Page 47 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 2 Fungsi Kuadratik
SPM

PRAKTIS PdPR Jawapan
Bab 2 PRAKTIS PdPR Bab 2

Kertas 1 3. Cari julat nilai x bagi 2x(x – 5) – 12  9(1 – x).
Find the range of values of x for 2x(x – 5) – 12  9(1 – x).
[3 markah / 3 marks]
1. Selesaikan persamaan kuadratik
3 – 8(x – 1) = 2x(x + 1). Berikan jawapan anda Jawapan / Answer :
betul kepada empat angka bererti. 2x(x − 5) − 12  9(1 − x)
2
Solve the quadratic equation 2x − 10x − 12  9 − 9x
2
3 – 8(x – 1) = 2x(x + 1). Give your answers correct to four 2x − x − 21  0
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significant figures. (2x − 7)(x + 3)  0
[3 markah / 3 marks] 7
x  −3, x 
Jawapan / Answer : 2
3 – 8(x – 1) = 2x(x + 1)
3 − 8x + 8 = 2x + 2x
2
2x + 10x − 11 = 0
2
2
10
2
x = −10 ±  − 4(2)(−11) 4. Diberi fungsi kuadratik y = h + kx – x dalam
2
2(2) bentuk verteks ialah y = q – (x + p) .
Given quadratic function y = h + kx – x in the vertex form is
2
x = −10 ± 188 y = q – (x + p) .
2
4 (a) Ungkapkan setiap yang berikut dalam
x = 0.9278 , −5.928 sebutan h dan/atau k.
Express each of the following in terms of h and/or k.
(i) p
(ii) q
(b) Jika k = 5, cari paksi simetri bagi graf fungsi
2. Diberi salah satu daripada punca persamaan kuadratik itu.
kuadratik x – px – 27 = 0 ialah kuasa dua punca If k = 5, state the axis of symmetry of the graph of the
2
satu lagi. quadratic function.
Given one of the roots of the quadratic equation x – px – 27 = 0 [4 markah / 4 marks]
2
is the square of the other root. Jawapan / Answer :
(a) Nyatakan punca-punca persamaan kuadratik (a) y = h + kx − x 2
itu. = −(x − kx) + h
2
State the roots of the quadratic equation.  k  2 k 2 
(b) Cari nilai p. = – x – 2 – 4 + h
Find the value of p. k 2 k 2

[4 markah / 4 marks] = – x – 2  + 4 + h
Jawapan / Answer :
2
(a) Katakan puncanya ialah α dan α . p = – k
Let the roots are α and α . 2 2
Hasil darab punca / Product of roots: q = k 2 + h
α(α ) = –27 4
2
α = –27 (b) Paksi simetri / Axis of symmetry
3
α = –3 k
x =
Maka, punca-puncanya ialah –3 dan 9. 2
Thus, the roots are –3 and 9. x = 5
2
(b) p = Hasil tambah punca / Sum of roots
= –3 + 9
= 6

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