Additional Mathematics - Chapter 3
-
Upload
nurazrreen -
Category
Documents
-
view
198 -
download
1
Transcript of Additional Mathematics - Chapter 3
Success in SPM – Additional Mathematics – Form 4
1
Chapter 3: Quadratic Functions
1. Find the range of values of � for which the line � = � + 4 intersects the curve
� = " − 4 + 5 at two distinct points.
Success in SPM – Additional Mathematics – Form 4
2
2. Given that � = ( " + 8 + 10 − (, find the range of values of ( for which � is always
positive.
Success in SPM – Additional Mathematics – Form 4
3
3. Find the range of values of . of which 8 − 3 − " ≤ . for all real values of .
Success in SPM – Additional Mathematics – Form 4
4
4. Find the range of values of � for which line � = � + 1 does not intersect the curve
�" = 8 .
Success in SPM – Additional Mathematics – Form 4
5
5. Show that the equation 12 + 13 " + 122 + 33 + 12 + 23 = 0 has real roots for all real
values of 2.
Success in SPM – Additional Mathematics – Form 4
6
6. Find the value of 2 for which the equation 11 − 223 " + 82 − 12 + 823 = 0 has two
equal roots.
Success in SPM – Additional Mathematics – Form 4
7
7. Show that the line + � = 6 will intersect the curve " − 2 + 2�" = 3 at two distinct
points if 6" < 26 + 5.
Success in SPM – Additional Mathematics – Form 4
8
8. Find the range of values of � for which the straight line � = � − 5 intersects the curve
� = " − 1 at two distinct points.
Success in SPM – Additional Mathematics – Form 4
9
9. Find the value of 2 for which the line � = 6 is a tangent to the curve
� = " + 11 − 23 + 22.
Success in SPM – Additional Mathematics – Form 4
10
10. Find the range of values of 6 for which the line + 2� = 6 meets the curve
1 + �3 + 8 = 0.
Success in SPM – Additional Mathematics – Form 4
11
11. Find the range of the values of 2 for which equation " − 22 + 32 = 0 has real roots.
Success in SPM – Additional Mathematics – Form 4
12
12. Calculate the value of . for which the line � = 2 + . is a tangent to the curve
� = 2 " − 4 + 5.
Success in SPM – Additional Mathematics – Form 4
13
13. Given that the curve whose equation is � = 2 − 1 − 63" crosses the -axis at the points
11, 03 and 13, 03, find
i. The value of 2 and 6
ii. The maximum value of �
Success in SPM – Additional Mathematics – Form 4
14
14. Find the range of values of for which 2 1 − 13 < 3 − .
Success in SPM – Additional Mathematics – Form 4
15
15. Find the values of for which < " − 6.
Success in SPM – Additional Mathematics – Form 4
16
16. Find the range of values of = for which 12 − 3=3 " + 14 − =3 + 2 = 0 has no real roots.
Success in SPM – Additional Mathematics – Form 4
17
17. Find the value for . for which the line � = + . is a tangent to the curve
" + � + 2 = 0.
Success in SPM – Additional Mathematics – Form 4
18
18. Calculate the smallest positive integer 2 for which the equation 3 " + 2 + 7 = 0 has
real roots.
Success in SPM – Additional Mathematics – Form 4
19
19. Find the range of values of for which > " − 12.
Success in SPM – Additional Mathematics – Form 4
20
20. Find the value of 2 for which the equation 12 + 23 " − 2122 + 13 + 42 = 0 has equal
roots.
Success in SPM – Additional Mathematics – Form 4
21
21. Find the range of values of for which 12 − 33 < " − 2.