Core 1 - Ch 1 - 5 - Transformations and Graphs

7/27/2019 Core 1 - Ch 1 - 5 - Transformations and Graphs

http://slidepdf.com/reader/full/core-1-ch-1-5-transformations-and-graphs 1/6

1. (a) Factorise completely x3 − 4 x.

(3)

(b) Sketch the curve with equation y = x3 − 4 x, showing the coorinates o! the points where

the curve crosses the x"a#is.(3)

(c) $n a separate iagram, sketch the curve with equation

y = ( x − %)3 − 4( x − %),

showing the coorinates o! the points where the curve crosses the x"a#is.(3)

(Total 9 marks)

2.

O & 4

P ( 3 , ' & )

x

y

his iagram shows a sketch o! the curve with equation y = !( x). he curve crosses the x"a#is at

the points (&, ) an (4, ). he minimum point on the curve is P (3, '&).

*n separate iagrams sketch the curve with equation

(a) y = '!( x),(3)

(b) y = !(& x).(3)

$n each iagram, give the coorinates o! the points at which the curve crosses the x"a#is, an

the coorinates o! the image o! P uner the given trans!ormation.(Total 6 marks)

Holland Park School 1



3.

O

( 3 , + )

( , ) x

y

he iagram shows a sketch o! the curve with equation y = !( x). he curve passes through the

origin O an through the point (, ). he ma#imum point on the curve is (3, +).

$n separate iagrams, sketch the curve with equation

(a) y = 3!( x),(2)

(b) y = !( x - &).

(3)

$n each iagram, show clearly the coorinates o! the ma#imum point an o! each point at

which the curve crosses the x"a#is.(Total 5 marks)

4. $n separate iagrams, sketch the graphs o!

(a) y = ( x + 3)&,

(3)

(b) y = ( x + 3)&

- k , where k is a positive constant.(2)

Show on each sketch the coorinates o! each point at which the graph meets the a#es.(Total 5 marks)

5.




( , 3 )

( 4 , )

( % , )O x

y

he !igure above shows a sketch o! the curve with equation y = !( x). he curve passes through

the points (, 3) an (4, ) an touches the x"a#is at the point (%, ).

$n separate iagrams sketch the curve with equation

(a) y = !( x - %),(3)

(b) y = &!( x),(3)

(c).&

%

!

= x y

(3)

$n each iagram show clearly the coorinates o! all the points where the curve meets the a#es.(Total 9 marks)

6. iven that !( x) = x

%

, x / ,

(a) sketch the graph o! y = !( x) - 3 an state the equations o! the asymptotes.(4)




(b) Fin the coorinates o! the point where y = !( x) - 3 crosses a coorinate a#is.(2)

(Total 6 marks)

7. (a) $n the same a#es sketch the graphs o! the curves with equations

(i) y = x&( x ' &),

(3)

(ii) y = x( ' x),(3)

an inicate on your sketches the coorinates o! all the points where the curves cross the

x"a#is.

(b) 0se algebra to !in the coorinates o! the points where the graphs intersect.(7)

(Total 13 marks)

8.

y

xO

he iagram above shows a sketch o! the curve with equation.),

3≠= x

x y




(a) $n a separate iagram, sketch the curve with equation

,&,&

3−≠

+= x

x y

showing the

coorinates o! any point at which the curve crosses a coorinate a#is.(3)

(b) 1rite own the equations o! the asymptotes o! the curve in part (a).(2)

(Total 5 marks)

9.

y

x

( & , + )

% 4

he iagram above shows a sketch o! the curve with equation y = !( x). he curve crosses the x"

a#is at the points (%, ) an (4, ). he ma#imum point on the curve is (&, +). *n separate

iagrams sketch the curves with the !ollowing equations. $n each iagram show clearly the

coorinates o! the ma#imum point an o! each point at which the curve crosses the x"a#is.

(a) y = &!( x),(3)

(b) y = !(' x).(3)




he ma#imum point on the curve with equation y = !( x - a) is on the y"a#is.

(c) 1rite own the value o! the constant a.(1)

(Total 7 marks)

10.

y

( , 2 ) y = ! ( x )

O ( 2 , ) x

he iagram above shows a sketch o! the curve with equation y = !( x). he curve passes through

the point (, 2) an has a minimum point at (2, ).

$n separate iagrams, sketch the curve with equation

(a) y = !( x) - 3,(3)

(b) y = !(& x).(2)

$n each iagram, show clearly the coorinates o! the minimum point an the coorinates o! the

point at which the curve crosses the y"a#is.(Total 5 marks)


Documents

Core 1 - Ch 1 - 5 - Transformations and Graphs