Pre-Calc 40s Past Achievement Test Questions on Polynomials
June 2015
Question 8
1 mark
Explain howthe value of n affects the behaviour of the graph of the polynomial function
p(x)=(x+3)(x—1)",as p(x) approaches the x-intercept at x = 1.
2 y= \ ane Qc w tll Cress Drroyht =|
°
=
\
L
. \¢< nN is odd and G cea Aner re qa ue
wll level ff as tk crosses He xK-Gus
\f£ WwW is even the Amen enki U Dienek elf tLe
K Mtetpr
Question 19
1 mark
Identify the graph ofthe function f(x) = —(x—2)(x=1)7(x+1).
qe
dence
a) F : Negehor leading « [i A.
Co exc iz i@)
=VL.
Zz
po
A ¥Question 28
3 marks
Determine the equation of the polynomial function represented bythe graph.
A
ad = 4
\i
2
=A
2 *
p(s)=_ dC x43)%-2)
Question 39
a) 2 marks b)1mark c) 1 mark
Christine dives off a diving board.
* ° 4 4 . * 3 3 . e *
Herdive is modelled bythe function A(t) = 1° - 317 -*+3, where h is her height in metres,
relative to the water surface and f is the time in secondsafter diving off the diving board. a) Given that (1+ 1) is a factor for the function (1), determinethe other factors.
“(|
fs => -b
3
The obhec factons
«4 4 ~3 ace
( €- 3) and
C¥-\)
=
(&+*\) (4t 4k? )
= (ee) (b-3) (EY)
week)
b) Sketch the graph ofthe function A(t) for the timeinterval t = 0 tor = 3.
hA
>
oO
/Y” [! GQc) Determine how manyseconds Christine is underwater.
a Seconds
January 2015
Prom \su —2
ZSEC-Question 9
2 marks
Is (x ~ 2) a factor of the polynomial p(x) = =x4 —3x3+11n7 +3x-10?
Justify your response.
e Cab ee Ss te Kee)” + 3(2) -—
= = V& =3 Le\+ wl) 4 & ~O
= =U - U4 ed -Y
~
oO
(a-e%) tha Qaeree.
Question A S MCE. C2) =o we Ca erent Traorem stales 1 mark ot Lx)
Explain howthe end behaviours of the graphs ofpolynomial functions with an even degree and with an odd degree are different.
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or
aosen
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QW ns
VUdule gad A egece pol yao ats
evtier so doun rho
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and ve we QL
Oo
—_—_——
Question 24 1 mark Whatis the degree ofthe polynomial function represented bythe graph below?
a) 2 b) 3 c) 4
d) 5
, & &Question 27
x 2 marks . . . 2 ogDetermineall of the zeroes of the function p(x)= x3 - 5x7 -2xt 24, given one of the factors
of p(x) is (x—3).
3
L
-S
-2
24
4 =G& =24
Question 33
| | -2
8
©
os (v3) (x an-k)
O= CxK-32)C%- 4) (xeZ)
i Sy ty =
3 marksSketch the graph of y = -2(x-1)(x-3)(x+1).
*
y= - zC-v\)(3) cy)
yak:
June 2014
Question 8
a) i mark b) 1 mark
Let PLK) =
a) Determine the remainder when x* -— 3x7 +1 is divided by x+2.
Pl-2) = €2 yt 3-274
=
(b—3 (4) +\
=
Ss
Question 16
2 marks
2.KSA x —-x—-4
K+Divide (x> — 5x —4) by (x +1).
Question 28
1 mark
A sheet ofpaper 12 cm long and 8 cmwideis used to make a box withnolid. Equal squares of
side length x cm are cut fromeach ofthe comers andthe sides are folded up to makethe box.
xf T T cree re t I I | ! }8 cm I I
late fe we zo J
I IWhich of the following expresses the volumeof the box?
a) V(x)=x(12+x)(8+ x)
b) V(x) =x(12-x)(8— x)
c) V(x) =x(12 + 2x)(8 + 2x)
(a)) V(x) = x(12 — 2x)(8 — 2x)
Question 42
2 marks
Write the equation for f(x) that satisfies all of the following conditions:
¢ f(x) isa polynomial function of degree 4
¢ f(x) has zero at 2 with a multiplicity of 3
3* f(x) has a zero at —5
.
Wao C™« xS)) («- =)
¢ f(x) has ay-intercept of 80
w= als \(-e)
—Q = G4
4 >-a Cxs) ix-2°
Question 45
3 marks
Sketch the graph of f(x) =(x—- 1)7( x+2 ;
‘ fe
Label the x-intercepts and the y-intercept.
=
5
i
Sc@)y= C1) (+2)
January 2014
Question 20 1 mark
- * be
LY
¥
Given the above graph of a polynomial function, which one of the following statements can be true?
a) The function has a degree of 4 with a positive leading coefficient. b) The function has a degree of 4 with a negative leading coefficient. c) The function has a degree of 3 with a positive leading coefficient. (@)The function has a degree of 3 with a negative leading coefficient.
Question 21
1 mark
Given that (x+ 3) is a factor of polynomial P(x), which ofthe followingis true?
a) P(-3)=0
b) P(0)=-3
c) P(0)=3
d) P(3)=0
Question 26
2 marks
,
4
P(+2)=0
One ofthe factors of P(x) = x" — kx” — 7x +10 is (x-2).
Findthe valueof k.
O= ry = Kary’ -4Fz)4tO
O= *£% “HK —-Ws4rL0
~ My. = ~-4K
Question 35
,
= te
1 mark
When P(x) is divided by x —3, it has a quotient of 2x7 +x —6 anda remainderof4.
Determine P(x).
ex) ~—
axrexrlo +4
x<3
X~-3
Question 40 4 marks
2 z 4 ‘
Sketch the graph of y= ta? —5e43 given that one ofthe x-intercepts is 1. Identify the x-intercepts and y-intercept.
a June 2013
Question 24
45 Cet) (x4 rx-3)
4 = (x ~\) Cx 3x)
+4
_ (3)
4
)
=
3
4 >
1 mark
Whatis the degree of the polynomial represented below?
fo
a) y
A b) 3
-Question 29
\y_3 marks
a
Sketch the graphof:
BSC),
f(x) =(2 -—x)(x + 3)(x + 1°
Question 31
1 mark
5
The graph belowrepresents the equation v= ax? + 6x" + 5x -10.
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A
V\
Vv
What must be true about the value of a? Explain your reasoning.
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+s
Rename »
Since tore
exc
Vy erwvi oF Ls ve ino Q w a~d dosa cable QW
Question 35
2 marks
Giventhat (x — 1) is one ofthe factors, express x — 57x 456 asa productoffactors.
-st
Sb
&
)
ij} =
Cx 1) Cx *e x - SG
Pr.
\ -Se 0
Cremt) C xe OF)
Question 44
2 marks
(4
4.3. 4.2
.-Is (x — 3) a factor of x" —x° — 3x7 +x-1?
Justify your answer.
4
ar
2
_
e Ca) =
3'_ 33 _3(3)~ 3!
=«at -ages-!
=-2Q1
‘atiee:
P(3) # O
(«~3) ds
not we FACroe
January 2013
Question 27
ad
Sketch the graph of y =(x+1)(x- 2)? (x+5).
Identify the v-intercepts and 1-intercept.
Lo
y-intercepts:__— Ss ] Tit,
y-intercept:
a* Cv Ne z)* is){~~ =
113 marks
Question 31
5 marks
A box inthe shape of a rectangular prismhasside lengths x. + 2. andy +10.
Write a function. V(x). to express the volumeof the box in terms of x.
-
.
3
Find all possible values of x. given that the volume of the box is 96 cm”.
State the dimensions of the box.
V Cx) =
*(x*2) ( x+t0)
PLix)= (x-2) (x *e14% +48)
Vo = an
é ©Pix) = Cree) ( +8) (eb)
= x x + IBTxkto
“
3
. 2
oO = (ye - BY LeBIC x +b)
O = * ¥\ITK *+a0% =e
|
4 PLxK)= %? eIUK* FaA0x -TS
w = 2 , ~f# \ Me
(2) £0
2. \ i~ wo - %&2
2%
AL
} § Wo 4S
0
Question 40
1 mark
Giventhat h(x) = 2x7 + Sx —3 and that h(x) = f(x)« g(x). determine f(x) and g(x).
hdx)= C(ax-t) (x4 3)
prise
Sexy = @x-3)
Cuxy= Aax**Sx-5
.
Acx) - Cx 3) Cx) = A
Question 47
+ mark
If p(x)= x? —12x +1. determine the remainder when p(x) is divided by (x+2).
P\X
P
elt) = C2 ster) +1
= -ZS27 +a +] (Lemtadat