Page 24 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Quadratic Functions
2. The quadratic equation x – 2(6x – p) = 0, (a) State the coordinates of point M.
2
where p is a constant, has two different (b) Find the value of a.
real roots. One of the roots is five times (c) If the curve is reflected in the x-axis,
the root t, where t ≠ 0. state the new equation of the curve.
Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
(a) Find the value of t and of p.
(b) Hence, form a quadratic equation 7. The quadratic equation k – 3x = x – x + 3,
2
which has the roots of t – 17 and where k is a constant, has roots α and β.
t + 11. (a) Find the range of values of k if
α ≠ β.
3. Given a quadratic equation (b) Given that α + 3 and β + 3 are the Form 4
h(x + 36) = –4kx has two equal roots, roots of another quadratic equation
2
find the ratio h : k. Hence, solve the 4x – hx + 12 = 0, where h is a
2
equation.
constant. Find the value of h and of
4. The diagram below shows the graph of k.
f(x) = –2x – 5x + 12.
2
8. The quadratic equation x = 10(n – x),
2
f(x)
where n is a constant, has roots m and
12 –3m, where m ≠ 0.
(a) Find the value of m and of n.
x (b) Hence, form a quadratic equation
–4 0 3 n n
2 which has the roots and in the
4
5
2
(a) Make generalisations on the shape form of ax + bx + c = 0.
and position of the graph when the
value of b changes from –5 to 5. 9. Given a quadratic function
2
(b) Sketch the new graph. f(x) = –x + 7x – 10.
(c) State an equivalent transformation (a) Express f(x) in the form
2
on the change of the new graph f(x) = a(x + p) + q.
compared to the graph of f(x). (b) Find the minimum or maximum
value of the quadratic function f(x).
5. (a) Find the range of values of x for (c) Sketch the graph of
x – 8x + 12  0 and x – 8x  0. f(x) = –x + 7x – 10 for 0  x  7.
2
2
2
(b) Hence, solve the inequality (d) State the equation of the curve when
–12  x – 8x  0. the graph f(x) is reflected in the
2
6. The diagram below shows the graph of x-axis.
quadratic function f(x) = a(x + f ) + g
2
where a, f and g are constants. The 10. A rectangular piece of paper has a length
straight line y = 9 is a tangent to the and a width, in cm, of 3x and (12 – x)
curve at point M. respectively.
(a) Find the perimeter, in cm, of the
f(x) paper if the area of the paper is
M maximum.
(b) Hence, state the maximum area, in
cm , of the paper.
2
x
–1 0 5

31

02 Ranger Add Mathematics Tg4.indd 31 25/02/2022 9:10 AM