Pre Semester 2 Math Test For Grade 8( Part One)

1) 7.The number of possible one-one correspondence between set A = { a,b,c,d } and Set B = { 1,2,3,4 } is …

A. 4 x 4

B.44

C. 42

D. 4 x 3 x 2 x 1

The number of possible one-one correspondences between two sets can be calculated using the formula n!, where n is the number of elements in the set. In this case, there are 4 elements in set A and 4 elements in set B. Therefore, the number of possible one-one correspondences is 4 x 3 x 2 x 1.

Explanation

The number of possible one-one correspondences between two sets can be calculated using the formula n!, where n is the number of elements in the set. In this case, there are 4 elements in set A and 4 elements in set B. Therefore, the number of possible one-one correspondences is 4 x 3 x 2 x 1.

2) 1. The sum of (5ab² – 2 a²b + 5ab ) and ( 3a²b – 4ab – 3ab² ) is….

A.2(- a2b + ab2 + ab)

B.2(a2b + ab2 – ab )

C.2a2b + ab2 – ab

D.2a2b + ab2 + ab

The given question asks for the sum of two expressions: (5ab2 – 2a2b + 5ab) and (3a2b – 4ab – 3ab2). To find the sum, we simply add the corresponding terms together. In this case, we have 5ab2 + 3a2b – 2a2b – 4ab + 5ab – 3ab2. Simplifying this expression, we get 2a2b + ab2 + ab, which matches option d. Therefore, the correct answer is d. 2a2b + ab2 + ab.

Explanation

The given question asks for the sum of two expressions: (5ab2 – 2a2b + 5ab) and (3a2b – 4ab – 3ab2). To find the sum, we simply add the corresponding terms together. In this case, we have 5ab2 + 3a2b – 2a2b – 4ab + 5ab – 3ab2. Simplifying this expression, we get 2a2b + ab2 + ab, which matches option d. Therefore, the correct answer is d. 2a2b + ab2 + ab.

3) 4.The product of ( 4x – 5) ( x + 5 ) is …

A.4x2 + 15x – 25

B.4x2 + 15x + 25

C.4x2 - 15x – 25

D.4x2 + 5x – 25

The given expression represents the product of two binomials. To find the product, we can use the distributive property. Multiplying the first terms of each binomial gives 4x * x = 4x^2. Multiplying the outer terms gives 4x * 5 = 20x. Multiplying the inner terms gives -5 * x = -5x. And finally, multiplying the last terms gives -5 * 5 = -25. Combining all these terms, we get the product as 4x^2 + 15x - 25. Therefore, the correct answer is a. 4x^2 + 15x - 25.

Explanation

The given expression represents the product of two binomials. To find the product, we can use the distributive property. Multiplying the first terms of each binomial gives 4x * x = 4x^2. Multiplying the outer terms gives 4x * 5 = 20x. Multiplying the inner terms gives -5 * x = -5x. And finally, multiplying the last terms gives -5 * 5 = -25. Combining all these terms, we get the product as 4x^2 + 15x - 25. Therefore, the correct answer is a. 4x^2 + 15x - 25.

4) 6.If the area of a rectangle is ( 2x² – 5x – 3) cm². and its length is ( 2x + 1 ) cm,so its Width is …..cm.

A. ( x + 3 ) cm

B. ( x – 3 ) cm

C. ( 2x + 3 ) cm

D. ( 2x – 3 ) cm

The area of a rectangle is equal to its length multiplied by its width. In this case, the area is given as (2x^2 - 5x - 3) cm^2 and the length is given as (2x + 1) cm. To find the width, we can divide the area by the length. So, (2x^2 - 5x - 3) cm^2 / (2x + 1) cm = (x - 3) cm. Therefore, the width of the rectangle is (x - 3) cm.

Explanation

The area of a rectangle is equal to its length multiplied by its width. In this case, the area is given as (2x^2 - 5x - 3) cm^2 and the length is given as (2x + 1) cm. To find the width, we can divide the area by the length. So, (2x^2 - 5x - 3) cm^2 / (2x + 1) cm = (x - 3) cm. Therefore, the width of the rectangle is (x - 3) cm.

5) 2. Subtracted of – 4(x² – 5x + 2) from 2(3x² – x + 1 ) is …

A. 10x2 – 22x + 10

B. 10x2 + 23x – 16

C. 2x2 + 18x + 10

D. 2x2 – 18x – 16

The expression can be simplified by distributing the coefficients to each term within the parentheses. After distributing, we can combine like terms by adding or subtracting them. In this case, when we subtract 4(x^2 - 5x + 2) from 2(3x^2 - x + 1), we get 10x^2 - 22x + 10.

Explanation

The expression can be simplified by distributing the coefficients to each term within the parentheses. After distributing, we can combine like terms by adding or subtracting them. In this case, when we subtract 4(x^2 - 5x + 2) from 2(3x^2 - x + 1), we get 10x^2 - 22x + 10.

6) 3.The simplest form of 9 – 3 ( 4m – 1 ) is…

A. – 12m + 12

B. – 24m – 6

C. 24m – 6

D. m

The given expression can be simplified by applying the distributive property. First, distribute the 3 to both terms inside the parentheses: 3 * 4m = 12m and 3 * -1 = -3. Then, subtract the result from 9: 9 - (12m - 3). Simplifying further, we have -12m + 12 as the final answer.

Explanation

The given expression can be simplified by applying the distributive property. First, distribute the 3 to both terms inside the parentheses: 3 * 4m = 12m and 3 * -1 = -3. Then, subtract the result from 9: 9 - (12m - 3). Simplifying further, we have -12m + 12 as the final answer.

7) 5.One of the factors of 18b² – 2 is …

A. 9b – 1

B. 3b + 2

C. 3b – 1

D. 2( b – 2 )

The expression 18b^2 - 2 can be factored as (3b - 1)(6b + 2). Therefore, one of the factors of 18b^2 - 2 is 3b - 1.

Explanation

The expression 18b^2 - 2 can be factored as (3b - 1)(6b + 2). Therefore, one of the factors of 18b^2 - 2 is 3b - 1.

8) 13. Which of the following sets of ordered pairs is a mapping ? It is …

A. { (-1, 6), ( 0,5), ( 1,4 ), (1,3) }

B. { (0, 0), ( 4,2), ( 9,3 ), (9, -3) }

C. { (-2, 2), ( -1,2), ( 0,2 ), (2,2) }

D. { (4, 1), ( 4,2), ( 4,3 ), (4,4) }

A mapping is a relation between two sets where each element in the first set is paired with exactly one element in the second set. In option c, each element in the first set (-2, -1, 0, 2) is paired with the element 2 in the second set. Therefore, option c is a mapping. In the other options, there are elements in the first set that are paired with multiple elements in the second set, which violates the definition of a mapping.

Explanation

A mapping is a relation between two sets where each element in the first set is paired with exactly one element in the second set. In option c, each element in the first set (-2, -1, 0, 2) is paired with the element 2 in the second set. Therefore, option c is a mapping. In the other options, there are elements in the first set that are paired with multiple elements in the second set, which violates the definition of a mapping.

9) 14.Let P = { 1,2,3,4 } and g is rule of the mapping of P into Q ,n is member of P such that (i) if n is odd ,then n will be 1 (ii) if n is even ,then n will be 0.5 n The range of this mapping is…

A. { 1, 2, 3 }

B. { 1, 3, 5 }

C. { 2, 3, 5 }

D. { 2, 4, 6 }

The mapping rule states that if a number in set P is odd, it will be mapped to 1, and if it is even, it will be mapped to 0.5 times the number. The set P consists of the numbers 1, 2, 3, and 4. Applying the mapping rule, the odd numbers in P (1 and 3) will be mapped to 1, and the even numbers (2 and 4) will be mapped to 1 and 2 respectively. Therefore, the range of this mapping is { 1, 2, 3 }.

Explanation

The mapping rule states that if a number in set P is odd, it will be mapped to 1, and if it is even, it will be mapped to 0.5 times the number. The set P consists of the numbers 1, 2, 3, and 4. Applying the mapping rule, the odd numbers in P (1 and 3) will be mapped to 1, and the even numbers (2 and 4) will be mapped to 1 and 2 respectively. Therefore, the range of this mapping is { 1, 2, 3 }.