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7/23/2019 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
7/23/2019 1st Mid-term Test (Add Maths f4)
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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
7/23/2019 1st Mid-term Test (Add Maths f4)
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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$
#
7/23/2019 1st Mid-term Test (Add Maths f4)
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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
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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
5
6repared b% <=>; ?? 1st midterm test @ '
'341*