Podcast
Questions and Answers
Which of these is a rational number?
Which of these is a rational number?
If a + b + c = 0, then a² + b² + c² = ?
If a + b + c = 0, then a² + b² + c² = ?
If (x + 5) is a factor of x² - 20x + 5k, then k = ?
If (x + 5) is a factor of x² - 20x + 5k, then k = ?
If an angle is 140° more than its complementary angle, then the angle is:
If an angle is 140° more than its complementary angle, then the angle is:
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If x + y = 12 and xy = 32, find the value of x² + y².
If x + y = 12 and xy = 32, find the value of x² + y².
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Which of the following represents a rational number?
Which of the following represents a rational number?
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What is the value of $25 × 5$?
What is the value of $25 × 5$?
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If $a + b + c = 0$, what does $a² + b² + c²$ equal?
If $a + b + c = 0$, what does $a² + b² + c²$ equal?
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What is the remainder when $(x + 5)$ is divided by $(x + 1)$?
What is the remainder when $(x + 5)$ is divided by $(x + 1)$?
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What is the value of $25² - 24²$?
What is the value of $25² - 24²$?
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If $(x + 5)$ is a factor of $x² - 20x + 5k$, what value must $k$ be?
If $(x + 5)$ is a factor of $x² - 20x + 5k$, what value must $k$ be?
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An angle that is 140° more than its complementary angle must be what?
An angle that is 140° more than its complementary angle must be what?
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If quadrilateral ABCD has ∠A = 90° and sides AB = BC = CA = DA, then it is classified as what type of shape?
If quadrilateral ABCD has ∠A = 90° and sides AB = BC = CA = DA, then it is classified as what type of shape?
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Study Notes
Rational Numbers
- A rational number is a number that can be expressed as a fraction.
- Examples of rational numbers: 1/2, 3, 0.5, 2/7
Simplifying Expressions
- Rationalizing the denominator of √2+1 / √2-1 involves multiplying both numerator and denominator by √2+1 resulting in (√2+1)² / (√2)² - 1² = 3 + 2√2
Exponents and Multiplication
- (25) × (5) = 125
- (25) × (24) = 600
Algebraic Identities
- If a + b + c = 0, then a² + b² + c² = 2(ab + ac + bc)
- If 49x² - b = (7x + √b)(7x - √b), then b = 49
- If (x + 5) is a factor of x² - 20x + 5k, then k = -25
Angles and Geometry
- Complementary angles add up to 90 degrees.
- An angle that is 140° more than its complementary angle is 110 degrees.
- If in quadrilateral ABCD, ∠A = 90° and AB = BC = CA = DA, then ABCD is a square.
Polynomials
- The degree of a polynomial is the highest power of the variable in the polynomial.
- The coefficient of x in the polynomial p(x) = x³ + x² + x + 1 is 1.
Finding Values
- If (x - 1) = 8, x = 9.
- The complement of 30 degrees is 60 degrees.
- (2 - √2)(2 + √2) = 4 - 2 = 2, which is a rational number.
- If (3³/2)³/2 = 81, then x = 4.
Factoring Expressions
- x³ + 27 = (x + 3)(x² - 3x + 9)
- x² + 6√x + 27 = (√x + 3)²
- x² + 7x + 12 = (x + 3)(x + 4)
- 7m²n - 7mn = 7mn(m - 1)
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Description
Test your understanding of rational numbers, exponents, and algebraic identities with this quiz. Explore concepts like simplifying expressions, complementary angles, and the properties of polynomials. Perfect for students in 10th grade looking to reinforce their algebra skills.
