i
i
i
i
i
i
Kumon Level N Test questions and answers
i i i i i i i
i
100% guaranteed success. i i
i
i
i
i
i
i
i
1. iGiven ithe ifixed ipoints iF(0 i,√5) iand iF' i(0 i,-√5), iobtain ithe iequation iof ithe ilocus ipoint
i
P(x, iy), isuch ithat iPF i+PF' i= i8 i- i icorrect ianswer. i i i√[x^2+(y-V5)^2]+√[x^2+(y+V5)^2]=8
i
x^2/11+y^2/16 i= i1
i
2 iGraph ithe iregion isatisfying ithe igiven isystem iof iinequalities, iand ithen istate ithe irange
i
i
of ivalues ix iand iy
i
x-y+1 i≥ i0
i
5-2x-y i≥ i0 i- i icorrect ianswer. i i iall ireal inumbers ifor ix, iy i≤
i7/3
i
3. iObtain ithe i30th iterm iof ian iarithmetic isequence iwhose i5th iterm iis i-3 iand iwhose i14th
i
i
term iis i24. i- i icorrect ianswer. i i ia+4d=-3, ia+13d=24, ia=-15, id=3
i
72
i
i
4. iObtain ithe isum iof ithe ifollowing iarithmetic isequence.
-15, i-10, i-5, i0, i... i(through ithe i12th iterm) i- i icorrect ianswer. i i i150
i
i
5. i4
i
Σ i(3k i- i2) i=
k=1 i- i icorrect ianswer. i i i22
i
6. iObtain ithe i1st iterm iand icommon iratio iof ia igeometric isequence iwhose i5th iterm iis
i24 i
i
and i7th iterm iis i96
i
First iterm:
i
Common iratio: i- i icorrect ianswer. i i iar^4=24, iar^6=96
i
1st iterm: i3/2
i
Common iratio: i±2
i
7. iGiven ia igeometric isequence iwhose isum iof ithe ifirst i10 iterms iis i4, iand iwhose isum
iof i
i
the iterms ifrom ithe i11th ithrough i30th iterm iis i48, iobtain ithe isum iof ithe iterms ifrom
ithe
, i
31st ithrough ithe i60th iterm. i- i icorrect ianswer. i i iS10=a(r^10-1)/r-1=4
i
S30=a(r^30-1)/r-1=52
i
r^10=3, ir^60= i1456
i
1404
i
8. iGiven ithe isequence i[an]: i2, i5, i10, i17, i26, i37, i50, i..., iobtain ithe igeneral iterm ian,
iand i
i
the isum iof ithe ifirst in iterms, iSn i- i icorrect ianswer. i i ibn=2n+1, ian=n^2+1
i
an i= in^2+1
i
Sn i= in/6(2n^2 i+3n i+7)
i
9. ilim i2n^2 i- i1/3n^2 i+4 i= i- i icorrect ianswer. i i i2-1/n^2/3+4/n^2
i
2/3
i
i i
10. ilim i√3n/√2n+1 i= -
i correct ianswer. i i i√3/√2+1/n
i
√6/2
i
i
11. lim i5^n i+ i2^n/3^2n i+4^n i= i- i icorrect ianswer. i i i(5/9)^n+(2/9)^n/1+(4/9)^n
i0 i
i
i
i
i
i
i
Kumon Level N Test questions and answers
i i i i i i i
i
100% guaranteed success. i i
i
i
i
i
i
i
i
1. iGiven ithe ifixed ipoints iF(0 i,√5) iand iF' i(0 i,-√5), iobtain ithe iequation iof ithe ilocus ipoint
i
P(x, iy), isuch ithat iPF i+PF' i= i8 i- i icorrect ianswer. i i i√[x^2+(y-V5)^2]+√[x^2+(y+V5)^2]=8
i
x^2/11+y^2/16 i= i1
i
2 iGraph ithe iregion isatisfying ithe igiven isystem iof iinequalities, iand ithen istate ithe irange
i
i
of ivalues ix iand iy
i
x-y+1 i≥ i0
i
5-2x-y i≥ i0 i- i icorrect ianswer. i i iall ireal inumbers ifor ix, iy i≤
i7/3
i
3. iObtain ithe i30th iterm iof ian iarithmetic isequence iwhose i5th iterm iis i-3 iand iwhose i14th
i
i
term iis i24. i- i icorrect ianswer. i i ia+4d=-3, ia+13d=24, ia=-15, id=3
i
72
i
i
4. iObtain ithe isum iof ithe ifollowing iarithmetic isequence.
-15, i-10, i-5, i0, i... i(through ithe i12th iterm) i- i icorrect ianswer. i i i150
i
i
5. i4
i
Σ i(3k i- i2) i=
k=1 i- i icorrect ianswer. i i i22
i
6. iObtain ithe i1st iterm iand icommon iratio iof ia igeometric isequence iwhose i5th iterm iis
i24 i
i
and i7th iterm iis i96
i
First iterm:
i
Common iratio: i- i icorrect ianswer. i i iar^4=24, iar^6=96
i
1st iterm: i3/2
i
Common iratio: i±2
i
7. iGiven ia igeometric isequence iwhose isum iof ithe ifirst i10 iterms iis i4, iand iwhose isum
iof i
i
the iterms ifrom ithe i11th ithrough i30th iterm iis i48, iobtain ithe isum iof ithe iterms ifrom
ithe
, i
31st ithrough ithe i60th iterm. i- i icorrect ianswer. i i iS10=a(r^10-1)/r-1=4
i
S30=a(r^30-1)/r-1=52
i
r^10=3, ir^60= i1456
i
1404
i
8. iGiven ithe isequence i[an]: i2, i5, i10, i17, i26, i37, i50, i..., iobtain ithe igeneral iterm ian,
iand i
i
the isum iof ithe ifirst in iterms, iSn i- i icorrect ianswer. i i ibn=2n+1, ian=n^2+1
i
an i= in^2+1
i
Sn i= in/6(2n^2 i+3n i+7)
i
9. ilim i2n^2 i- i1/3n^2 i+4 i= i- i icorrect ianswer. i i i2-1/n^2/3+4/n^2
i
2/3
i
i i
10. ilim i√3n/√2n+1 i= -
i correct ianswer. i i i√3/√2+1/n
i
√6/2
i
i
11. lim i5^n i+ i2^n/3^2n i+4^n i= i- i icorrect ianswer. i i i(5/9)^n+(2/9)^n/1+(4/9)^n
i0 i
i
