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Prueba de Diagnóstico de Matemáticas

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Prueba de Diagnóstico de Matemáticas

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Evaluación de álgebra, ecuaciones y trigonometría

Created by

Luis Pullotasig
Luis Pullotasig
Ecuador

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Prueba de Diagnóstico de Matemáticas
 

Prueba de Diagnóstico de MatemáticasOnline version

Evaluación de álgebra, ecuaciones y trigonometría

by Luis Pullotasig
1

1) Aplica las propiedades de la potenciación para simplificar: ((2^3·2^2)^2)/2^5.

2

2) Calcula: √50+√18-√8.

3

3) Factoriza: a) x^2-7x+12; b) 4x^2-25.

4

4) Resuelve: (2x-1)/3 = (x+4)/2 y encuentra x.

5

5) Resuelve la inecuación: 3x-5 ≤ 7x+3. ¿Qué conjunto es?

6

6) En un triángulo rectángulo, catetos 6 cm y 8 cm. ¿Longitud de la hipotenusa?

7

7) Si seno θ = 3/5 para un ángulo agudo, determina cos θ y tan θ.

8

8) Usando identidades, simplifica: sin^2 x + cos^2 x + tan^2 x.

9

9) Resuelve la inecuación: 5x+2 < 3x+8.

10

10) Si tan θ = 3/4 y θ es agudo, ¿cuáles son sin θ y cos θ?

Explicación

La potencia total es 2^(3+2)=2^5, elevado al cuadrado da 2^10; dividir entre 2^5 da 2^5=32.

Cada radical se reduce a múltiplos de √2: (5+3-2)√2=6√2.

a) busca factores que sumen -7; b) diferencia de cuadrados.

Cruza: 2(2x-1)=3(x+4) → 4x-2=3x+12 → x=14.

Restas y simplificas: -8 ≤ 4x → x ≥ -2.

Aplicar Pitágoras: 6^2+8^2=36+64=100, hipotenusa=10.

Para θ agudo, cos>0; tan=sin/cos.

Sin^2+Cos^2=1; tan^2 = sec^2-1; suma da 1+tan^2.

Restar 3x y 2: 2x < 6 → x < 3.

Triángulo pitagórico 3-4-5.

 
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