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MTAP competitions

MTAP competitions
Subject

General Education

10 Documents
Students shared 10 documents in this course
Academic year: 2021/2022
Uploaded by:
Student
Angeneque Bascones
Deparo High School
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MMC 2019 Grade 10 National Individual Orals 1

Easy

E 1 If f (x) = 3 − 2 x − x 3 , what is f (− 2 )? [ 15 ]

E 2 Question not posted online.

E 3 What is the area of the circle with equation x 2 + y 2 − 2 x = 4? [ 5 units 2 ]

E4 When a polynomial is divided by x + 2 , the quotient is x − 3 and the remainder is − 2. What is the polynomial? [x 2 − x − 8 ]

E5 What is the slope of the line tangent to the circle x 2 + y 2 = 10 at the point (− 1 , − 3 )? [−

1

3

]

E 6 If

√

2 x − 2 = 10 , what is

√

x + 1? [ 2

√

13 ]

E 7 What is the radius of the circle inscribed in a 3 -4- 5 triangle? [ 1 unit]

E8 If 1 + 2 + 3 + ⋯ + n = 7 8, what is n? [ 12 ]

E 9 From 1 2 noon to 3 : 40 pm, how many degrees does the tip of the hour hand travel? [ 110 ○]

E 10 What is the probability that three randomly chosen people were born on three different days of the

week? [

30

49

]

Average

A 1 Find an equation of the perpendicular bisector of the segment joining the points ( 4 , 3 ) and ( 1 , − 2 ).

[y = −

3

5

x + 2 ]

A 2 If x 2 + y 2 + 25 = 2 ( 4 y − 3 x), what is x − y? [− 7 ]

A 3 The highest point of a parabola has coordinates (− 1 , 4 ). If it passes through the point (− 3 , − 4 ), find the x-intercepts of the parabola. [− 1 ±

√

2 ]

A4 Of ten fifty-peso bills, three are counterfeit. Six bills are chosen at random. What is the probability that

all counterfeit bills are chosen? [

1

6

]

A5 Solve for x in the inequality ∣√x +

√

5 ∣ < 4. [[ 0 , 21 − 8

√

5 )]

Difficult

D 1 Two positive numbers differ by 6 , and their reciprocals differ by

1

36

. What are the numbers?

[ 12 , 18 ]

D 2 The zeros of the polynomial P(x) = x 3 + bx 2 + cx + d are three times those of Q(x) = x 3 − 4 x 2 + 2 x − 5. Find b, c, and d. [(b, c, d) = (− 12 , 1 8, − 135 )]

D 3 In △ABC, AB = 4 cm, BC = 6 cm, and AC = 8 cm. Let D be a point on AC so that BD = AB. Find

AD. [

11

2

cm]

D4 In how many ways can the letters of the word DIV ISIBLE be arranged without having 2 I’s next to each other? [ 25 200 ]

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MTAP competitions

Subject: General Education

10 Documents
Students shared 10 documents in this course

School: Deparo High School

Was this document helpful?
MMC2019 Grade 10National Individual Orals1
Easy
E1Iff(x)=3−2x−x3,whatisf(−2)?[15]
E2Question notposted online.
E3Whatis the area ofthe circlewithequation x2+y2−2x=4?[5units2]
E4 Whenapolynomial isdivided byx+2,thequotientisx−3andtheremainderis−2.Whatis the
polynomial?[x2−x−8]
E5 Whatis theslopeofthelinetangent tothe circlex2+y2=10at thepoint(−1,−3)?[−1
3]
E6If√2x−2=10,whatis√x+1?[2√13]
E7Whatis theradius ofthe circleinscribed in a3-4-5triangle?[1unit]
E8 If1+2+3+⋯+n=78, whatisn?[12]
E9From 12noon to3:40pm,howmanydegreesdoes thetip ofthehour handtravel?[110○]
E10Whatis theprobabilitythat three randomlychosen peoplewere born on three differentdaysofthe
week?[30
49]
Average
A1Find anequation oftheperpendicularbisectorofthesegmentjoining thepoints (4,3)and(1,−2).
[y=−3
5x+2]
A2Ifx2+y2+25=2(4y−3x),whatisx−y?[−7]
A3Thehighest pointof a parabolahascoordinates(−1,4). Ifitpasses through thepoint(−3,−4), findthe
x-intercepts oftheparabola.[−1±√2]
A4 Oftenfifty-pesobills,three are counterfeit.Sixbillsare chosenat random. Whatis theprobabilitythat
all counterfeitbillsare chosen?[1
6]
A5 Solve forxin theinequality∣√x+√5∣<4. [[0,21−8√5)]
Difficult
D1Two positivenumbers differby6, andtheir reciprocalsdifferby1
36.Whatarethenumbers? [12,18]
D2ThezerosofthepolynomialP(x)=x3+bx2+cx+darethree times thoseofQ(x)=x3−4x2+2x−5.
Findb,c, andd.[(b,c,d)=(−12,18, −135)]
D3In △ABC,AB =4cm,BC =6cm, andAC =8 cm. LetDbe a pointon AC sothatBD =AB.Find
AD.[11
2cm]
D4 In howmany wayscantheletters ofthewordDIVISIBLEbe arranged without having 2I’s next to
each other? [25200]

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