Page 17 - PBD Plus Matematik T4 (EG)

Matematik Tingkatan 4 Bab 1 Fungsi dan Persamaan Kuadratik dalam Satu Pemboleh Ubah
7 x
KERTAS 2 (c) – =
2x – 9 3x – 2
−7(3x − 2) = x(2x − 9)
1. Selesaikan persamaan kuadratik berikut: sp 1.1.6
2
Solve the following quadratic equation: −21x + 14 = 2x − 9x
(a) (x + 5) = 3x + 43 [2 markah / 2 marks] 2x + 12x − 14 = 0
2
2
(b) 6x + 17x = 14 [2 markah / 2 marks] x + 6x − 7 = 0
2
2
(x − 1)(x + 7) = 0
TIP Menjawab
Menyelesaikan persamaan kuadratik bermaksud x − 1 = 0 atau / or x + 7 = 0
mencari punca-punca bagi persamaan tersebut. x = 1 x = −7
Solving the quadratic equation means to find the roots of ∴ x = 1, −7
the equation.
Jawapan / Answer :
(a) (x + 5)(x + 5) = 3x + 43 3. (a) Tunjukkan bahawa persamaan
x + 10x + 25 = 3x + 43 4(2x – 3) = x + 9 boleh dipermudahkan
2
2
x + 10x − 3x + 25 − 43 = 0 x – 2 x – 2
x + 7x − 18 = 0 kepada x² – 10x + 21 = 0. sp 1.1.6 9
2
4(2x – 3)
(x − 2)(x + 9) = 0 Show that the equation x – 2 = x + x – 2 can be
x − 2 = 0 simplified to x² – 10x + 21 = 0.
x = 2 [3 markah / 3 marks]
atau / or (b) Seterusnya, selesaikan persamaan tersebut.
Hence, solve the equation.
x + 9 = 0 [2 markah / 2 marks]
x = −9 Jawapan / Answer :
∴ x = 2, −9
(a) 4(2x – 3) = x + 9
x – 2
x – 2
(b) 6x + 17x = 14 4(2x – 3) = x(x – 2) + 9
2
6x + 17x – 14 = 0 8x – 12 = x² – 2x + 9
2
(3x − 2)(2x + 7) = 0 x² – 10x + 21 = 0
3x − 2 = 0
2
x = (b) x² – 10x + 21 = 0
3
atau / or (x – 7)(x – 3) = 0
2x + 7 = 0 x – 7 = 0 atau / or x – 3 = 0
x = 3
x = 7
x = − 7
2

4. Jawab soalan berikut. sp 1.1.7
2. Selesaikan persamaan kuadratik berikut: sp 1.1.6 Answer the following questions.
Solve the following quadratic equation: (a) Nyatakan bentuk graf fungsi kuadratik
(a) (x + 2)² = 7x + 2 [2 markah / 2 marks] f(x) = (−x + 7)(x − 7).
(b) 3x² – 18x = 48 [2 markah / 2 marks] State the shape of quadratic function f(x) = (−x + 7)(x − 7).
(c) – 7 = x [3 markah / 3 marks] (b) Nyatakan pintasan-y dan persamaan paksi
2x – 9 3x – 2 simetri bagi graf tersebut.
Jawapan / Answer : State the y-intercept and the equation of the axis of
(a) x² + 4x + 4 = 7x + 2 symmetry of the graph.
x² – 3x + 2 = 0 (c) Tentukan koordinat titik maksimum atau
(x – 2)(x – 1) = 0 titik minimum graf tersebut.
x – 2 = 0 atau / or x – 1 = 0 Determine the coordinates of the maximum or minimum
point of the graph.
x = 2 x = 1 (d) Selesaikan untuk (−x + 7)(x − 7) = 0
dan seterusnya lakarkan graf bagi f(x)
(b) 3x² – 18x – 48 = 0 berdasarkan maklumat dari (a), (b), (c) dan
(3x + 6)(x – 8) = 0 (d).
3x + 6 = 0 atau / or x – 8 = 0 Solve for (−x + 7)(x − 7) = 0 and hence, sketch the graph
x = –2 x = 8 for f(x) based on the information from (a), (b), (c) and (d).
[10 markah / 10 marks]

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