5 x - 2 ) , find T H x ) .

H { ( - 1 , 4 ) , ( - 2 , 3 ) , ( 9 , 6 ) , ( 5 , 8 ) } J { ( - 1 , - 2 ) , ( 9 , 5 ) , ( 4 , 3 ) , ( 6 , 8 ) }

12.

13.

14.

15.

16.

17.

18.

C f-\x)^

F f-\x) = 5x + 2 8

G f~\x) = 5 x - 2 8

H f-\x) = X - 16 4 0

D f-\x) = -4-3x 19.

/ - H x ) = ^ ^ 20..

B

H

B

©

a I I ±

Bonus W h a t i s t h e y - i n t e r c e p t o f a l i n e t h r o u g h ( 2 , 7 ) a n d p e r p e n d i c u l a r t o t h e g r a p h o f y = — - j r x - t - 6 ?

17 B :


NAME DATE PERIOD

Chapter 4 Test, Form 2C S C O R E

1. W r i t e a l i n e a r e q u a t i o n i n s l o p e - i n t e r c e p t form t o m o d e l t h e s i t u a t i o n : A t e l e p h o n e c o m p a n y c h a r g e s $ 2 8 . 7 5 p e r m o n t h p l u s $ 0 . 1 0 a m i n u t e for l o n g - d i s t a n c e c a l l s .

2. W r i t e a n e q u a t i o n i n s t a n d a r d form o f t h e l i n e t h a t p a s s e s t h r o u g h ( 7 , - 3 ) a n d h a s a y - i n t e r c e p t o f 2 .

3. W r i t e t h e s l o p e - i n t e r c e p t f o r m o f a n e q u a t i o n f o r t h e l i n e g r a p h e d a t t h e r i g h t .

2 ! ]

o

4 . G r a p h t h e l i n e w i t h a y - i n t e r c e p t o f 3 a n d s l o p e — —.

5. W r i t e a n e q u a t i o n i n s l o p e - i n t e r c e p t f o r m f o r t h e l i n e t h a t p a s s e s t h r o u g h ( — 1 , — 2 ) a n d ( 3 , 4 ) .

6. W r i t e a n e q u a t i o n i n s t a n d a r d f o r m f o r t h e l i n e t h a t h a s a n u n d e f i n e d s l o p e a n d p a s s e s t h r o u g h ( — 6 , 4 ) .

7. W r i t e a n e q u a t i o n i n p o i n t - s l o p e f o r m f o r t h e l i n e t h a t h a s s l o p e \d p a s s e s t h r o u g h ( — 2 , 8 ) .

, y = 0.10x +28.75

2. 5x - f 7y = 14

3.

6.

y = | x - 2

x = - 6

^ y - 8 = l ( x + 2)

8. W r i t e t h e s t a n d s u - d f o r m o f t h e e q u a t i o n y + 4 = — - y - C ^ - D -

9. W r i t e t h e s l o p e - i n t e r c e p t f o r m o f t h e e q u a t i o n y - 2 = 3 ( x - 4 ) .

a 12xH-7y=-16

9. y = 3x -10

1 0 . W r i t e t h e s l o p e - i n t e r c e p t f o r m o f t h e e q u a t i o n o f t h e l i n e p a r a l l e l t o t h e g r a p h o f 2 x + y = 5 t h a t p a s s e s t h r o u g h ( 0 , 1 ) . 10. / ~ "^ '

11. W r i t e t h e s l o p e - i n t e r c e p t f o r m o f t h e e q u a t i o n o f t h e l i n e p e r p e n d i c u l a r t o t h e g r a p h o f y = ~ ^ \hat p a s s e s t h r o u g h (3 , - 2 ) . 11.

y = | x - 4

12. A s c a t t e r p l o t o f d a t a s h o w i n g t h e p e r c e n t a g e o f t o t a l I n t e r n e t u s e r s w h o v i s i t e d a n o n l i n e s t o r e o n a g i v e n d a y i n D e c e m b e r i n c l u d e s t h e p o i n t s ( 2 0 0 8 , 2 . 0 ) a n d ( 2 0 1 0 , 4 . 5 ) . W r i t e t h e lA — 1 25x — 2508 s l o p e - i n t e r c e p t f o r m o f a n e q u a t i o n f o r t h e l i n e o f fit. 12. ^ ~ '


NAME DATE PERIOD

4 Chapter 4 Test, Form 2C (continued)

F o r Questions 13-15, use the data i n the table. 13.

Time Spent Studying (min) 10 20 30 40 50

Score Received (percent) 53 67 78 87 95

13. M a k e a s c a t t e r p l o t r e l a t i n g t i m e s p e n t s t u d y i n g t o t h e s c o r e r e c e i v e d .

14. W r i t e t h e s l o p e - i n t e r c e p t f o r m o f t h e e q u a t i o n f o r a l i n e o f fit f o r t h e d a t a . U s e y o u r e q u a t i o n t o p r e d i c t a s t u d e n t ' s s c o r e i f t h e s t u d e n t s p e n t 3 5 m i n u t e s s t u d y i n g .

15. I s i t r e a s o n a b l e t o u s e t h e e q u a t i o n t o e s t i m a t e t h e s c o r e r e c e i v e d f o r a n y l e n g t h o f t i m e s p e n t s t u d s d n g ?

F o r Questions 16 and 17, use the data i n the table showing the number of congressional seats apportioned to Cali fornia each decade.

Decade 1940s 1950s 1970s 1990s 2000s

S e a t s 23 30 43 52 53

S o u r c e : Office of the Clerk, U.S. House of Representatives

16. F i n d a n e q u a t i o n f o r t h e m e d i a n - f i t l i n e .

17. P r e d i c t t h e n u m b e r o f s e a t s a p p o r t i o n e d t o C a l i f o r n i a i n t h e 1 9 3 0 s .

18. G r a p h t h e i n v e r s e o f t h e f u n c t i o n g r a p h e d a t t h e r i g h t .

19. I f = ~ ~ . find f Hx). 1 5

y

A 4

- i J - 4 0 4 \

a i

20. W r i t e t h e i n v e r s e o f 6x + 8y ^ 1 3 i n f-\x) n o t a t i o n .

100

S g 80

8 60

10 20 30 40 50 Time Spent Studying

(minutes)

Sample answer: using data points (20, 67) and

14 . ( 40 ,87 ) . y^x + 47;82

No, because thie maximum score is 100%, even for very large amounts of time studying.

Tfi. y = 0.52X - 983.73

17. 30

19. f - \ x ) = 5 - 15x

20. f - \ x ) = 13 - 8x

Bonus I n a c e r t a i n l a k e , a 1 - y e a r - o l d b l u e g i l l fish i s 3 i n c h e s l o n g , w h i l e a 4 - y e a r - o l d b l u e g i l l fish i s 6 . 6 i n c h e s l o n g . A s s u m i n g t h e g r o w t h r a t e c a n b e a p p r o x i m a t e d b y a l i n e a r e q u a t i o n , w r i t e a n e q u a t i o n i n s l o p e - i n t e r c e p t f o r m f o r t h e l e n g t h ^ o f a b l u e g i l l fish i n i n c h e s a f t e r t y e a r s . T h e n u s e t h e e q u a t i o n t o d e t e r m i n e t h e a g e o f a 9 - i n c h b l u e g i l l . B : ^ = 1.2f + 1.8; 6 years


NAME DATE PERIOD

4 Chapter 4 Test, Form 3 S C O R E

F o r Questions 1-4, write a n equation i n slope-intercept form of the line satisfying the given conditions.

1. h a s y - i n t e r c e p t - 8 a n d s l o p e 3

2. h a s s l o p e a n d p a s s e s t h r o u g h ( 4 , — 1 )

3. p a s s e s t h r o u g h ( - 3 , 7) a n d (2, 4 )

1. y = 3 x - 8

2. y = f x - i i

3. ^ 5 ^ + 5

4 . i s h o r i z o n t a l a n d p a s s e s t h r o u g h ( - 4 , 6 ) 4, y = 6

5. W r i t e t h e p o i n t - s l o p e f o r m o f a n e q u a t i o n o f t h e h n e t h a t h a s o

a s l o p e o f a n d p a s s e s t h r o u g h ( 2 , 1 ) . o

y - 1 = - f ( x - 2 ) 5 5

6. W r i t e a n e q u a t i o n i n s t a n d a r d f o r m o f t h e l i n e t h a t p a s s e s t h r o u g h ( 2 , - 3 ) a n d ( ~ 3 , 7). 6. 2x -H y = 1

7. G r a p h a l i n e t h a t h a s a n x - i n t e r c e p t o f 5 a n d a s l o p e o f -—. 7. y

8. W r i t e 3/ - f 4 = — ~ ( x — 9 ) i n s t a n d a r d f o r m . 3

R 2x -h 3y = 6

9. W r i t e t h e p o i n t - s l o p e t b r m o i t h e e q u a t i o n t o r t h e l i n e t h a t y ..j. 2 = — — x h a s x - i n t e r c e p t — 3 a n d y - i n t e r c e p t —2. 9. 3

F o r Questions 10-13, write an equation i n slope-intercept form of the l ine satisfying the given conditions.

10. i s p a r a l l e l t o t h e y - a x i s a n d h a s a n x - i n t e r c e p t o f 3 10. x = 3

11. i s p e r p e n d i c u l a r t o 4 y = 3 x — 8 a n d p a s s e s t h r o u g h ( -12, 7)

12. i s p a r a l l e l t o 3 x — 5 y = 7 a n d p a s s e s t h r o u g h ( 0 , - 6 )

y = - ^ x - 9 11. 3

y = | x - 6 12. . 1

13. i s p e r p e n d i c u l a r t o t h e y - a x i s a n d p a s s e s t h r o u g h (—2, 5) 13. y = 5

Chapter 4 65 G / e n c o f ? Algebra 1

NAME DATE PERIOD

4 Chapter 4 Test, Form 3 (continued)

F o r Questions 1 4 - 1 6 , use the data i n the table.

1 4 . M a k e a s c a t t e r p l o t r e l a t i n g t h e v e r b a l s c o r e s a n d t h e m a t h s c o r e s .

State Graduation Scores Year Verbal Score Math Score 1975 460 488

1985 424 466

1995 410 463

2005 420 460

1 5 . D o e s t h e s c a t t e r p l o t i n Q u e s t i o n 1 4 s h o w a positive, a negative, o r no correlation! W h a t d o e s t h a t r e l a t i o n s h i p r e p r e s e n t ?

1 6 . W r i t e t h e e q u a t i o n f o r a l i n e o f f i t . P r e d i c t t h e c o r r e s p o n d i n g m a t h s c o r e f o r a v e r b a l s c o r e o f 4 4 5 .

1 7 . T h e d a t a i n t h e t a b l e s h o w t h e n u m b e r o f c o n g r e s s i o n a l s e a t s a p p o r t i o n e d t o t h e s t a t e o f N e w Y o r k e a c h d e c a d e .

Decade 1940s 1960s 1980S 2000s Seats 4 5 41 3 4 2 9

S o u r c e : Office of the Clerk, U.S. House of Representatives

F i n d a n e q u a t i o n f o r t h e m e d i a n - f i t l i n e a n d p r e d i c t t h e n u m b e r o f s e a t s t h a t w i l l b e a p p o r t i o n e d t o N e w Y o r k i n t h e 2 0 2 0 s .

1 8 . G r a p h t h e i n v e r s e o f t h e f u n c t i o n g r a p h e d a t t h e r i g h t .

1 9 . lif{x) ^ i ^ i ^ i i l - , find f\x).

o y o

n 4

o 4 f

a

i

1 4 . 500

£ 490

^ 480

% 5 460

450

0 400 440 480 Verbal Score

positive; a verbal score is closely associated witli the

15. math score Sample answer: Using data points (424, 466) and (460,488); y = 0.6x +211.6;

Ig . about 479

y = -2.67X -I- 45.17; ^ _ about 24 s e a t s 1 7

1 8 . o V i 0

A 4

oV 4 i

1

1 9 . f - \ x ) 12 - 8x

15

20. W r i t e t h e i n v e r s e o f 4 x - 1 3 = 2a; + S y inf\x) n o t a t i o n . 20.

13 + 3x

Bonus T h e a r e a o f a c i r c l e v a r i e s d i r e c t l y a s t h e s q u a r e o f t h e r a d i u s . I f t h e r a d i u s i s t r i p l e d , b y w h a t f a c t o r w i l l t h e a r e a i n c r e a s e ?


3' a (0,6) b (0,-6) c (6,0) d (-6,0) 1. d 2. f 6 g 10 h 13...

Documents