Final Exam( Math) G10

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

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.

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Final Exam( Math) G10 - Quiz

This Final Exam for Grade 10 focuses on algebraic concepts including solving equations, understanding inequality symbols, and manipulating algebraic expressions.

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

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.

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

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).

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4) (8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2)

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.

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

Explanation

The correct answer is x

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

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.

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7) The solution of x + 3 < 9    is :

Explanation

The solution to the inequality x + 3

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8) The symbol ≤ is used for :

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.

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

Explanation

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

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

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.

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

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.

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

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.

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13) Determine the solution to the inequality 9x + 6 ≥ 11x

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.

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14) The product of a²b4 and a³b5  is

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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The answer of following (a³b)4  is :
A statement in which sign of equality " = " is used to link two...
What is the correct factorization ...
(8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2)
Determine which inequality matches the statement: A number is less...
By solving the following (5a²b³)², the answer will be :
The solution of x + 3 < 9    is :
The symbol ≤ is used for :
The product of y7 and y³ is equal to :
The solution to the following pair of simultaneous equations is: ...
By solving the (4x)³ , the answer will be : 
The answer of these simultaneous equations is ( 1 , 2 ) ...
Determine the solution to the inequality 9x + 6 ≥ 11x
The product of a²b4 and a³b5  is
The value of 'x' in 6x - 4 = 3x + 8 should be
The value of 'x' in √(x - 1) = 4      should be :
The solution of 4x - 2 > 6    is :
Find the roots: ( x + 6 ) ( x - 3 )
By solving a x (a²)9 , the answer will be :
What is the value of y? ...
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