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Algebra Quiz for 10th Class

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Questions and Answers

What property is used to prove that (-a) b = a (-b) = -ab?

Associative Property of Multiplication
Distributive Property of Multiplication over Subtraction (correct)
Closure Property of Multiplication
Commutative Property of Multiplication

What is the result of multiplying a by (-b)?

a/b
-a/b
-ab (correct)
ab

If a and b are real numbers, what can be concluded about the product (-a) (-b)?

It is equal to ab
It is always positive
It is equal to -ab (correct)
It is always negative

Which of the following is an example of the closure property of multiplication?

All of the above (D) Signup and view all the answers

If a and b are real numbers, what can be concluded about the expression a (-b)?

It is equal to -ab (C) Signup and view all the answers

Which of the following is an example of the associative property of multiplication?

a (bc) = (ab) c (B) Signup and view all the answers

What is the result of multiplying (-a) by b?

-ab (D) Signup and view all the answers

If a, b, c, and d are real numbers, what can be concluded about the expression c (bd)?

It is equal to (cb) d (B) Signup and view all the answers

Which of the following illustrates the closure property of multiplication?

a(bd) = (ab)d (C) Signup and view all the answers

What is the result of (4 % 5) % 8?

0 (D) Signup and view all the answers

Which property is used in the equation -3 < -2 ⇒ 0 < 1?

Transitive Property (B) Signup and view all the answers

Which of the following is a consequence of the multiplicative properties of inequality?

Multiplying both sides of an inequality by a positive number does not change its direction. (A) Signup and view all the answers

What is the distributive property of multiplication over addition?

a(b + c) = ab + ac (B) Signup and view all the answers

Which of the following is an example of a set operation?

a - a = 0 (C) Signup and view all the answers

What is the value of x in the equation x - x = 0?

Any real number (C) Signup and view all the answers

What is the result of 1000 % 1?

1000 (B) Signup and view all the answers

Which of the following is a property of a field?

Completeness axiom (A) Signup and view all the answers

What is the additive inverse of a number a?

-a (B) Signup and view all the answers

Which of the following sets possesses all the properties of a field?

Set of real numbers (B) Signup and view all the answers

What is the result of the set operation a ∪ (b ∩ c)?

a ∩ (b ∪ c) (D) Signup and view all the answers

What is the result of multiplying (a + b)c?

ac + bc (C) Signup and view all the answers

Which of the following is a consequence of the order properties of inequality?

If a > b and b > c, then a > c (D) Signup and view all the answers

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Study Notes

Quadratic Equations and Number Systems

Properties of Real Numbers

Addition and multiplication of real numbers are commutative, associative, and distributive.
Properties of inequality:
If both sides of an inequality are multiplied by a positive number, the direction of the inequality does not change.
If both sides of an inequality are multiplied by a negative number, the direction of the inequality is reversed.

Properties of Multiplication

Distributivity of multiplication over addition: a(b + c) = ab + ac and (a + b)c = ac + bc
Properties of equality of numbers:
a and (-a) are additive inverses of each other.
a(b - c) = ab - ac and (x - y)z = xz - yz

Order Properties

If a > b and c > d, then ac > bd.
If a < b and c < d, then ac < bd.

Properties of Inequality

If both sides of an inequality are multiplied by a positive number, the direction of the inequality does not change.
If both sides of an inequality are multiplied by a negative number, the direction of the inequality is reversed.