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)

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 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 Signup and view all the answers

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

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

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

-ab 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 Signup and view all the answers

Which of the following illustrates the closure property of multiplication?

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

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

0 Signup and view all the answers

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

Transitive Property 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. Signup and view all the answers

What is the distributive property of multiplication over addition?

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

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

a - a = 0 Signup and view all the answers

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

Any real number Signup and view all the answers

What is the result of 1000 % 1?

1000 Signup and view all the answers

Which of the following is a property of a field?

Completeness axiom Signup and view all the answers

What is the additive inverse of a number a?

-a Signup and view all the answers

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

Set of real numbers Signup and view all the answers

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

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

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

ac + bc 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 Signup and view all the answers

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.

Examples and Applications

(-a)b = a(-b) = -ab
(-a)(-b) = ab
a(b + c - d) = ab + ac - ad
1000 % 1 = 1000
4.1 + (-4.1) = 0
a - a = 0
a(b - c) = ab - ac and (x - y)z = xz - yz

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Test your understanding of algebra concepts, including quadratic equations, number systems, and multiplication addition law.