Excel 1
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SMK RAJA PEREMPUAN, IPOH ADDITIONAL MATHEMATICS FIRST SEMESTER BREAK EXERCISES FORM 4 YEAR 2009 ______________________
EXCEL 1
Instruction : Answer all questions. Show your working. It may help you to get marks. 1. Given set A = {–8, –7, –6, 3, 6, 7, 8} and set B = {9, 16, 25, 36, 49, 64}. The relation from set A to set B is f(x) = x 2 , state (a) the image of 8. (b) the objects of 49, [3 marks]
(c) the domain of the relation,
Answer: (a) ________________ (b) ________________ (c) ________________ 2.
Given the function f(x) = 4x, x ≠ 0 and the composite function fg(x) =
− 16 . Find x
(a) g(x), [3 marks]
(b) the value of x when g(x) = 8.
Answer: (a) ________________ (b) ________________ 3
Diagram 1 shows a function f : x → ax 2 + bx . f x ax 2 + bx 3
3
1
5 DIAGRAM 1
[3 marks]
Find the value of a and of b.
Answer: a = _______, b = _________
Additional Mathematics
2
09 Excel 1
4.
a) Solve the quadratic equation 3x2− 9x + 5 = 0 . Give your answer correct to four significant figures . b) Form the quadratic equation which has the roots m and 2m. Give your answer in the form ax2 + bx + c = 0, where a, b and c are constants. [ 4 marks ]
Answer : a) _________________ 5.
b) _________________ Solve the quadratic equation 2(x + 3)( 2 − x ) = x + 5 . Give your answer correct to three decimal places. [ 3 marks ]
Answer : _________________ 6.
The quadratic equation 2x2 + px + 2q – 5 = 0 has roots −2 and
3 . Find the value of p and 2
of q . [ 3 marks ]
Answer : p = ________________ q = ________________ 7.
Given the quadratic function y = −2( x + 3) 2 + 9 . State a) the coordinates of the maximum point
Additional Mathematics
3
09 Excel 1
b) the axis of symmetry [ 2 marks ]
Answer : a) ___________________ b) ___________________ 8.
Find the range of values of x if 4 x( x + 1) > 2 − 3 x .
[ 3 marks ]
Answer : _____________________ 9.
The straight line y = 5 x + 2 does not intersect the curve y = 2 x 2 − x + p . Find the range of values of p . [ 3 marks ]
Answer : a) _________________ b) _________________ 10.
Solve the simultaneous equations 2 x + y − 1 = 0 and y 2 + x = 2
Additional Mathematics
4
[ 5 marks ]
09 Excel 1
11.
12.
Solve the simultaneous equations 4 p + q + 8 = 0 and p 2 − 2 = q − p
Solve the simultaneous equations x + 2 y + 1 = 0 and x − 3 y 2 + 5 = 0 Give your answers correct to three decimal places.
Answer 1
a) Image of 8 is 64 b) Object of 49 = {7, –7}
Additional Mathematics
[ 5 marks ]
[ 5 marks ]
……………….(1) ……………….(1) 5
09 Excel 1
c) Many to one 2.
3. 4.
−4 ,x≠0 x 1 (b) x = − 2 a = – 2 and b = 7 a) 2.263 , 0.7362 (a) g(x) =
b) 5. 6. 7. 8. 9.
10.
……………….(1)
x 2 − 3mx + 2m 2 = 0
x = −2.766 , 1.266 1 p=1, q=− 2 a) (-3,9) b) x = −3 1 x < 2, x > 4 5 p> 2 x=−
1 4
or
x =1
3 or y = −1 2 p = −2 or p = −3 q = 0 or q = 4 x = −2.738 or x = 2.070 y = 0.869 or y = −1.535 y=
11. 12.
Additional Mathematics
6
09 Excel 1
EXCEL 1
Instruction : Answer all questions. Show your working. It may help you to get marks. 1. Given set A = {–8, –7, –6, 3, 6, 7, 8} and set B = {9, 16, 25, 36, 49, 64}. The relation from set A to set B is f(x) = x 2 , state (a) the image of 8. (b) the objects of 49, [3 marks]
(c) the domain of the relation,
Answer: (a) ________________ (b) ________________ (c) ________________ 2.
Given the function f(x) = 4x, x ≠ 0 and the composite function fg(x) =
− 16 . Find x
(a) g(x), [3 marks]
(b) the value of x when g(x) = 8.
Answer: (a) ________________ (b) ________________ 3
Diagram 1 shows a function f : x → ax 2 + bx . f x ax 2 + bx 3
3
1
5 DIAGRAM 1
[3 marks]
Find the value of a and of b.
Answer: a = _______, b = _________
Additional Mathematics
2
09 Excel 1
4.
a) Solve the quadratic equation 3x2− 9x + 5 = 0 . Give your answer correct to four significant figures . b) Form the quadratic equation which has the roots m and 2m. Give your answer in the form ax2 + bx + c = 0, where a, b and c are constants. [ 4 marks ]
Answer : a) _________________ 5.
b) _________________ Solve the quadratic equation 2(x + 3)( 2 − x ) = x + 5 . Give your answer correct to three decimal places. [ 3 marks ]
Answer : _________________ 6.
The quadratic equation 2x2 + px + 2q – 5 = 0 has roots −2 and
3 . Find the value of p and 2
of q . [ 3 marks ]
Answer : p = ________________ q = ________________ 7.
Given the quadratic function y = −2( x + 3) 2 + 9 . State a) the coordinates of the maximum point
Additional Mathematics
3
09 Excel 1
b) the axis of symmetry [ 2 marks ]
Answer : a) ___________________ b) ___________________ 8.
Find the range of values of x if 4 x( x + 1) > 2 − 3 x .
[ 3 marks ]
Answer : _____________________ 9.
The straight line y = 5 x + 2 does not intersect the curve y = 2 x 2 − x + p . Find the range of values of p . [ 3 marks ]
Answer : a) _________________ b) _________________ 10.
Solve the simultaneous equations 2 x + y − 1 = 0 and y 2 + x = 2
Additional Mathematics
4
[ 5 marks ]
09 Excel 1
11.
12.
Solve the simultaneous equations 4 p + q + 8 = 0 and p 2 − 2 = q − p
Solve the simultaneous equations x + 2 y + 1 = 0 and x − 3 y 2 + 5 = 0 Give your answers correct to three decimal places.
Answer 1
a) Image of 8 is 64 b) Object of 49 = {7, –7}
Additional Mathematics
[ 5 marks ]
[ 5 marks ]
……………….(1) ……………….(1) 5
09 Excel 1
c) Many to one 2.
3. 4.
−4 ,x≠0 x 1 (b) x = − 2 a = – 2 and b = 7 a) 2.263 , 0.7362 (a) g(x) =
b) 5. 6. 7. 8. 9.
10.
……………….(1)
x 2 − 3mx + 2m 2 = 0
x = −2.766 , 1.266 1 p=1, q=− 2 a) (-3,9) b) x = −3 1 x < 2, x > 4 5 p> 2 x=−
1 4
or
x =1
3 or y = −1 2 p = −2 or p = −3 q = 0 or q = 4 x = −2.738 or x = 2.070 y = 0.869 or y = −1.535 y=
11. 12.
Additional Mathematics
6
09 Excel 1
