Tema1 matemáticas 2ºeso

15 Jan 2015
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Tema1 matemáticas 2ºeso

• 1. PÁGINA 35 EJERCICIOS DE LA UNIDAD Suma y resta de enteros 1 Calcula: a) 5 – 3 – 7 + 1 + 8 b) 2 – 3 + 4 + 1 – 8 + 2 c) 1 – 3 + 5 – 7 + 9 – 11 d) 2 + 4 – 6 – 8 + 10 – 12 + 14 a) 5 – 3 – 7 + 1 + 8 = (5 + 1 + 8) – (3 + 7) = 14 – 10 = 4 b) 2 – 3 + 4 + 1 – 8 + 2 = (2 + 4 + 1 + 2) – (3 + 8) = 9 – 11 = –2 c) 1 – 3 + 5 – 7 + 9 – 11 = (1 + 5 + 9) – (3 + 7 + 11) = 15 – 21 = –6 d) 2 + 4 – 6 – 8 + 10 – 12 + 14 = (2 + 4 + 10 + 14) – (6 + 8 + 12) = 30 – 26 = 4 2 Quita paréntesis: a) a + (b + c) b) a – (b + c) c) a + (b – c) d) a – (b – c) a) a + (b + c) = a + b + c b) a – (b + c) = a – b – c c) a + (b – c) = a + b – c d) a – (b – c) = a – b + c 3 Quita paréntesis y después opera: a) 1 – (7 – 2 – 10) – (3 – 8) b) (8 – 4 – 3) – (5 – 8 – 1) c) (3 – 5) – (1 – 4) + (5 – 8) d) 3 – (5 – 8) – (11 – 4) + (13 – 9) a) 1 – (7 – 2 – 10) – (3 – 8) = 1 – 7 + 2 + 10 – 3 + 8 = (1 + 2 + 10 + 8) – (3 + 7) = = 21 – 10 = 11 b) (8 – 4 – 3) – (5 – 8 – 1) = 8 – 4 – 3 – 5 + 8 + 1 = (8 + 8 + 1) – (4 + 3 + 5) = = 17 – 12 = 5 c) (3 – 5) – (1 – 4) + (5 – 8) = 3 – 5 – 1 + 4 + 5 – 8 = (3 + 4 + 5) – (5 + 1 + 8) = = 12 – 14 = –2 d) 3 – (5 – 8) – (11 – 4) + (13 – 9) = 3 – 5 + 8 – 11 + 4 + 13 – 9 = = (3 + 8 + 4 + 13) – (5 + 11 + 9) = 28 – 25 = 3 Pág. 1 SOLUCIONES A LOS EJERCICIOS DE LA UNIDAD Unidad 1. Números enteros y divisibilidad 1
• 2. Pág. 2 4 Calcula operando primero dentro de los paréntesis: a) (2 – 6 – 3) + (5 – 3 – 1) – (2 – 4 – 6) b) (8 – 11 – 5) – (12 – 13) + (11 + 4) c) 15 + (6 – 18 + 11) – (7 + 15 – 19) + (1 – 3 – 6) a) (2 – 6 – 3) + (5 – 3 – 1) – (2 – 4 – 6) = (–7) + (1) – (– 8) = –7 + 1 + 8 = 2 b) (8 – 11 – 5) – (12 – 13) + (11 + 4) = (– 8) – (–1) + (15) = –8 + 1 + 15 = 8 c) 15 + (6 – 18 + 11) – (7 + 15 – 19) + (1 – 3 – 6) = 15 + (–1) – (3) + (– 8) = = 15 – 1 – 3 – 8 = 3 5 Quita paréntesis y calcula: a) 3 – [(5 – 8) – (3 – 6)] b) 1 – (3 – [4 – (1 – 3)]) c) (2 + 7) – (5 – [6 – (10 – 4)]) a) 3 – [(5 – 8) – (3 – 6)] = 3 – [(–3) – (–3)] = 3 – [–3 + 3] = 3 b) 1 – (3 – [4 – (1 – 3)]) = 1 – (3 – [4 – (–2)]) = 1 – (3 – 6) = 1 + 3 = 4 c) (2 + 7) – (5 – [6 – (10 – 4)]) = 9 – (5 – [6 – 6]) = 9 – 5 = 4 6 Calcula: a) (–7) · (+11) b) (–6) · (–8) b) (+5) · (+7) · (–1) d) (–2) · (–3) · (–4) a) (–7) · (+11) = –77 b) (–6) · (–8) = 48 c) (+5) · (+7) · (–1) = –35 d) (–2) · (–3) · (–4) = –24 7 Opera: a) (–45) : (+3) b) (+85) : (+17) b) (+36) : (–12) d) (–85) : (–5) a) (–45) : (+3) = –15 b) (+85) : (+17) = 5 c) (+36) : (–12) = –3 d) (–85) : (–5) = 17 8 Opera las expresiones siguientes: a) (+400) : (–40) : (–5) b) (+400) : [(–40) : (–5)] c) (+7) · (–20) : (+10) d) (+7) · [(–20) : (+10)] e) (+300) : (+30) · (–2) f) (+300) : [(+30) · (–2)] SOLUCIONES A LOS EJERCICIOS DE LA UNIDAD Unidad 1. Números enteros y divisibilidad 1
• 3. a) (+400) : (–40) : (–5) = (–10) : (–5) = 2 b) (+400) : [(–40) : (–5)] = (+400) : (+8) = 50 c) (+7) · (–20) : (+10) = –140 : 10 = –14 d) (+7) · [(–20) : (+10)] = 7 · (–2) = –14 e) (+300) : (+30) · (–2) = 10 · (–2) = –20 f ) (+300) : [(+30) · (–2)] = 300 : (–60) = –5 Operaciones combinadas 9 Calcula: a) 6 · 4 – 5 · 6 – 2 · 3 b) 15 – 6 · 3 + 2 · 5 – 4 · 3 c) 5 · (–4) + (–2) · 4 – 6 · (–5) – 3 · (–6) d) 18 – 3 · 5 + 5 · (–4) – 3 · (–2) a) 6 · 4 – 5 · 6 – 2 · 3 = 24 – 30 – 6 = –12 b) 15 – 6 · 3 + 2 · 5 – 4 · 3 = 15 – 18 + 10 – 12 = –5 c) 5 · (–4) + (–2) · 4 – 6 · (–5) – 3 · (–6) = –20 – 8 + 30 + 18 = 20 d) 18 – 3 · 5 + 5 · (–4) – 3 · (–2) = 18 – 15 – 20 + 6 = –11 10 Opera estas expresiones: a) (–5) · (8 – 13) b) (2 + 3 – 6) · (–2) c) (+4) · (1 – 9 + 2) : (–3) d) (–12 – 10) : (–2 – 6 – 3) a) (–5) · (8 – 13) = (–5) · (–5) = 25 b) (2 + 3 – 6) · (–2) = (–1) · (–2) = 2 c) (+4) · (1 – 9 + 2) : (–3) = 4 · (–6) : (–3) = (–24) : (–3) = 8 d) (–12 – 10) : (–2 – 6 – 3) = (–22) : (–11) = 2 11 Calcula: a) 13 – [8 – (6 – 3) – 4 · 3] : (–7) b) 5 · (8 – 3) – 4 · (2 – 7) – 5 · (1 – 6) c) 12 · (12 – 14) – 8 · (16 – 11) – 4 · (5 – 17) Pág. 3 SOLUCIONES A LOS EJERCICIOS DE LA UNIDAD Unidad 1. Números enteros y divisibilidad 1
• 4. Pág. 4 a) 13 – [8 – (6 – 3) – 4 · 3] : (–7) = 13 – [8 – 3 – 12] : (–7) = 13 – (–7) : (–7) = = 13 – 1 = 12 b) 5 · (8 – 3) – 4 · (2 – 7) – 5 · (1 – 6) = 5 · 5 – 4 · (–5) – 5 · (–5) = = 25 + 20 + 25 = 70 c) 12 · (12 – 14) – 8 · (16 – 11) – 4 · (5 – 17) = 12 · (–2) – 8 · 5 – 4 · (–12) = = –24 – 40 + 48 = –16 12 Realiza las operaciones siguientes: a) 18 – 40 : (5 + 4 – 1) – 36 : 12 b) 4 + 36 : 9 – 50 : [12 + (17 – 4)] c) 48 : [5 · 3 – 2 · (6 – 10) – 17] d) 3 · 4 – 15 : [12 + 4 · (2 – 7) + 5] a) 18 – 40 : (5 + 4 – 1) – 36 : 12 = 18 – 40 : 8 – 3 = 18 – 5 – 3 = 10 b) 4 + 36 : 9 – 50 : [12 + (17 – 4)] = 4 + 4 – 50 : 25 = 8 – 2 = 6 c) 48 : [5 · 3 – 2 · (6 – 10) – 17] = 48 : [15 + 8 – 17] = 48 : 6 = 8 d) 3 · 4 – 15 : [12 + 4 · (2 – 7) + 5] = 12 – 15 : [12 + 4 · (–5) + 5] = = 12 – 15 : [12 – 20 + 5] = 12 – 15 : (–3) = 12 + 5 = 17 13 Calcula: a) (–2)7 b) (–3)5 c) (–5)3 d) (–10)3 e) (–1)16 f) (–1)17 a) (–2)7 = –128 b) (–3)5 = –243 c) (–5)3 = –125 d) (–10)3 = –1000 e) (–1)16 = +1 f) (–1)17 = –1 14 Expresa como una única potencia: a) (–2)4 · (–2)3 b) (+2)3 · (–2)3 c) (–3)5 : (–3)3 d) (–5)6 : (–5)3 a) (–2)4 · (–2)3 = (–2)7 b) (+2)3 · (–2)3 = (+2)3 · (–2)3 = –(23 · 23 ) = –26 c) (–3)5 : (–3)3 = (–3)2 d) (–5)6 : (–5)3 = (–5)3 15 Calcula: a) (–2)3 + (–3)3 – (–4)3 b) (–5)2 · (–2)2 + (+3)2 · (–3) c) (–2)2 · [(–5)2 – (+4)2 ] d) (–6)3 : (–3)3 + (–8)2 : (–4)2 SOLUCIONES A LOS EJERCICIOS DE LA UNIDAD Unidad 1. Números enteros y divisibilidad 1
• 5. a) (–2)3 + (–3)3 – (–4)3 = (–8) + (–27) – (–64) = –8 – 27 + 64 = 64 – 35 = 29 b) (–5)2 · (–2)2 + (+3)2 · (–3) = [(–5) · (–2)]2 – 33 = 102 – 33 = 100 – 27 = 73 c) (–2)2 · [(–5)2 – (+4)2 ] = 4 · (25 – 16) = 4 · 9 = 36 d) (–6)3 : (–3)3 + (–8)2 : (–4)2 = [(–6) : (–3)]3 + [(–8) : (–4)]2 = 23 + 22 = = 8 + 4 = 12 16 Calcula, si existe: a) ͙(–6)2 ෆ b) ͙(–6)3 ෆ c) ͙(–5)3 ෆ d) ͙(–5)4 ෆ e) ͙(–1)7 ෆ f) ͙(–1)8 ෆ a) ͙(–6)2 ෆ = ͙36ෆ = ±6 b) ͙(–6)3 ෆ = ͙–216ෆ → No existe c) ͙(–5)3 ෆ = ͙–125ෆ → No existe d) ͙(–5)4 ෆ = ͙625ෆ = ±25 e) ͙(–1)7 ෆ = ͙–1ෆ → No existe f) ͙(–1)8 ෆ = ͙1ෆ = ±1 17 Calcula, si existe: a) ͙(+2)2 ·ෆ(–2)4 ෆ b) ͙(–2)7 :ෆ(–2)3 ෆ c) ͙83 : (–2ෆ)5 ෆ d) ͙(–6)3 :ෆ33 ෆ a) ͙(+2)2 ·ෆ(–2)4 ෆ = ͙26 ෆ = ͙64ෆ = ±8 b) ͙(–2)7 :ෆ(–2)ෆ3 = ͙(–2)4 ෆ = ͙16ෆ = ±4 c) ͙83 : (–2ෆ)5 ෆ = ͙29 : (–2ෆ)5 ෆ = ͙–24 ෆ = ͙–16ෆ → No existe d) ͙(–6)3 :ෆ33 ෆ = ͙(–6 : 3ෆ)3 ෆ = ͙(–2)3 ෆ = ͙–8ෆ → No existe PÁGINA 36 Múltiplos y divisores 18 Verdadero o falso: a) 195 es múltiplo de 13. b) 13 es divisor de 195. c) 745 es múltiplo de 15. d) 18 es divisor de 258. e) 123 es divisor de 861. Pág. 5 SOLUCIONES A LOS EJERCICIOS DE LA UNIDAD Unidad 1. Números enteros y divisibilidad 1