Page 8 - Modul A+1 MM Tingkatan 4

7. Bentukkan persamaan kuadratik daripada maklumat yang diberikan.
Form a quadratic equation from the given information. TP 3
Contoh/Example (a) (b)
A (3x + 2) cm B A (x + 7) cm B BAB 1
(x + 5) cm (x + 2) cm
D C
(2x – 3) cm C D x cm C
Luas segi tiga ABC = 85 cm 2 Luas trapezium ABCD
A (x + 6) cm B 2 2
Luas segi empat tepat ABCD Area of triangle ABC = 85 cm = 162 cm 2
Area of trapezium ABCD = 162 cm
1
= 50 cm 2 — × (x + 5) × (3x + 2) = 85
2
1
Area of rectangle ABCD = 50 cm 2 3x + 2x + 15x + 10 = 170 — × 3(x + 7) + x4 × (x + 2) = 162
2
2
(x + 6)(2x – 3) = 50 3x + 17x – 160 = 0 (2x + 7)(x + 2) = 324
2
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2x – 3x + 12x – 18 = 50 2x + 4x + 7x + 14 = 324
2
2
2x + 9x – 68 = 0 2x + 11x – 310 = 0
2
2
8. (a) Lengkapkan rajah berikut.
Complete the following diagram. TP 3
Contoh/Example = 1 – 1 – 2
2
= 1 – 1 – 2
= –2
x = 1
2
Nilai bagi/Value of = (–1) – (–1) – 2
(i) x = –1 x – x – 2 = 1 + 1 – 2
2
= 0
(ii) x = 2
2
= 2 – 2 – 2
= 4 – 2 – 2
= 0

(b) Tandakan ✓ bagi nilai-nilai x yang merupakan punca persamaan kuadratik x – x – 2 = 0.
2
Mark ✓ for the values of x that are the roots of the quadratic equation x – x – 2 = 0.
2
x = 1 x = –1 ✓ x = 2 ✓
9. Cari punca-punca bagi persamaan kuadratik yang berikut.
Find the roots of the following quadratic equations. TP 3

Contoh/Example (a) x(2x + 3) = 0 (b) (x – 1)(x – 4) = 0
x = 0 atau/or 2x + 3 = 0 x – 1 = 0 atau/or x – 4 = 0
(x – 7)(3x + 1) = 0 3 x = 1 atau/or x = 4
x – 7 = 0 atau/or 3x + 1 = 0 x = 0 atau/or x = – —
2
1
x = 7 atau/or x = – —
3

10. Selesaikan./Solve. TP 3
Contoh/Example (a) (4f – 1)(3f + 2) = 0
4f – 1 = 0 atau/or 3f + 2 = 0
(4k + 5)(2k – 3) = 0 4f = 1 atau/or 3f = –2
1
4k + 5 = 0 atau/or 2k – 3 = 0 f = — atau/or f = – —
2
4k = –5 atau/or 2k = 3 4 3
3
5
k = – — atau/or k = —
2
(b) (5 – 3p)(1 + 5p) = 0 (c) (3 + 2m)(2 + 7m) = 0
5 – 3p = 0 atau/or 1 + 5p = 0 3 + 2m = 0 atau/or 2 + 7m = 0
3p = 5 atau/or 5p = –1 2m = –3 atau/or 7m = –2
1
5
2
3
p = — atau/or p = – — m = – — atau/or m = – —
3 5 2 7

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