1st Mid-term Test (Add Maths f4)

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SMK CHUNG HUA, SIBU

1st Mid-Term Test 2007

ADDITIONAL MATHEMATICS

CLASS: A ! B

"eri#d :1

22

$rs

Se%ti#& A '(0)*

Answer all the questions. Write your answers clearly i& t$e s+%es +r#ided i& t$e ./esti#& ++er. Show

your working, it may help you to get marks.

"+er 1

1. The set of ordered pairs below shows the relation between the coordinates.

( ) ( ) ( ) ( ){ }1, 2 , 1,2 , 2, 4 , 5, p- -

(a) State the value of p,

(b) Write down the imae for 2,(c) State the ob!ect for imae 2. "#$

(a)

(b)

(c)

2. The diaram below shows part of the raph of the function2( ) 1 f x x= + . State

(a) the domain,

(b) the rane,(c) the t%pe of relation

of the raph of the function. "#$

(a)

(b)

(c)

#. &iven that1

( ) cos2

g x x= and ( ) '.5 g k = , find the values of with ' 2 x p£ £ . "#$

4. n the a*es in the answer space, setch the raph of the function ( ) 2 f x x= + for the domain

# 1 x− ≤ ≤ . "4$

1



5. &iven the function1

( ) f x x

= and composite function2( ) 1 2 gf x x x= + + , find

(a) ( ) g x "#$

(b) (#) g "1$

(a)

(b)

+. &iven the function ( ) 4 f x x c= + and its inverse1 4( )

# f x mx- = + , find

(a) m and c, "#$

(b) 1(2) f - "1$

(a) (b)

. Solve the e-uation ( )2

5( 5)

x x

x+ =

-. &ive %our answer correct to three sinificant fiures.

"#$

. /orm a -uadratic e-uation whose roots are 2 #+ and 2 #- . "2$

2



0. f a and b are the roots of the -uadratic e-uation2# ( #) ' x px p+ + + = and 5a b+ =- . /ind the

value p.

"#$

1'. /ind the rane of the values of h if2( ) # 5 g x h x x= + − is alwa%s neative. "#$

11. f the -uadratic e-uation2 2 4 25 ' p x qx+ + = has real and e-ual roots such that ' p > and 'q > , find

p q . "4$

12. /ind the rane of * which satisf%( ) ( ) ( )# 5 5 x x x+ - ³ -

. "4$

#



1#. /ind the value of t if y tx= is a tanent to curve24 5 1 y x x= + + "#$

14. /ind the minimum value of22 4 5 y x x= - + b% usin the completin the s-uare method. 3ence, solve

the e-uation 22 4 # 2 x x- + = . "4$

15. (a) &iven (2,#) is the minimum point for the curve2( ) 4 y x p q= - + - , find the values of p and -.

(b) f the curve in (a) is reflected on %a*is, write down the e-uation of the new curve. "#$

,

Se%ti#& B '(0)*

Answer all the questions. Write your answers clearly i& #/r #& riti& ++er. Show your working, it

may help you to get marks. Please stapler all the answer sheets and pass on with the question paper.

1+. n the arrow diaram, the function

1

( ) 2 5 f x x

-

= - maps set onto set 6 whereas the function( ) g x mx= maps set onto set 7.

/ind(a) (i)the value of t,

(ii) the value of m,(iii) the function which maps set 6 onto set 7.

(b) &iven ( ) 4 # f x x= - and ( ) 5 fg x x= , find ( ) g x . "$

4



1. The diaram below shows the function f that maps x onto y and the function g that maps y onto z . The

function f and g are defined b%2

( )2

x f x

-= and ( ) # 5 g y y= - respectivel%.

/ind(a) the function that maps x onto z , "#$

(b) the value of1( 2) g - - "#$

1. 8iaram shows a rihtanled trianle 9:;.

(i) Show that 2 + #1 ' x x- - = . "#$

(ii) Then, find the value of *. "#$

10. f a and b are the roots for the -uadratic e-uation 2 # x x= - .

(a) find the value of 2 2

1 1

a b+ , "5$

(b) show that 4 + 5a a= - . "5$

2'. The ma*imum value of the -uadratic function2 2 y x kx k =- + + is 0, where is a constant.

(a) /ind the values of , "#$

(b) 3ence, usin the positive value of in (a), setch the raph of2 2 y x kx k =- + + . "4$

(c) /ind the rane of %. "#$

21. The diaram shows the raphs of the curves2( 2) 1 y x= + - and

21 y x kx p= - + + - which intersect

at point 9 and point : on the *a*is.

(a) /ind the values of and p, "4$(b) 3ence, find the ma*imum point of the raph

21 y x kx p= - + + - . "1$

22. /ind the coordinates of the points of intersection between the curve2 2 2 # 4 ' x y x y+ + - - = and

2 ' x+ = . "5$

End of Paper

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1st Mid-term Test (Add Maths f4)