Đề thi tuyển sinh đại học, cao đẳng năm 2002 môn thi: toán, khối b thời gian làm bài: 180 phút, không kể thời gian phát đề32895

Χηο ηνη χη⌠π Σ ΑΒΧD... Χη νγ mινη ρ νγ.

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Χυ 1 (3 đι m)

Χηο η◊m σ 1 3 2

ψ= ξ +mξ − ξ− m−1 (1) (m λ◊ τηαm σ )

1 Χηο 1

2

m= α) Κη ο σ〈τ ϖ◊ ϖ đ τη (Χ) χ α η◊m σ (1)

β) ςι τ πη νγ τρνη τι π τυψ ν χ α đ τη ( )Χ , βι τ ρ νγ τι π τυψ ν đ⌠ σονγ σονγ ϖ ι

đ νγ τη νγ δ ψ: =4ξ+ 2

2 Τm mτηυ χ κηο νγ 0;5

6

⎛

⎜

⎞

⎟ σαο χηο ηνη πη νγ γι ι η ν β ι đ τη η◊m σ (1) ϖ◊ χ〈χ

đ νγ τη νγ ξ=0, 2, 0ξ= ψ= χ⌠ δι ν τχη β νγ 4

Χυ 2 (2 đι m)

1 Γι ι η πη νγ τρνη

ξ ψ

⎪

⎨

⎪⎩

2 Γι ι πη νγ τρνη ( 2 )

4

4

2 σιν 2 σιν 3

χοσ

τγ ξ

ξ

− + =

Χυ 3 (2 đι m)

1 Χηο ηνη χη⌠π Σ ΑΒΧD χ⌠ đ〈ψ λ◊ ηνη ϖυνγ χ νη , α ΣΑ ϖυνγ γ⌠χ ϖ ι m τ πη νγ

(ΑΒΧD) ϖ◊ Γ ι λ◊ τρυνγ đι m χ α χ νη Τνη τηεο κηο νγ χ〈χη τ đι m

đ ν đ νγ τη νγ

2 Τρονγ κηνγ γιαν ϖ ι η τ α đ Οξ χηο đ νγ τη νγ ψζ

:

2 0

ξ ψ ζ

ξ ψ ζ

+ + + =

⎧

∆ ⎨ + + + =

⎩

0 ϖ◊ m τ πη νγ ( )Π : 4ξ−2ψ+ − =ζ 1 0

ςι τ πη νγ τρνη ηνη χηι υ ϖυνγ γ⌠χ χ α đ νγ τη νγ ∆ τρν m τ πη νγ (Π)

Χυ 4 (2 đι m)

1 Τνη γι ι η ν

3 0

ξ

Ι

ξ

→

=

2 Τρονγ m τ πη νγ ϖ ι η τ α đ Οξ χηο ηαι đ νγ τρ∫ν ψ

Χ ξ +ψ − ψ− = ϖ◊ ( ) 2 2

Χ ξ +ψ − ξ+ ψ+ =

ςι τ πη νγ τρνη χ〈χ τι π τυψ ν χηυνγ χ α ηαι đ νγ τρ∫ν ( )Χ1 ϖ◊ ( )Χ2

Χυ 5 (1 đι m)

Γι σ ξ ψ λ◊ ηαι σ δ, νγ τηαψ đ ι τη α mν đι υ κι ν 5

4

ξ+ =ψ Τm γι〈 τρ νη νη τ χ α

βι υ τη χ σαυ 4 1

4

Σ

ξ ψ

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Η τ−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Γηι χη: Χ〈ν βじ χοι τηι κηνγ γιＶι τηχη γ τηm

Η ϖ◊ τν τη σινη Σ β〈ο δανη

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

δ β 2

Μν τηι: ΤΟℑΝ, ΚΗ 渦Ι Β

Τη ι γιαν λ◊m β◊ι: 180 πητ, κηνγ κ τη ι γιαν πη〈τ đ

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Χυ 1 (2,5 đι m)

Χηο η◊m σ

2 2 2

ψ

ξ

=

− (1) (m λ◊ τηαm σ )

1 Ξ〈χ đ νη đ η◊m σ (1) νγη χη βι ν τρν κηο νγ m (−1; 0 )

2 Κη ο σ〈τ ϖ◊ ϖ đ τη χ α η◊m σ (1) κηι m=0

3 Τm α đ πη νγ τρνη σαυ χ⌠ νγηι m

9+ −ξ − α+2 3+ −ξ +2α+ =1 0

ν

Χυ 2 (2 đι m)

1 Τm σ νγυψν δν νγ τη α mν β τ πη νγ τρνη Α3+2Χ −2 ≤9ν κ

ν

( Α ϖ◊ λ ν λ τ λ◊

σ χη νη η π ϖ◊ σ τ η π χη π χ α πη ν τ )

κ ν

Χ

2 Γι ι πη νγ τρνη ( ) ( )8 (

2

Χυ 3 (1,5 đι m)

1 Γι ι πη νγ τρνη

γ ξ

2 Τνη δι ν τχη ταm γι〈χ ΑΒΧ, βι τ ρ νγ β.σινΧ β( χοσΧ+χ.χοσΒ)=20

(β χ, λ ν λ τ λ◊ đ δ◊ι χ〈χ χ νη ΑΧ ΑΒ χ α ταm γι〈χ , ΑΒΧ)

Χυ 4 (3 đι m)

1 Χηο τ δι ν ΟΑΒΧ χ⌠ βα χ νη đι m τ ϖυνγ γ⌠χ ϖ ι νηαυ Γ ι λ ν

λ τ λ◊ χ〈χ γ⌠χ γι α m τ πη νγ

, ,

(ΑΒΧ) ϖ ι χ〈χ m τ πη νγ (ΟΒΧ) (, , ΟΧΑ) (ΟΑΒ)

Χη νγ mινη ρ νγ χοσα +χοσβ +χοσγ ≤ 3

2 Τρονγ κηνγ γιαν ϖ ι η τ α đ Οξ χηο m τ πη νγ ψζ ( )Π :ξ− + + =ψ ζ 3 0 ϖ◊ ηαι đι m

( 1; 3; 2 ,) ( 5; 7;12

α) Τm τ α đ đι m Χ đ ι ξ νγ ϖ ι đι m θυα m τ πη νγ Α ( )Π

β) Τm τ α đ đι m Μ τηυ χ m τ πη νγ ( )Π σαο χηο τ νγ ΜΑ ΜΒ+ đ τ γι〈 τρ νη νη τ

Χυ 5 (1 đι m)

Τνη τχη πην

λν 3

3 0

1

ξ

ξ

ε δξ Ι

ε

=

+

∫

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Η τ−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Γηι χη: Χ〈ν βじ χοι τηι κηνγ γιＶι τηχη γ τηm

Η ϖ◊ τν τη σινη Σ β〈ο δανη

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Χυ 1 (2 đι m)

Χηο η◊m σ ( ) ( 2 )

1

ψ= ξ− ξ +mξ m+ (1) (m λ◊ τηαm σ )

1 Τm m đ đ τη η◊m σ (1) χ τ τρ χ ηο◊νη τ ι βα đι m πην βι τ

2 Κη ο σ〈τ σ βι ν τηιν ϖ◊ ϖ đ τη η◊m σ (1) κηι m=4

Χυ 2 (2 đι m)

1 Γι ι πη νγ τρνη 3χοσ 4ξ−8 χοσ6ξ+2 χοσ2ξ+ = 3 0

2 Τm m đ πη νγ τρνη

2

4 λογ ξ −λογ ξ+ =m 0 χ⌠ νγηι m τηυ χ κηο νγ ( )0;1

Χυ 3 (3 đι m)

1 Τρονγ m τ πη νγ ϖ ι η τ α đ Οξψ χηο đ νγ τη νγ δ ξ: −7ψ+10= ςι τ πη νγ τρνη 0

đ νγ τρ∫ν χ⌠ τm τηυ χ đ νγ τη νγ : 2∆ ξ+ = ϖ◊ τι π ξχ ϖ ι đ νγ τη νγ τ ι ψ 0

đι m

δ

( )4; 2

Α

2 Χηο ηνη λ π πη νγ ΑΒΧD Α Β Χ D ∋ ∋ ∋ ∋ Τm đι m Μ τηυ χ χ νη ΑΑ∋ σαο χηο m τ πη νγ

(ΒD Μ∋ ) χ τ ηνη λ π πη νγ τηεο m τ τηι τ δι ν χ⌠ δι ν τχη νη νη τ

3 Τρονγ κηνγ γιαν ϖ ι η τ α đ Οξψζχηο τ δι ν ΟΑΒΧ ϖ ι

(0; 0; 3 ,) ( ; 0; 0 ,) (0; 3; 0)

Α α Β α Χ α Γ ι Μ λ◊ τρυνγ đι m χ α ΒΧ Τνη κηο νγ χ〈χη

γι α ηαι đ νγ τη νγ ΑΒ ϖ◊ ΟΜ

Χυ 4 (2 đι m)

1 Τm γι〈 τρ λ ν νη τ ϖ◊ γι〈 τρ νη νη τ χ α η◊m σ ( )3

6 4 1

ψ=ξ + −ξ2

τρν đο ν [−1;1]

2 Τνη τχη πην

λν 5 2

λν 2

1

ξ

ξ

ε δξ Ι

ε

=

−

∫

Χυ 5 (1 đι m)

Τ χ〈χ χη σ 1, 2, 3, 4, 5, 6 χ⌠ τη λ π đ χ βαο νηιυ σ τ νηιν, m ι σ χ⌠ 6 χη σ ϖ◊ τη α mν đι υ κι ν: Σ〈υ χη σ χ α m ι σ λ◊ κη〈χ νηαυ ϖ◊ τρονγ m ι σ đ⌠ τ νγ χ α βα χη σ đ υ

νη η ν τ νγ χ α βα χη σ χυ ι m τ đ ν ϖ ?

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Η τ−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Γηι χη: Χ〈ν βじ χοι τηι κηνγ γιＶι τηχη γ τηm

Η ϖ◊ τν τη σινη .Σ β〈ο δανη

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

δ β 2

Μν τηι: ΤΟℑΝ, ΚΗ 渦Ι Β

Τη ι γιαν λ◊m β◊ι: 180 πητ, κηνγ κ τη ι γιαν πη〈τ đ

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Χυ 1 (2 đι m)

Χηο η◊m σ 2 1

1

ξ ψ ξ

−

=

− (1)

1 Κη ο σ〈τ σ βι ν τηιν ϖ◊ ϖ đ τη ( )Χ χ α η◊m σ (1)

2 Γ ι Ι λ◊ γιαο đι m ηαι đ νγ τι m χ ν χ α ( )Χ Τm đι m Μ τηυ χ ( σαο χηο τι π τυψ ν

χ α τ ι

)

Χ

( )Χ Μ ϖυνγ γ⌠χ ϖ ι đ νγ τη νγ ΙΜ

Χυ 2 (2 đι m)

1 Γι ι πη νγ τρνη

2 3 χοσ 2 σιν

2 4

1

2 χοσ 1

ξ ξ

ξ

π

⎝ ⎠ =

−

2 Γι ι β τ πη νγ τρνη 1 1( ) 2

λογ ξ+2 λογ ξ− +1 λογ 6≤ 0

Χυ 3 (3 đι m)

1 Τρονγ m τ πη νγ ϖ ι η τ α đ Οξψ χηο ελιπ ( )

:

ξ ψ

)

ϖ◊ χ〈χ đι m

( 2;3 ,) (5;

Μ − Ν ν ςι τ πη νγ τρνη χ〈χ đ νγ τη νγ δ δ1, 2 θυα Μ ϖ◊ τι π ξχ ϖ ι ( )Ε Τm

đ τρονγ σ χ〈χ τι π τυψ ν χ α

ν ( )Ε đι θυα χ⌠ m τ τι π τυψ ν σονγ σονγ ϖ ι ηο χ Ν δ1 δ2

2 Χηο ηνη χη⌠π đ υ Σ ΑΒΧ , χ νη đ〈ψ β νγ , m τ βν τ ο ϖ ι đ〈ψ m τ γ⌠χ β νγ α ϕ

Τνη τη τχη κη ι χη⌠π ϖ◊ κηο νγ χ〈χη τ đ νη đ ν m τ πη νγ

( 0

0 < ϕ <900)

(ΣΒΧ)

3 Τρονγ κηνγ γιαν ϖ ι η τ α đ Οξψζ χηο ηαι đι m Ι(0; 0;1 ,) (Κ 3; 0; 0) ςι τ πη νγ τρνη

m τ πη νγ đι θυα ηαι đι m ,Ι Κ ϖ◊ τ ο ϖ ι m τ πη νγ Οξψ m τ γ⌠χ β νγ 300

Χυ 4 (2 đι m)

1 Τ m τ τ γ m 7 η χ σινη ν ϖ◊ 5 η χ σινη ναm χ ν χη ν ρα 6 εm τρονγ đ⌠ σ η χ σινη ν

πη ι νη η ν 4 Η ι χ⌠ βαο νηιυ χ〈χη χη ν νη ϖ ψ ?

2 Χηο η◊m σ ( )

1

ξ α

ξ

+ ξε Τm α β, βι τ ρ νγ

( )

φ = − ϖ◊ 1 ( )

0

5

φ ξ δξ=

∫

Χυ 5 (1 đι m)

Χη νγ mινη ρ νγ

2

2

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Η τ−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Γηι χη: Χ〈ν βじ χοι τηι κηνγ γιＶι τηχη γ τηm

Η ϖ◊ τν τη σινη .Σ β〈ο δανη

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Χυ 1 (2 đι m)

Χηο η◊m σ ψ=ξ3−2mξ2+m ξ2 − (1) (m λ◊ τηαm σ ) 2

1 Κη ο σ〈τ η◊m σ (1) κηι m=1

2 Τm m đ η◊m σ (1) đ τ χ χ τι υ τ ι ξ=1

Χυ 2 (2 đι m)

1 Γι ι πη νγ τρνη 2 2 χοσ 1 1

ξ

π

2 Γι ι β τ πη νγ τρνη

1

4

2

ξ ξ ξ

− + − >

−

Χυ 3 (3 đι m)

1 Τρονγ m τ πη νγ ϖ ι η τ α đ Οξ χηο đι m ψ Ι(−2; 0)ϖ◊ ηαι đ νγ τη νγ

1: 2 5 0, 2: 3 0

δ ξ− + =ψ δ ξ+ − = ψ

ςι τ πη νγ τρνη đ νγ τη νγ đι θυα đι m δ Ι ϖ◊ χ τ ηαι đ νγ τη νγ δ δ1, 2 λ ν λ τ τ ι ,

Α Β σαο χηο ΙΑiif=2.ΙΒiif

2 Τρονγ κηνγ γιαν ϖ ι η τ α đ Οξ ψζχηο Α(4; 2; 2 ,) (Β 0; 0; 7) ϖ◊ đ νγ τη νγ

δ − = − = −1

−

Χη νγ mινη ρ νγ ηαι đ νγ τη νγ ϖ◊ δ ΑΒ τηυ χ χνγ m τ m τ πη νγ Τm đι m τρν

đ νγ τη νγ δ σαο χηο ταm γι〈χ

Χ ΑΒΧ χν τ ι đ νη Α

3 Χηο ηνη χη⌠π Σ ΑΒΧ χ⌠ ΣΑ=3α ϖ◊ ϖυνγ γ⌠χ ϖ ι đ〈ψ ΑΒΧ, ταm γι〈χ ΑΒΧ χ⌠

2 ,

ΑΒ=ΒΧ= α γ⌠χ Β β νγ 1200 Τνη κηο νγ χ〈χη τ đ νη Α đ ν m τ πη νγ (ΣΒΧ)

Χυ 4 (2 đι m)

1 Τνη τχη πην

3 3 1

δξ Ι

ξ ξ

= +

∫

2 Βι τ ρ νγ ( )100 100

2+ξ =α +α ξ+ + α ξ Χη νγ mινη ρ νγ, ς ι γι〈 τρ ν◊ο χ α τη (

2

α <α3

κ α κ <α κ+1 0≤ ≤ 9κ 9 )?

Χυ 5 (1 đι m)

Χηο η◊m σ

2

2

ψ=ε − ξ+ Τm γι〈 τρ νη νη τ χ α η◊m σ φ ξ( ) ϖ◊ χη νγ mινη ρ νγ πη νγ τρνη φ ξ( )=3 χ⌠ đνγ ηαι νγηι m

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Η τ−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Γηι χη: Χ〈ν βじ χοι τηι κηνγ γιＶι τηχη γ τηm

Η ϖ◊ τν τη σινη Σ β〈ο δανη

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

δ β 2

Μν τηι: ΤΟℑΝ, ΚΗ 渦Ι Β

Τη ι γιαν λ◊m β◊ι: 180 πητ, κηνγ κ τη ι γιαν πη〈τ đ

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Χυ 1 (2 đι m)

Χηο η◊m σ

2 2 1

ξ mξ ψ

ξ

=

−

2

(1) (m λ◊ τηαm σ )

1 Κη ο σ〈τ η◊m σ (1) κηι m=1

2 Τm m đ đ τη η◊m σ (1) χ⌠ ηαι đι m χ χ τρ Α Β Χη νγ mινη ρ νγ κηι , đ⌠ đ νγ

τη νγ ΑΒ σονγ σονγ ϖ ι đ νγ τη νγ δ: 2ξ− −ψ 10= 0

Χυ ΙΙ (2 đι m)

1 Γι ι πη νγ τρνη σιν 4 σιν 7ξ ξ=χοσ 3 χοσ 6 ξ ξ

2 Γι ι β τ πη νγ τρνη λογ3ξ>λογ 3.ξ

Χυ 3 (3 đι m)

1 Τρονγ m τ πη νγ ϖ ι η τ α đ Οξ χηο ελιπ ψ ( )

:

ξ ψ

Ε + =1 ςι τ πη νγ τρνη χ〈χ τι π τυψ ν χ α ( )Ε σονγ σονγ ϖ ι đ νγ τη νγ :δ ξ+ 2ψ− = 1 0

2 Τρονγ κηνγ γιαν ϖ ι η τ α đ Οξ ψζχηο ηαι đι m Α(2; 0; 0) ϖ◊ Μ(1;1;1 )

α) Τm τ α đ đι m Ο∋đ ι ξ νγ ϖ ι Ο θυα đ νγ τη νγΑΜ

β) Γ ι ( )Π λ◊ m τ πη νγ τηαψ đ ι λυν đι θυα đ νγ τη νγ ΑΜ χ τ χ〈χ τρ χ , λ ν λ τ

τ ι χ〈χ đι m

,

Οψ Οζ

,

Β Χ Γι σ Β(0; ; 0 ,β ) (Χ 0; 0;χ β), >0,χ>0 Χη νγ mινη ρ νγ

2

βχ

β+ =χ

Ξ〈χ đ νη β χ, σαο χηο δι ν τχη ταm γι〈χ ΑΒΧ νη νη τ

Χυ 4 (2 đι m)

1 Τνη τχη πην

2 χοσ 0 σιν 2

ξ

π

2 Γι σ (1 2 )ν 0 1 ν

ν

+ = + + + Βι τ ρ νγ α0+ + + +α1 α2 α ν =729 Τm ϖ◊ σ λ ν

νη τ τρονγ χ〈χ σ

ν

0, ,1 2, , ν

Χυ 5 (1 đι m)

Χηο ταm γι〈χ ΑΒΧ τη α mν Α≤900 ϖ◊ σιν 2 σιν σιν

2

Α

Α= Β Χτγ Τm γι〈 τρ νη νη τ χ α βι υ

τη χ

1 σιν

2 σιν

Α Σ

Β

−

=

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Η τ−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Γηι χη: Χ〈ν βじ χοι τηι κηνγ γιＶι τηχη γ τηm

Η ϖ◊ τν τη σινη Σ β〈ο δανη