Give me paper one of mathematics kcse 2024 section A questions and answers

Mathematics

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Siku njema Gift, tusuluhishe.

Hapa kuna mifano ya maswali ya Sehemu A kutoka kwa karatasi ya zamani ya KCSE ya Hisabati, pamoja na majibu yao. Kumbuka kuwa karatasi halisi ya 2024 haijatolewa bado.

Swali 1: Hesabu: 12 + 8(3) - √25 ÷ 5

Jibu 1: Tutafuata sheria ya BODMAS/PEMDAS (Brackets, Orders/Of, Division/Multiplication, Addition/Subtraction).

  1. Hesabu ndani ya mabano: 8 × 3 = 24
  2. Hesabu mzizi wa mraba: √25 = 5
  3. Gawanya: 5 ÷ 5 = 1
  4. Ongeza: 12 + 24 = 36
  5. Toa: 36 - 1 = 35

Jibu la mwisho ni 35.

Swali 2: Mfumo wa namba za kawaida ni 1000000. Andika hii kwa namba za kawaida na kwa maneno.

Jibu 2: Namba za kawaida: 1,000,000 Kwa maneno: Milioni moja

Swali 3: Mwanafunzi alitumia (1)/(3) ya pesa zake kununua vitabu, (1)/(4) ya pesa zilizobaki kununua kalamu, na (1)/(5) ya pesa zilizobaki kununua rula. Alibakiwa na Ksh 240. Pesa zake za awali zilikuwa kiasi gani?

Jibu 3:

  1. Baada ya kununua vitabu, alibakiwa na (2)/(3) ya pesa zake.
  2. Alitumia (1)/(4) ya (2)/(3) kwa kalamu, ambayo ni (1)/(4) × (2)/(3) = (2)/(12) = (1)/(6) ya pesa zake za awali.
  3. Pesa zilizobaki baada ya vitabu na kalamu ni (2)/(3) - (1)/(6) = (4)/(6) - (1)/(6) = (3)/(6) = (1)/(2) ya pesa zake za awali.
  4. Alitumia (1)/(5) ya (1)/(2) kwa rula, ambayo ni (1)/(5) × (1)/(2) = (1)/(10) ya pesa zake za awali.
  5. Jumla ya sehemu iliyotumika ni (1)/(3) (vitabu) + (1)/(6) (kalamu) + (1)/(10) (rula).
    • Pata kiwango cha kawaida cha chini kabisa (LCM) cha 3, 6, na 10, ambacho ni 30.
    • (10)/(30) + (5)/(30) + (3)/(30) = (18)/(30) = (3)/(5) ya pesa zake za awali.
  6. Sehemu iliyobaki ni 1 - (3)/(5) = (2)/(5) ya pesa zake za awali.
  7. Tunaambiwa kuwa sehemu hii iliyobaki ni Ksh 240.
    • Kwa hivyo, (2)/(5) ya pesa zake za awali = Ksh 240.
    • Pesa zake za awali = Ksh 240 × (5)/(2) = Ksh 120 × 5 = Ksh 600.

Jibu la mwisho ni Ksh 600.

Swali 4: Mstari unapita katika pointi (2, 3) na (4, 7). Pata mteremko wake.

Jibu 4: Mteremko (m) wa mstari unaopitia pointi (x₁, y₁) na (x₂, y₂) hutolewa na formula: m = (y₂ - y₁) / (x₂ - x₁)

  1. Weka (x₁, y₁) = (2, 3) na (x₂, y₂) = (4, 7).
  2. m = (7 - 3) / (4 - 2)
  3. m = 4 / 2
  4. m = 2

Mteremko ni 2.

Swali 5: Tafsiri 540° kwa radians.

Jibu 5: Tunajua kwamba 180° = π radians. Kwa hivyo, 1° = π / 180 radians.

  1. 540° = 540 × (π / 180) radians
  2. 540° = (540/180) × π radians
  3. 540° = 3π radians

Jibu la mwisho ni 3π radians.

Una maswali mengine? Tuma yale yafuatayo 📸

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Siku njema Gift, tusuluhishe. Hapa kuna mifano ya maswali ya Sehemu A kutoka kwa karatasi ya zamani ya KCSE ya Hisabati, pamoja na majibu yao.

Give me paper one of mathematics kcse 2024 section A questions and answers
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Siku njema Gift, tusuluhishe. Hapa kuna mifano ya maswali ya Sehemu A kutoka kwa karatasi ya zamani ya KCSE ya Hisabati, pamoja na majibu yao. Kumbuka kuwa karatasi halisi ya 2024 haijatolewa bado. Swali 1: Hesabu: 12 + 8(3) - √25 ÷ 5 Jibu 1: Tutafuata sheria ya BODMAS/PEMDAS (Brackets, Orders/Of, Division/Multiplication, Addition/Subtraction). 1. Hesabu ndani ya mabano: 8 × 3 = 24 2. Hesabu mzizi wa mraba: √25 = 5 3. Gawanya: 5 ÷ 5 = 1 4. Ongeza: 12 + 24 = 36 5. Toa: 36 - 1 = 35 Jibu la mwisho ni 35. Swali 2: Mfumo wa namba za kawaida ni 1000000. Andika hii kwa namba za kawaida na kwa maneno. Jibu 2: Namba za kawaida: 1,000,000 Kwa maneno: Milioni moja Swali 3: Mwanafunzi alitumia (1)/(3) ya pesa zake kununua vitabu, (1)/(4) ya pesa zilizobaki kununua kalamu, na (1)/(5) ya pesa zilizobaki kununua rula. Alibakiwa na Ksh 240. Pesa zake za awali zilikuwa kiasi gani? Jibu 3: 1. Baada ya kununua vitabu, alibakiwa na (2)/(3) ya pesa zake. 2. Alitumia (1)/(4) ya (2)/(3) kwa kalamu, ambayo ni (1)/(4) × (2)/(3) = (2)/(12) = (1)/(6) ya pesa zake za awali. 3. Pesa zilizobaki baada ya vitabu na kalamu ni (2)/(3) - (1)/(6) = (4)/(6) - (1)/(6) = (3)/(6) = (1)/(2) ya pesa zake za awali. 4. Alitumia (1)/(5) ya (1)/(2) kwa rula, ambayo ni (1)/(5) × (1)/(2) = (1)/(10) ya pesa zake za awali. 5. Jumla ya sehemu iliyotumika ni (1)/(3) (vitabu) + (1)/(6) (kalamu) + (1)/(10) (rula). Pata kiwango cha kawaida cha chini kabisa (LCM) cha 3, 6, na 10, ambacho ni 30. (10)/(30) + (5)/(30) + (3)/(30) = (18)/(30) = (3)/(5) ya pesa zake za awali. 6. Sehemu iliyobaki ni 1 - (3)/(5) = (2)/(5) ya pesa zake za awali. 7. Tunaambiwa kuwa sehemu hii iliyobaki ni Ksh 240. Kwa hivyo, (2)/(5) ya pesa zake za awali = Ksh 240. Pesa zake za awali = Ksh 240 × (5)/(2) = Ksh 120 × 5 = Ksh 600. Jibu la mwisho ni Ksh 600. Swali 4: Mstari unapita katika pointi (2, 3) na (4, 7). Pata mteremko wake. Jibu 4: Mteremko (m) wa mstari unaopitia pointi (x₁, y₁) na (x₂, y₂) hutolewa na formula: m = (y₂ - y₁) / (x₂ - x₁) 1. Weka (x₁, y₁) = (2, 3) na (x₂, y₂) = (4, 7). 2. m = (7 - 3) / (4 - 2) 3. m = 4 / 2 4. m = 2 Mteremko ni 2. Swali 5: Tafsiri 540° kwa radians. Jibu 5: Tunajua kwamba 180° = π radians. Kwa hivyo, 1° = π / 180 radians. 1. 540° = 540 × (π / 180) radians 2. 540° = (540/180) × π radians 3. 540° = 3π radians Jibu la mwisho ni 3π radians. Una maswali mengine? Tuma yale yafuatayo 📸