Prueba Diagnostica De Matematicas 7mo

1. La siguiente figura está representada por :

Rectángulos y triángulos

Triángulos y rombos

Cuadrados y triángulos

Trapecio y rectángulos

Trapecio y Cuadrilateros

The correct answer is "Rectángulos y triángulos." This suggests that the figure in question is composed of both rectangles and triangles.

Explanation

The correct answer is "Rectángulos y triángulos." This suggests that the figure in question is composed of both rectangles and triangles.

2. El maratón sobre el Puente Teodoro Moscoso tiene 10 kilómetros de largo ¿ A cuántos metros equivale esta distancia?

5,000 m

10,000 m

15,000 m

20,000 m

1,000 m

The correct answer is 10,000 m. This is because 1 kilometer is equal to 1,000 meters, so to convert 10 kilometers to meters, we multiply 10 by 1,000, which equals 10,000 meters.

Explanation

The correct answer is 10,000 m. This is because 1 kilometer is equal to 1,000 meters, so to convert 10 kilometers to meters, we multiply 10 by 1,000, which equals 10,000 meters.

3. Selecciona el número mayor :

1/2

0.67

3/4

1

7/12

The number 1 is the largest among the given options because it is a whole number and does not have any fractions or decimals. The other options are either fractions or decimals, which are smaller than 1.

Explanation

The number 1 is the largest among the given options because it is a whole number and does not have any fractions or decimals. The other options are either fractions or decimals, which are smaller than 1.

4. De acuerdo al patrón establecido, el valor de la Y cuando X = 13 es :

X	3	5	8	10	13
Y	12	20	32	40	?

26

36

48

52

60

Based on the established pattern, the value of Y increases by 8 each time X increases by 5. Therefore, when X = 13, the value of Y would be 40 + 8 = 48.

Explanation

Based on the established pattern, the value of Y increases by 8 each time X increases by 5. Therefore, when X = 13, the value of Y would be 40 + 8 = 48.

5. Juan ahorra $120 semanales. ¿Cuál de las siguientes ecuaciones representa los ahorros de Juan en tres semanas?

3x = 360

3x = 120

x + 3 = 120

x + 3 = 360

2x + 3 = 180

The correct answer is 3x = 360. This equation represents the savings of Juan in three weeks. Since Juan saves $120 weekly, multiplying this amount by 3 gives us the total savings in three weeks, which is $360.

Explanation

The correct answer is 3x = 360. This equation represents the savings of Juan in three weeks. Since Juan saves $120 weekly, multiplying this amount by 3 gives us the total savings in three weeks, which is $360.

6. ¿Cuáles de estas velocidades es más lenta que 50 millas por hora?

1.25 millas por minuto

0.25 millas en 30 segundos

16 millas en 18 minutos

20 millas en 15 minutos

0.25 millas en 30 segundos is slower than 50 miles per hour because it takes 30 seconds to travel a distance of 0.25 miles. In comparison, 50 miles per hour means traveling a distance of 50 miles in one hour, which is much faster than 0.25 miles in 30 seconds.

Explanation

0.25 millas en 30 segundos is slower than 50 miles per hour because it takes 30 seconds to travel a distance of 0.25 miles. In comparison, 50 miles per hour means traveling a distance of 50 miles in one hour, which is much faster than 0.25 miles in 30 seconds.

7. Determina cuál propiedad está representada en la expresión (3 + x )+4 = 3 + (x + 4)

Distributiva

Conmutativa

Igualdad

Asociativa

Identidad del cero

The correct answer is "Asociativa." This property states that the grouping of numbers in an addition or multiplication expression does not affect the final result. In the given expression, both sides are equal because the grouping of numbers is changed but the order of addition remains the same.

Explanation

The correct answer is "Asociativa." This property states that the grouping of numbers in an addition or multiplication expression does not affect the final result. In the given expression, both sides are equal because the grouping of numbers is changed but the order of addition remains the same.

8. Si x = 3, entonces el valor de la expresión 2(3x + 9) es:

18

29

36

52

45

The expression 2(3x + 9) can be simplified by substituting x with the given value of 3. This gives us 2(3(3) + 9), which simplifies to 2(9 + 9) and further simplifies to 2(18). Multiplying 2 by 18 gives us the final result of 36.

Explanation

The expression 2(3x + 9) can be simplified by substituting x with the given value of 3. This gives us 2(3(3) + 9), which simplifies to 2(9 + 9) and further simplifies to 2(18). Multiplying 2 by 18 gives us the final result of 36.

9. José quiere comprar una cubierta para su piscina, en forma de rectángulo, con un ancho de 9m y un largo de 5.5 m. ¿ Cuál será el tamaño de la cubierta?

14.5 m2

29 m2

49.5 m2

495 m2

4 m2

José quiere comprar una cubierta para su piscina en forma de rectángulo. El ancho de la piscina es de 9m y el largo es de 5.5m. Para calcular el tamaño de la cubierta, debemos multiplicar el ancho por el largo. Entonces, 9m x 5.5m = 49.5m2. Por lo tanto, el tamaño de la cubierta será de 49.5m2.

Explanation

José quiere comprar una cubierta para su piscina en forma de rectángulo. El ancho de la piscina es de 9m y el largo es de 5.5m. Para calcular el tamaño de la cubierta, debemos multiplicar el ancho por el largo. Entonces, 9m x 5.5m = 49.5m2. Por lo tanto, el tamaño de la cubierta será de 49.5m2.

10. ¿Qué clase de triángulo es aquel cuya suma de dos de sus ángulos es igual al tercer ángulo?

Acutángulo

Obtusángulo

Rectángulo

Equilátero

Cuadrado

Un triángulo rectángulo es aquel cuya suma de dos de sus ángulos es igual al tercer ángulo. En un triángulo rectángulo, uno de los ángulos es un ángulo recto, es decir, mide 90 grados. Los otros dos ángulos son agudos, es decir, miden menos de 90 grados. Por lo tanto, la suma de los dos ángulos agudos es igual a 90 grados, que es igual al tercer ángulo recto.

Explanation

Un triángulo rectángulo es aquel cuya suma de dos de sus ángulos es igual al tercer ángulo. En un triángulo rectángulo, uno de los ángulos es un ángulo recto, es decir, mide 90 grados. Los otros dos ángulos son agudos, es decir, miden menos de 90 grados. Por lo tanto, la suma de los dos ángulos agudos es igual a 90 grados, que es igual al tercer ángulo recto.

11. 1/4 x 3/5 x 7/3 =

60/21

7/20

11/12

15/84

1/2

The given expression represents the product of three fractions. To find the product, we multiply the numerators together and the denominators together. So, (1/4) x (3/5) x (7/3) = (1 x 3 x 7) / (4 x 5 x 3) = 21 / 60. Simplifying the fraction by dividing both numerator and denominator by 3, we get 7 / 20. Therefore, the correct answer is 7/20.

Explanation

The given expression represents the product of three fractions. To find the product, we multiply the numerators together and the denominators together. So, (1/4) x (3/5) x (7/3) = (1 x 3 x 7) / (4 x 5 x 3) = 21 / 60. Simplifying the fraction by dividing both numerator and denominator by 3, we get 7 / 20. Therefore, the correct answer is 7/20.

12. Coloca las siguientes fracciones en orden ascendente: 4/8, 6/2, 1/8, 3/4

4/8, 1/8, 3/4, 6/2

6/2 , 3/4, 4/8, 1/8

1/8, 4/8, 3/4, 6/2

1/8, 3/4, 4/8, 6/2

6/2 , 1/8, 3/4, 4/8

The fractions are being arranged in ascending order. To determine the order, we compare the numerators of the fractions. The fraction with the smallest numerator, 1/8, comes first. Then, we compare the remaining fractions with the same numerator, 4/8. Since 3/4 has a smaller numerator than 6/2, it comes before 6/2. Therefore, the correct order is 1/8, 4/8, 3/4, 6/2.

Explanation

The fractions are being arranged in ascending order. To determine the order, we compare the numerators of the fractions. The fraction with the smallest numerator, 1/8, comes first. Then, we compare the remaining fractions with the same numerator, 4/8. Since 3/4 has a smaller numerator than 6/2, it comes before 6/2. Therefore, the correct order is 1/8, 4/8, 3/4, 6/2.

13. ¿Qué enunciado sobre la siguiente figura es verdadera?

∠1 y ∠8 son congruentes

∠3 y ∠5 son ángulos correspondientes

La medida del ∠8 es 95º

∠2 y ∠3 son son ángulos opuestos por el vértice

La medida del ∠8 es 45º

∠8 is measured at 95º.

Explanation

∠8 is measured at 95º.

14. Observando la siguiente gráfica, determina el dinero ganado desde el año 1995 hasta el año 1998.

$950

$975

$1,000

$1,050

$105

Based on the given graph, the amount of money earned from 1995 to 1998 is $1,000. This can be determined by observing the highest point on the graph, which corresponds to the year 1998, and noting that the value is $1,000. Therefore, the correct answer is $1,000.

Explanation

Based on the given graph, the amount of money earned from 1995 to 1998 is $1,000. This can be determined by observing the highest point on the graph, which corresponds to the year 1998, and noting that the value is $1,000. Therefore, the correct answer is $1,000.

15. Selecciona la alternativa que representa mejor la propiedad distributiva:

5(a+b) = (a+b)5

2x + 3c = 3c + 2x

4(3+c) = 4(3) + 4c

3(a) +4 = 3a +4

3(a +4 )= 3a +4

The given equation represents the property of distributivity, where multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the results. In this case, 4 is being multiplied by the sum of 3 and c. The equation shows that multiplying 4 by the sum of 3 and c is equal to multiplying 4 by 3 and then adding the product of 4 and c.

Explanation

The given equation represents the property of distributivity, where multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the results. In this case, 4 is being multiplied by the sum of 3 and c. The equation shows that multiplying 4 by the sum of 3 and c is equal to multiplying 4 by 3 and then adding the product of 4 and c.

16. El triangulo ABC es semejante al triangulo DEF, cuál es el valor de X

2

10

8

12

6

The value of X is 2 because when two triangles are similar, the corresponding sides are proportional. In this case, the corresponding sides of triangle ABC and triangle DEF are in the ratio of 2:10, which simplifies to 1:5. Therefore, the value of X, which represents the ratio between the corresponding sides, is 2.

Explanation

The value of X is 2 because when two triangles are similar, the corresponding sides are proportional. In this case, the corresponding sides of triangle ABC and triangle DEF are in the ratio of 2:10, which simplifies to 1:5. Therefore, the value of X, which represents the ratio between the corresponding sides, is 2.

17. ¿Cuál expresión representa la suma de las partes sombreadas en las dos figuras?

1/2

8/24

12/10

12/24

30/40

not-available-via-ai

Explanation

not-available-via-ai

18. Halla la medida de los tres ángulos del triángulo:

44º, 92º, 92º

15º, 73º, 92º

45º, 45º, 92º

44º, 44º, 92º

45º, 65º, 92º

The given triangle has two angles that are equal to 44º and one angle that is equal to 92º. Therefore, the correct answer is 44º, 44º, 92º.

Explanation

The given triangle has two angles that are equal to 44º and one angle that is equal to 92º. Therefore, the correct answer is 44º, 44º, 92º.

19. La rueda delantera de tu bicicleta tiene un diametro de 26 pulgadas. ¿Cuánto haz recorrido al completar una vuelta? Usa la fórmula C = лd

26 pulgadas

40.84 pulgadas

81.64 pulgadas

163.36 pulgadas

0 pulgadas

The formula C = лd is used to calculate the circumference of a circle, where C is the circumference and d is the diameter. In this case, the diameter of the front wheel is given as 26 inches. By substituting this value into the formula, we can calculate the circumference. Therefore, the correct answer is 81.64 inches, which represents the distance traveled when completing one full rotation of the wheel.

Explanation

The formula C = лd is used to calculate the circumference of a circle, where C is the circumference and d is the diameter. In this case, the diameter of the front wheel is given as 26 inches. By substituting this value into the formula, we can calculate the circumference. Therefore, the correct answer is 81.64 inches, which represents the distance traveled when completing one full rotation of the wheel.

20. Evalúa x²y , para cuando x = 3, y = -2

-18

12

-12

18

20

To evaluate x2y when x = 3 and y = -2, we substitute the given values into the expression.
Replacing x with 3 and y with -2, we get (3)^2 * (-2) = 9 * (-2) = -18.
Therefore, the correct answer is -18.

Explanation

To evaluate x2y when x = 3 and y = -2, we substitute the given values into the expression.
Replacing x with 3 and y with -2, we get (3)^2 * (-2) = 9 * (-2) = -18.
Therefore, the correct answer is -18.

21. Los siguientes cuadrados son semejantes. El cuadrado grande tiene un perímetro de 48 cm y es el doble del perímetro del cuadrado pequeño, ¿cuál es el área del cuadrado pequeño?

576 cm2

144 cm2

36 cm2

24 cm2

48 cm2

The question states that the large square has a perimeter of 48 cm and is double the perimeter of the small square. Since the perimeter is the sum of all sides, we can divide the perimeter of the large square by 4 to find the length of one side, which is 12 cm. Since the large square is double the perimeter of the small square, the small square has a perimeter of 24 cm and each side measures 6 cm. The area of a square is calculated by multiplying the length of one side by itself, so the area of the small square is 6 cm * 6 cm = 36 cm2.

Explanation

The question states that the large square has a perimeter of 48 cm and is double the perimeter of the small square. Since the perimeter is the sum of all sides, we can divide the perimeter of the large square by 4 to find the length of one side, which is 12 cm. Since the large square is double the perimeter of the small square, the small square has a perimeter of 24 cm and each side measures 6 cm. The area of a square is calculated by multiplying the length of one side by itself, so the area of the small square is 6 cm * 6 cm = 36 cm2.

22. La siguiente tabla representa los resultados del torneo intramural de baloncesto de la escuela.

Equipo (Grado)	Juegos Ganados
Cuarto	18
Quinto	15
Sexto	11
Séptimo	16

Cuales son los % de los valores en la grafica comenzando desde cuarto a septimo.

30%, 25%, 18%, 27%

33%, 24%, 17%, 26%

36%, 13%, 20%, 31%

40%, 14%, 30%, 16%

50%, 10%, 20%, 20%

The correct answer is 30%, 25%, 18%, 27%. This can be determined by calculating the percentage of games won for each team in the tournament. The team in fourth place won 18 out of their total games, which is 30% of their games. The team in fifth place won 15 out of their total games, which is 25% of their games. The team in sixth place won 11 out of their total games, which is 18% of their games. The team in seventh place won 16 out of their total games, which is 27% of their games.

Explanation

The correct answer is 30%, 25%, 18%, 27%. This can be determined by calculating the percentage of games won for each team in the tournament. The team in fourth place won 18 out of their total games, which is 30% of their games. The team in fifth place won 15 out of their total games, which is 25% of their games. The team in sixth place won 11 out of their total games, which is 18% of their games. The team in seventh place won 16 out of their total games, which is 27% of their games.

23. La siguiente gráfica muestra los juegos ganados por un equipo de baloncesto durante 4 meses. Determina la media aritmética de los juegos ganados.

36

14

9

8

0

The given data represents the number of games won by a basketball team over a period of 4 months. To find the arithmetic mean, we need to sum up all the values and divide by the total number of values. Adding up the numbers given (36 + 14 + 9 + 8 + 0) gives us a total of 67. Since there are 5 values, we divide 67 by 5 to find the average, which is 13.4. Therefore, the arithmetic mean of the games won is 13.4.

Explanation

The given data represents the number of games won by a basketball team over a period of 4 months. To find the arithmetic mean, we need to sum up all the values and divide by the total number of values. Adding up the numbers given (36 + 14 + 9 + 8 + 0) gives us a total of 67. Since there are 5 values, we divide 67 by 5 to find the average, which is 13.4. Therefore, the arithmetic mean of the games won is 13.4.

24. Resuelve para x: 4x – 12 = 2x + 12

0

4

12

24

8

To solve the equation 4x - 12 = 2x + 12, we need to isolate the variable x. First, we can simplify both sides of the equation by combining like terms. This gives us 2x = 24. Next, we can divide both sides of the equation by 2 to solve for x. This gives us x = 12. Therefore, the correct answer is 12.

Explanation

To solve the equation 4x - 12 = 2x + 12, we need to isolate the variable x. First, we can simplify both sides of the equation by combining like terms. This gives us 2x = 24. Next, we can divide both sides of the equation by 2 to solve for x. This gives us x = 12. Therefore, the correct answer is 12.

25. ¿Cuáles de los siguientes conjuntos de medidas representa las longitudes de los lados de un triángulo rectángulo?

2, 3 y 4

5, 6 y 7

6, 9 y 12

9, 12 y 15

10, 11 y 12

The set of measures 9, 12, and 15 represents the lengths of the sides of a right triangle because it satisfies the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 9^2 + 12^2 = 81 + 144 = 225, which is equal to 15^2. Therefore, these measurements form a right triangle.

Explanation

The set of measures 9, 12, and 15 represents the lengths of the sides of a right triangle because it satisfies the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 9^2 + 12^2 = 81 + 144 = 225, which is equal to 15^2. Therefore, these measurements form a right triangle.

26. La probabilidad de sacar una canica roja de una bolsa es de 1/5: para una canica verde es de 1/10: para una azul es de 3/10 y para una amarilla es de 2/5. ¿Cuál es la probabilidad de sacar, al azar, una canica que sea roja o azúl?

11/20

6/10

4/10

5/10

1/25

The probability of drawing a red marble is 1/5 and the probability of drawing a blue marble is 3/10. To find the probability of drawing either a red or blue marble, we add the probabilities together: 1/5 + 3/10 = 2/10 + 3/10 = 5/10. Therefore, the probability of drawing a red or blue marble is 5/10.

Explanation

The probability of drawing a red marble is 1/5 and the probability of drawing a blue marble is 3/10. To find the probability of drawing either a red or blue marble, we add the probabilities together: 1/5 + 3/10 = 2/10 + 3/10 = 5/10. Therefore, the probability of drawing a red or blue marble is 5/10.

27. ¿Cuál es la probabilidad de seleccionar un doctor entre las edades de 45 a 54 años?

Doctores Hospital San Luis
Edad	Masculino	Femenino
Menos 35 35 – 44 45 – 54 55 – 64	29 36 19 17	18 8 3 2

3%

17%

19%

22%

33%

The correct answer is 17%. This can be determined by calculating the percentage of doctors between the ages of 45 to 54 out of the total number of doctors. In this case, there are 19 doctors between the ages of 45 to 54 out of a total of 112 doctors (29+36+19+17), which gives us a percentage of approximately 17%.

Explanation

The correct answer is 17%. This can be determined by calculating the percentage of doctors between the ages of 45 to 54 out of the total number of doctors. In this case, there are 19 doctors between the ages of 45 to 54 out of a total of 112 doctors (29+36+19+17), which gives us a percentage of approximately 17%.