9.?What?is?the?solution?to?the?system?of?equations?shown?below??
2x-y+3z?= 8?ì ?
í x-6y-z?= 0?? -6x+3y-9z = 24??
(A)?(0,?4,?4)?
(B)??1,4,?
?
è10?? ÷ 3 ?
(C)?No?solution?(D)?Infinitely?many?solutions?
10.?What?is?thenth?term?in?the?arithmetic?series?below??
3?+?7?+?11?+?15?+?19?.....?
(A)?4n?(B)?3?+?4n?(C)?2n?+?1?
(D)?4n?–?1?
11.?A?train?is?made?up?of?a?locomotive,?7?different?cars,?and?a?caboose.?If?the?locomotive?must?be?first,?and?the?caboose?must?be?last,?how?many?different?ways?can?the?train?be?ordered??(A)?5040?(B)?181,440?(C)?362,880?(D)?823,543?12.?If?A+B=?
(A)?1?
p
then?value?of?(1?+?tanA)?(1?+?tanB)?equals?4
(B)?2?(C)?–2?
(D)?–1?
13.?What?are?the?coordinates?of?the?image?of?pointP(–3,?–7)?after?a?reflection?about?the?liney=?2??
(A)?(–?3,?9)?(B)?(–?3,?11)?(C)?(5,?–?7)?(D)?(7,?–?7)?14.?Look?at?this?function?As?the?value?of?xincreases,?they-values?form?a?repeating?pattern.?If?this?pattern?continues,?what?is?the?y-value?when?x=?26??(A)?–?2?(B)?–?1?(C)?1?(D)?2?y?3?2?1–1?–1?1?2?3?4?5?6?7?8?x?–2?–3?15.?What?is?the?range?of?the?function?f(x)?=?x2??+?3?if?the?domain?is?{–?3,?0,?3}??
(A)?{3,?12}?(B)?{–?6,?3,?12}?(C)?All?real?numbers?(D)?All?real?numbers?greater?than?or?equal?to?3?16.?The?sum?of?three?consecutive?odd?integers?is?21.?If?x?is?the?least?of?these?odd?integers,?which?equation?must?be?true??(A)?3x?=?21?(B)?3x?+?3?=?21?(C)?3x?+?4?=?21?(D)?3x?+?6?=?21?17.?The?harmonic?mean?of?the?roots?of?the?equation 2+3x2?-3+5x?+6+25= 0?is?
(A)?2?
(B)?7?
(C)?8?
EVERYDAYMATHEMATICS?18.?Julie?works?at?the?amusement?park?with?the?maintenance?crew.?She?needs?to?replace?a?string?of?burned-out?lights?along?the?arc?shown?between?seat?1?and?seat?6.?The?arc?makes?up?1/4?of?the?Gaint?Wheel.?
The?20?seats?of?the?wheel?are?equally?spaced,?and?the?supports?from?the?center?of?the?wheel?to?each?seat?are?15?feet?in?length.?How?long,?to?the?nearest?foot,?does?the?string?of?replacement?lights?need?to?be??(A)?24?feet?(B)?30?feet?(C)?47?feet?(D)?90?feet?
Gaint?Wheel?( ) ( ) ( ) (D)?4?
Seat?6?15?feet?Seat?1?19.?The?typical?wingspan?of?the?little?blue?heron?is?4?inches?more?than?half?the?typical?wingspan?of?the?great?
blue?heron.?Ifgrepresents?the?typical?wingspan?of?the?great?blue?heron,?which?expression?represents?the?typical?wingspan?of?the?little?blue?heron??
1?1??1??
g?÷ g?+ 4?(g?+ 4)?(A) 4??(B) (C)?2g?+?4?(D) è2?? 2?2?20.?This?diagram?shows?the?angle?of?inclination?of?the?triangular?faces?of?the?Great?
Pyramid?in?Egypt.?
When?it?was?built,?the?length?of?each?side?of?the?square?base?was?230?meters.?Which?equation?represents?the?height,h,?of?the?Great?Pyramid?when?it?was?built??(A)?h?=?115?sin?52°?(B)?h?=?115?tan?52°?
(C) h?=
115?
sin52?°
h?52°?(D) h=
115?
tan52?°
230?m?7?Class?11?
印度国家科学-数学-网络奥林匹克竞赛高二年级样题
