7/23/2019 Quadratic Equations - Practice Test.doc

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FIRST QUARTER ASSESSMENTName: _____________________________________ Date:_________________Teacher:_____________________________________ Score: ________________

Solving Quadratic Equations(Algebraically)

Part I: Multiple ChoiceDirections: Place the correct choice on the line to the left ofeach question. (3oints)

_____1) The equation 062 =+x has a deree o!"1) 1 "#) $ "$) # "%) &

_____#) 'inear equations ha(e a deree o!"1) 1 "#) $ "$) # "%) &

_____$) hich o! the !o**o+in is a quadratic equation,"1) 062 =+x "#) xx = 322 3 "$) 15102 =x "%) 102 =+x

_____%) hat is-are the !actor"s) o! the equationy#. /%,"1) "y0 ) "#) 23 "$) "y0 )"y4 ) "%) 245 3

_____6) hat is-are the !actor"s) o! the equationy#

. %7,"1) "y0 8) "#) 283 "$) "y0 8)"y4 8) "%) 2485 83_____/) The sma**er so*ution o! the equation 0)5)(6( =+ xx is

"1) 6 "#) 6 "$) 6 "%) 6_____8) The so*ution to the equation!#4 /!. & is

"1) &5 on*9 "#) & and / "$) /5 on*9 "%) 6_____8) The length of a rectangular window is 5 feet more than its width, w.

The area of the window is 36 suare feet. !hich euation could

"e used to find the dimensions of the window#

(1) w(w$ 5) % 36 (2) w$ w$ 5 % 36 (3) w(w& 5) % 36 (') 2w $ 10 % 36

_____) The length of a rectangular window is 5 feet less than twice the width, w.

!hich e*ression re*resents the areaof the window#(1) 2w& 3 (2) 2w2& 3w (3) 2w& 5 (') 2w2& 5w

_____10) !hat is the solution set ofxx

x 3

2

2 =

+

,

(1) +&2, 3 (2) +&1, 6- (3) +&3, &2 (') +&6, 1

_____11) It is a polynomial equation of degree two that can be written in the form ax2+ bx + c = 0, where a, b, and c are real numbers and a 0.

(! "inear #quation (2! "inear Inequality ($! %uadratic #quation(&! %uadratic Inequality

'''''2! hich of the following is a quadratic equation)

(! 2r2+ &r * (2! $t =2 ($! s 2 + 5s 1% . & "%) #;# 8; < $

_____1$)In the quadratic equation $2+ + & = 0 which is thw quadratic term)(! (2! & ($! $2 (&! 0

''''&! -ow many real roots does the quadratic equation 2+ + = 0 ha/e)(! 0 (2! ($!$ (&! &

''''! he roots of a quadratic equation are 1 and $. hich of the following quadratic equations has these roots)

(1)2 8 $ 15 % 0 (2) 2 2 $ 15 % 0 (3) 2 2 & 15 % 0 (') 2$2 & 15 % 0

____16) hich of the following /alues ofx mae the equation 2+ + 3= 0true)

I. 14 II. 2 III. 4(! I and II (2!. II and III ($!. I and III (&!. I, II, and III

''''. hat is the nature of the roots of the quadratic equation if the /alue of its

discriminant is 5ero) (!. he roots are not real. (2!. he roots are rational and not equal.

($!. he roots are irrational and not equal. (&!. he roots are rational and equal.

''''3. 6ne of the roots of 221$ + 20= is &. hat is the other root)

(! 127 (2!172 ($!27 (&! 72

''''4. hat are the roots of the quadratic equationx2+ x 56 = 0)

(!. 2 and 1 (2!. 3 and 1 ($!. 13 and (&!. $ and 12

''''20. hat is the sum of the roots of the quadratic equation 22 + 8 * &= 0)

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(!. 1 (2!. 1$ ($!. 8 (&!. &

''''2. hich of the following quadratic equations can be sol/ed easily by etracting squareroots)

(!. 921 + 2=0 (2!. &t2 14 = 0 ($!. 22+ + $= 0 (&!. $2+213 = 0

''''22. he length of a garden is m longer than its width and the area is & m2. -ow long is thegarden)

(!. 4 m (2!. m ($!. m (&!. 2 m''''2$. : car tra/els 20 ph faster than a truc. he car co/ers &30 m in two hours less

than the time it taes the truc to tra/el the same distance. -ow fast does the car tra/el)(! &&ph (2! 80ph ($!30ph (&! &0ph

''''2&. : 2 cm by 8 cm picture is mounted with border of uniform width on arectangular frame. If the total area of the border is 233 cm 2, what is the length ofthe side of the frame) (!. 3 cm (2! . 8 cm ($!. 20 cm (&!. 2& cm

''''2. ;am;on #lectronics ) (!. 28 in. (2!. $0 in ($!. $$ in. (&!. $8 in.

''''28. he length of a garden is 2 m more than twice its width and its area is 2& m2.hich of the following equations represents the gi/en situation)

(! 2+ = 2 (2! 2+ 2 = 2 ($! 2+ = 2& (&! 2+ 2 = 2&''''2. ?rom 200& through 202, the a/erage weely income of an employee in a certain

company is estimated by the quadratic epression 0.8n2 + .&&n + 22&0, where

n is the number of years after 200&. In what year was the a/erage weely incomeof an employee equal to @hp2,2.20)

(!. 200 (2!. 2003 ($!. 2004 (&!. 200

;ol/e the following by completing the squareABatching ype

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= =0

c. 2+ = $0 has two solutions since both = and = 18 satisfy the equation.

hen =

hen = 18

Part II: Short Answer

Directions: Sho" A## "or$ to receive full credit. SOLVE ALGEBRAICALLY!

1) Find the so*ution set !or 62 = xx >"6 ?oints)

2) a) So*(e a*e@raica**9>( *oints)

@) hat is the sma**est mem@er o! the so*ution set o!#

!#. $& 4 1$!$) Find the positiveroot o! the equation!"! #) . $6>

( *oints)

%) So*(e !or!:x

x 1''

= (6

*oints)Part III: Lon Answer ( *oints each)

Directions: Sho" A## "or$ to receive full credit. SOLVE ALGEBRAICALLY!

') The suare of a num"er is 256. ind the num"er.

5) ind the two integers in the ratio '3 whose *roduct is 108.

3

2 $ = $0

52

$ 5 % 3012 + = $0

$0 = $02 $ = $0

(18!2 + (8! % 30$8 * 8 = $0

$0 = $0