Podcast
Questions and Answers
Which of these is a rational number?
Which of these is a rational number?
- √21 / √3
- √3 + √4
- 1 + √3 / √3 (correct)
- √1
If a + b + c = 0, then a² + b² + c² = ?
If a + b + c = 0, then a² + b² + c² = ?
- -2ab - 2bc - 2ca (correct)
- 0
- a² + b² + c²
- 3abc
If (x + 5) is a factor of x² - 20x + 5k, then k = ?
If (x + 5) is a factor of x² - 20x + 5k, then k = ?
- 100
- 25
- 0
- -25 (correct)
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:
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.
Which of the following represents a rational number?
Which of the following represents a rational number?
What is the value of $25 × 5$?
What is the value of $25 × 5$?
If $a + b + c = 0$, what does $a² + b² + c²$ equal?
If $a + b + c = 0$, what does $a² + b² + c²$ equal?
What is the remainder when $(x + 5)$ is divided by $(x + 1)$?
What is the remainder when $(x + 5)$ is divided by $(x + 1)$?
What is the value of $25² - 24²$?
What is the value of $25² - 24²$?
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?
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?
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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