Final Exam( Math) G10

1. The answer of following (a³b)⁴ is :

A14 b5

A8 b4

A12 b4

A10 b³

The given expression (a³b)⁴ can be simplified by raising each term inside the parentheses to the power of 4. This means that a³ is raised to the power of 4, which gives us a^12, and b is raised to the power of 4, which gives us b^4. Therefore, the simplified expression is a^12 b^4, which matches the given answer a12 b4.

Explanation

The given expression (a³b)⁴ can be simplified by raising each term inside the parentheses to the power of 4. This means that a³ is raised to the power of 4, which gives us a^12, and b is raised to the power of 4, which gives us b^4. Therefore, the simplified expression is a^12 b^4, which matches the given answer a12 b4.

2. A statement in which sign of equality " = " is used to link two algebraic expressions is called

Formula

Equation

Fraction

Matrix

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An equation is a statement in which the sign of equality "=" is used to link two algebraic expressions. In an equation, the expressions on both sides are equal to each other. This allows us to solve for unknown variables by finding values that satisfy the equation. Formulas, fractions, and matrices are not necessarily statements of equality and do not involve the use of the "=" sign in the same way as an equation.

Explanation

An equation is a statement in which the sign of equality "=" is used to link two algebraic expressions. In an equation, the expressions on both sides are equal to each other. This allows us to solve for unknown variables by finding values that satisfy the equation. Formulas, fractions, and matrices are not necessarily statements of equality and do not involve the use of the "=" sign in the same way as an equation.

3. What is the correct factorization of x²+ 13 x + 40

( x -8) ( x -5 )

( x + 5 ) ( x + 8 )

The correct factorization of x^2 + 13x + 40 is (x + 5)(x + 8). This can be determined by finding two numbers that multiply to give 40 and add up to 13, which are 5 and 8. Therefore, the factors are (x + 5) and (x + 8).

Explanation

The correct factorization of x^2 + 13x + 40 is (x + 5)(x + 8). This can be determined by finding two numbers that multiply to give 40 and add up to 13, which are 5 and 8. Therefore, the factors are (x + 5) and (x + 8).

4. Determine which inequality matches the statement: A number is less than 4 :

X ≤ 4

X < 4

X > 4

X ≥ 4

The correct answer is x

Explanation

The correct answer is x

5. The solution of x + 3 < 9 is :

X > 4

X < 6

X < 5

X = 6

The solution to the inequality x + 3

Explanation

The solution to the inequality x + 3

6. (8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2)

True

False

The given statement (8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2) is true. This is because according to the order of operations, division should be performed from left to right. Therefore, first we divide 8 by 4 to get 2, and then we divide 2 by 2 to get 1 on both sides of the equation. Hence, both sides of the equation are equal, making the statement true.

Explanation

The given statement (8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2) is true. This is because according to the order of operations, division should be performed from left to right. Therefore, first we divide 8 by 4 to get 2, and then we divide 2 by 2 to get 1 on both sides of the equation. Hence, both sides of the equation are equal, making the statement true.

7. By solving the following (5a²b³)², the answer will be :

25a5 b6

25a4 b6

25a7 b5

25a³b4

The expression (5a²b³)² can be simplified by multiplying the exponents inside the parentheses by the exponent outside the parentheses. Therefore, (5a²b³)² becomes 5²a²(2)(b³)(2), which simplifies to 25a⁴b⁶.

Explanation

The expression (5a²b³)² can be simplified by multiplying the exponents inside the parentheses by the exponent outside the parentheses. Therefore, (5a²b³)² becomes 5²a²(2)(b³)(2), which simplifies to 25a⁴b⁶.

8. The symbol ≤ is used for :

Less than

Greater than

Less than and equal to

Greater than and equal to

The symbol ≤ is used to represent "less than or equal to". It indicates that the value on the left side of the symbol is either less than or equal to the value on the right side.

Explanation

The symbol ≤ is used to represent "less than or equal to". It indicates that the value on the left side of the symbol is either less than or equal to the value on the right side.

9. The product of y⁷ and y³ is equal to :

Y10

Y21

Y4

Y²

The product of y7 and y³ can be found by adding the exponents of y, which gives us y10.

Explanation

The product of y7 and y³ can be found by adding the exponents of y, which gives us y10.

10. The solution to the following pair of simultaneous equations is: 9 x - 4 y = -14 4 x - 9 y = 1

(2, 8)

(-2, -1)

(2, 1)

(1, 2)

The correct answer is (-2, -1) because when we substitute x = -2 and y = -1 into both equations, we get 9(-2) - 4(-1) = -14 and 4(-2) - 9(-1) = 1, which satisfies both equations. Therefore, (-2, -1) is the solution to the pair of simultaneous equations.

Explanation

The correct answer is (-2, -1) because when we substitute x = -2 and y = -1 into both equations, we get 9(-2) - 4(-1) = -14 and 4(-2) - 9(-1) = 1, which satisfies both equations. Therefore, (-2, -1) is the solution to the pair of simultaneous equations.

11. By solving the (4x)³ , the answer will be :

84x²

64x²

64x4

64x³

When solving (4x)³, we need to cube the expression 4x. To do this, we raise both the coefficient and the variable to the power of 3. The coefficient, 4, cubed is 64, and the variable, x, cubed is x³. Therefore, the answer is 64x³.

Explanation

When solving (4x)³, we need to cube the expression 4x. To do this, we raise both the coefficient and the variable to the power of 3. The coefficient, 4, cubed is 64, and the variable, x, cubed is x³. Therefore, the answer is 64x³.

12. Determine the solution to the inequality 9x + 6 ≥ 11x

X < 3

X > 3

X ≤ 3

X ≥ 3

The correct answer is x ≤ 3. To determine the solution to the inequality, we need to isolate the variable x. We can do this by subtracting 9x from both sides of the inequality, which gives us 6 ≤ 2x. Then, we divide both sides by 2 to solve for x, resulting in 3 ≤ x. However, since the question asks for the solution in terms of x, we reverse the inequality sign to get x ≤ 3.

Explanation

The correct answer is x ≤ 3. To determine the solution to the inequality, we need to isolate the variable x. We can do this by subtracting 9x from both sides of the inequality, which gives us 6 ≤ 2x. Then, we divide both sides by 2 to solve for x, resulting in 3 ≤ x. However, since the question asks for the solution in terms of x, we reverse the inequality sign to get x ≤ 3.

13. The answer of these simultaneous equations is ( 1 , 2 )

True

False

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The answer is true because when we substitute x = 1 and y = 2 into both equations, we get a true statement. This means that the values (1, 2) satisfy both equations simultaneously, making it the correct answer.

Explanation

The answer is true because when we substitute x = 1 and y = 2 into both equations, we get a true statement. This means that the values (1, 2) satisfy both equations simultaneously, making it the correct answer.

14. The product of a²b⁴ and a³b⁵ is

A10 b20

A5 b9

A4 b6

A6 b7

The product of a²b4 and a³b5 can be found by multiplying the coefficients of a and b separately. The coefficient of a is a raised to the power of 2 in the first term and raised to the power of 3 in the second term, so the product of the coefficients of a is a raised to the power of 2+3, which is a raised to the power of 5. Similarly, the coefficient of b is b raised to the power of 4 in the first term and raised to the power of 5 in the second term, so the product of the coefficients of b is b raised to the power of 4+5, which is b raised to the power of 9. Therefore, the product of a²b4 and a³b5 is a5 b9.

Explanation

The product of a²b4 and a³b5 can be found by multiplying the coefficients of a and b separately. The coefficient of a is a raised to the power of 2 in the first term and raised to the power of 3 in the second term, so the product of the coefficients of a is a raised to the power of 2+3, which is a raised to the power of 5. Similarly, the coefficient of b is b raised to the power of 4 in the first term and raised to the power of 5 in the second term, so the product of the coefficients of b is b raised to the power of 4+5, which is b raised to the power of 9. Therefore, the product of a²b4 and a³b5 is a5 b9.

15. The value of 'x' in 6x - 4 = 3x + 8 should be

3

6

5

4

To find the value of 'x' in the equation 6x - 4 = 3x + 8, we need to isolate the variable on one side of the equation. By subtracting 3x from both sides, we get 3x - 4 = 8. Then, by adding 4 to both sides, we get 3x = 12. Finally, dividing both sides by 3, we find that x = 4.

Explanation

To find the value of 'x' in the equation 6x - 4 = 3x + 8, we need to isolate the variable on one side of the equation. By subtracting 3x from both sides, we get 3x - 4 = 8. Then, by adding 4 to both sides, we get 3x = 12. Finally, dividing both sides by 3, we find that x = 4.

16. The value of 'x' in √(x - 1) = 4 should be :

23

17

19

20

The correct answer is 17 because when we substitute x=17 into the equation √(x-1) = 4, we get √(17-1) = 4, which simplifies to √16 = 4. Since the square root of 16 is indeed 4, the value of x=17 satisfies the equation and is therefore the correct answer.

Explanation

The correct answer is 17 because when we substitute x=17 into the equation √(x-1) = 4, we get √(17-1) = 4, which simplifies to √16 = 4. Since the square root of 16 is indeed 4, the value of x=17 satisfies the equation and is therefore the correct answer.

17. The solution of 4x - 2 > 6 is :

X > 2

X < 2

X = 4

X > 4

The given inequality is 4x - 2 > 6. To solve this inequality, we need to isolate the variable x. First, we add 2 to both sides of the inequality to get 4x > 8. Then, we divide both sides by 4 to get x > 2. Therefore, the solution to the inequality is x > 2.

Explanation

The given inequality is 4x - 2 > 6. To solve this inequality, we need to isolate the variable x. First, we add 2 to both sides of the inequality to get 4x > 8. Then, we divide both sides by 4 to get x > 2. Therefore, the solution to the inequality is x > 2.

18. Find the roots: ( x + 6 ) ( x - 3 )

3 , -6

-3 , 6

The given expression is a quadratic equation in the form of (x + 6)(x - 3). To find the roots of this equation, we set it equal to zero and solve for x. By using the zero product property, we can determine that the roots are x = -6 and x = 3. Therefore, the correct answer is 3, -6.

Explanation

The given expression is a quadratic equation in the form of (x + 6)(x - 3). To find the roots of this equation, we set it equal to zero and solve for x. By using the zero product property, we can determine that the roots are x = -6 and x = 3. Therefore, the correct answer is 3, -6.

19. By solving a x (a²)⁹ , the answer will be :

A15

A19

A18

A20

By solving a x (a²)9, we can simplify the expression to a x a^18. This is because when we raise a number to a power, we multiply the base number by itself the number of times indicated by the exponent. In this case, we have a² raised to the power of 9, which means we multiply a by itself 9 times. Therefore, the correct answer is a^18, which is equivalent to a19.

Explanation

By solving a x (a²)9, we can simplify the expression to a x a^18. This is because when we raise a number to a power, we multiply the base number by itself the number of times indicated by the exponent. In this case, we have a² raised to the power of 9, which means we multiply a by itself 9 times. Therefore, the correct answer is a^18, which is equivalent to a19.

20. What is the value of y? 2(y + 5) = 3(y - 8)

-34

-14

34

14

To find the value of y, we need to solve the equation. First, we distribute the 2 and 3 to the terms inside the parentheses, giving us 2y + 10 = 3y - 24. Next, we can subtract 2y from both sides to isolate the y term, resulting in 10 = y - 24. To solve for y, we add 24 to both sides, giving us 34 = y. Therefore, the value of y is 34.

Explanation

To find the value of y, we need to solve the equation. First, we distribute the 2 and 3 to the terms inside the parentheses, giving us 2y + 10 = 3y - 24. Next, we can subtract 2y from both sides to isolate the y term, resulting in 10 = y - 24. To solve for y, we add 24 to both sides, giving us 34 = y. Therefore, the value of y is 34.