1. The coordinates of the point of intersection of the lines px+y=3 and x+2y=q are (2, -3) Find the value of p and of q. 2. There are x chickens and y rabbits on a farm. Given that the animals have a total of 70 heads and 196 legs , formulate a pair of simmiltaneous equations involving x and y. solve the simultaneous ewuations to find the number of chickens and rabbits on the farm 3. Find the smallest value of x that satisfies the inequality -(1)/(2)geqslant 2-(3x)/(7) if it is divisible by 7. 4. There are 35 students in a class. Each boy is given two apples and an orange while each girl is given two oranges and an apple . If less than 60 apples were distributed, find the minimum number of oranges that were distributed 5. Simplify each of the following expressions. a) (a^2-7a+6)(3a-2)-a(2a^2-7) b) (b^2+(1)/(9))(b+(1)/(3))(b-(1)/(3)) 6. Factorise each of the following expressions fully a) 2c^2d^2+5cd-12 b) 25h^2k^2+10hk+1 c) 16-4(m+2)^2 d) x^3+x^2-4x-4 7. Without using a calculator , evaluate each of the following. a) 805^2 b) 903^2-97^2 8. (a) Factorise x^2-49 (b) Use your answer to part (a) to find two factors of 3551, other than 1 and 3551 9. The diagram shows a trapezium ABCD where AB=3x cm and DC=(5x+6)cm Given that the perpendicular distance between AB and DC,AH=(4x-3)cm , show that the area of the trapezium can be expressed as (16x^2-9)cm^2

Question

1. The coordinates of the point of intersection of the lines px+y=3 and x+2y=q are (2, -3) Find the value of p and of q. 2. There are x chickens and y rabbits on a farm. Given that the animals have a total of 70 heads and 196 legs , formulate a pair of simmiltaneous equations involving x and y. solve the simultaneous ewuations to find the number of chickens and rabbits on the farm 3. Find the smallest value of x that satisfies the inequality -(1)/(2)geqslant 2-(3x)/(7) if it is divisible by 7. 4. There are 35 students in a class. Each boy is given two apples and an orange while each girl is given two oranges and an apple . If less than 60 apples were distributed, find the minimum number of oranges that were distributed 5. Simplify each of the following expressions. a) (a^2-7a+6)(3a-2)-a(2a^2-7) b) (b^2+(1)/(9))(b+(1)/(3))(b-(1)/(3)) 6. Factorise each of the following expressions fully a) 2c^2d^2+5cd-12 b) 25h^2k^2+10hk+1 c) 16-4(m+2)^2 d) x^3+x^2-4x-4 7. Without using a calculator , evaluate each of the following. a) 805^2 b) 903^2-97^2 8. (a) Factorise x^2-49 (b) Use your answer to part (a) to find two factors of 3551, other than 1 and 3551 9. The diagram shows a trapezium ABCD where AB=3x cm and DC=(5x+6)cm Given that the perpendicular distance between AB and DC,AH=(4x-3)cm , show that the area of the trapezium can be expressed as (16x^2-9)cm^2

Answer 1

1. p = 1, q = -12. x = 42, y = 283. x = 144. 605. a) 3a^3 - 2a^2 - 21a + 12 b) b^4 - 1/816. a) (2cd - 3)(cd + 4) b) (5hk + 1)^2 c) 4(2 - m)(2 + m) d) (x + 2)(x^2 - 2x - 2)7. a) 648025 b) 8180008. a) (x - 7)(x + 7) b) 59 dan 609. Area trapezium = 1/2 * (AB + DC) * AH = 1/2 * (3x + 5x + 6) * (4x - 3) = 16x^2 - 9 cm^2

Answer 2

1. Menggantikan koordinat titik potong ke dalam kedua persamaan, kita mendapatkan sistem persamaan linear yang dapat diselesaikan untuk menemukan nilai p dan q.2. Dari informasi yang diberikan, kita dapat membuat dua persamaan linear dengan dua variabel, x dan y, yang mewakili jumlah ayam dan kelinci. Dengan menyelesaikan sistem persamaan ini, kita dapat menemukan jumlah ayam dan kelinci.3. Mengatur ulang ketidaksetaraan dan menyelesaikannya untuk x memberikan solusi dalam bentuk pecahan. Karena x harus kelipatan 7, kita memilih solusi terkecil yang memenuhi kondisi ini.4. Dengan mengetahui jumlah total apel yang didistribusikan dan jumlah siswa, kita dapat menemukan jumlah minimum jeruk yang didistribusikan.5. a) Menggunakan hukum distribusi dan menggabungkan istilah serupa memberikan hasil akhir. b) Menggunakan identitas a^2 - b^2 = (a - b)(a + b) memberikan hasil akhir.6. a) Menggunakan metode pembagian polinomial atau metode pembagian sintetik memberikan faktorisasi penuh. b) Menggunakan identitas a^2 + 2ab + b^2 = (a + b)^2 memberikan faktorisasi penuh. c) Menggunakan identitas a^2 - b^2 = (a - b)(a + b) memberikan faktorisasi penuh. d) Menggunakan metode pembagian polinomial atau metode pembagian sintetik memberikan faktorisasi penuh.7. a) Mengkuadratkan 805 memberikan hasil akhir. b) Menggunakan identitas a^2 - b^2 = (a - b)(a + b) dan menggantikan nilai yang diberikan memberikan hasil akhir.8. a) Menggunakan identitas a^2 - b^2 = (a - b)(a + b) memberikan faktorisasi penuh. b) Menggunakan faktorisasi penuh dari a^2 - b^2 memberikan dua faktor dari 3551 selain 1 dan 3551.9. Menggunakan rumus luas trapezium, 1/2 * (AB + DC) * AH, dan menggantikan nilai yang diberikan memberikan hasil akhir.

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