Paper 2 - Subjective
PENANG FREE SCHOOL
MATHEMATICS ELECTIVES- ADDITIONAL MATHEMATICS
DAVID CHNG YEANG SOON.
Try the following Questions. The answers are provided at the end
of the questions.
Topic 3 Moderate.
Name: ..
Class:..
1.Given that function f(x) = x2 + kx - 4k intersects the x-axis
at two different points,
find the range of values of k.
[5 marks]
2.Given that function f(x) = x2 + kx + 7k intersects the x-axis
at two different points,
find the range of values of k.
[5 marks]
3.Given a quadratic equation x2 - 4x - 12 = 0.(a) Find the roots
of the quadratic equation.(b) Sketch the graphs of the quadratic
equation.
[6 marks]
4.Given a quadratic equation x2 + 4x + 3 = 0.(a) Find the roots
of the quadratic equation.(b) Sketch the graphs of the quadratic
equation.
[6 marks]
5.Given that function f(x) = x2 + px + 12p intersects the x-axis
at two different points,
find the range of values of p.
[5 marks]
6.Find the range of value of j for the quadratic functions f(x)
= 2x2 + 12x - 2 - jwhich touches the x-axis at one point.
[5 marks]
7.Given a quadratic equation x2 + 10x + 24 = 0.(a) Find the
roots of the quadratic equation.(b) Sketch the graphs of the
quadratic equation.
[6 marks]
8.Given a quadratic equation x2 - 6x + 5 = 0.(a) Find the roots
of the quadratic equation.(b) Sketch the graphs of the quadratic
equation.
[6 marks]
9.Given that function f(x) = x2 + jx - 2j intersects the x-axis
at two different points,
find the range of values of j.
[5 marks]
10.Find the range of value of k for the quadratic functions f(x)
= x2 + 2x - kwhich touches the x-axis at one point.
[5 marks]
11.Find the range of value of q for the quadratic functions f(x)
= -x2 - 6x - 2 - qwhich touches the x-axis at one point.
[5 marks]
12.Given a quadratic equation x2 + 2x - 8 = 0.(a) Find the roots
of the quadratic equation.(b) Sketch the graphs of the quadratic
equation.
[6 marks]
13.Given a quadratic equation x2 - 8x + 15 = 0.(a) Find the
roots of the quadratic equation.(b) Sketch the graphs of the
quadratic equation.
[6 marks]
14.Given that function f(x) = x2 + rx + 4r intersects the x-axis
at two different points,
find the range of values of r.
[5 marks]
15.Find the range of value of j for the quadratic functions f(x)
= 3x2 + 24x + 1 - jwhich touches the x-axis at one point.
[5 marks]
16.Find the range of value of p for the quadratic functions f(x)
= 2x2 + 8x - 1 - pwhich intersects the x-axis at two different
points.
[5 marks]
17.Given a quadratic equation x2 - 4x - 12 = 0.(a) Find the
roots of the quadratic equation.(b) Sketch the graphs of the
quadratic equation.
[6 marks]
18.Given that function f(x) = x2 + rx - 5r does not intersect
the x-axis,
find the range of values of r.
[5 marks]
19.Given that function f(x) = x2 + qx - 9q does not intersect
the x-axis,
find the range of values of q.
[5 marks]
20.Find the range of value of n for the quadratic functions f(x)
= -3x2 - 12x + 2 - nwhich touches the x-axis at one point.
[5 marks]
Answers:1. k < -16 or k > 02. k < 0 or k > 283. (a)
x = -2, 6(b)
4. (a) x = -3, -1(b)
5. p < 0 or p > 486. j = -207. (a) x = -4, -6(b)
8. (a) x = 1, 5(b)
9. j < -8 or j > 010. k = -111. q = 712. (a) x = -4,
2(b)
13. (a) x = 5, 3(b)
14. r < 0 or r > 1615. j = -4716. p > -917. (a) x = 6,
-2(b)
18. -20 < r < 019. -36 < q < 020. n = 14
