Podcast
Questions and Answers
What is the result of expanding 3(x - 4)?
What is the result of expanding 3(x - 4)?
- x - 12
- 3x + 12
- x + 12
- 3x - 12 (correct)
What is the highest common factor (HCF) of 3780 and 3240 expressed as a product of prime factors?
What is the highest common factor (HCF) of 3780 and 3240 expressed as a product of prime factors?
2^2 × 3^3 × 5 × 7
The factorization of y^3 - 4y results in (y - 2)(y^2 + 2y).
The factorization of y^3 - 4y results in (y - 2)(y^2 + 2y).
False (B)
What is the lowest common multiple (LCM) of 3780 and 3240 expressed as a product of prime factors?
What is the lowest common multiple (LCM) of 3780 and 3240 expressed as a product of prime factors?
Simplify 8e + 2f - 11e + 3f.
Simplify 8e + 2f - 11e + 3f.
The area of the floor of the room is 12 m². Change 12 m² into ______ cm².
The area of the floor of the room is 12 m². Change 12 m² into ______ cm².
The factors of 9 are ______.
The factors of 9 are ______.
What is the lowest common multiple (LCM) of 15 and 70?
What is the lowest common multiple (LCM) of 15 and 70?
Match the following expressions to their simplifications:
Match the following expressions to their simplifications:
The mean of a set of numbers is always greater than the median.
The mean of a set of numbers is always greater than the median.
What is the factorization of t² - 10t?
What is the factorization of t² - 10t?
4500 grams is equivalent to 4.5 kilograms.
4500 grams is equivalent to 4.5 kilograms.
If a pie chart indicates that 16 buses went past a school, how many bicycles went past if 50 vehicles went by in total?
If a pie chart indicates that 16 buses went past a school, how many bicycles went past if 50 vehicles went by in total?
How much fruit juice does Lauren have left after making as many cups of drinks as possible, if each cup contains 225 millilitres?
How much fruit juice does Lauren have left after making as many cups of drinks as possible, if each cup contains 225 millilitres?
What is the mean number of matches if Becky counted 50 boxes with a total of 300 matches?
What is the mean number of matches if Becky counted 50 boxes with a total of 300 matches?
Match the following quantities with their respective calculations:
Match the following quantities with their respective calculations:
What is the simplified form of $g^6 \times g^4$?
What is the simplified form of $g^6 \times g^4$?
The expression $k^4 \div k^2$ simplifies to $k^2$.
The expression $k^4 \div k^2$ simplifies to $k^2$.
What is the simplified form of $(3cd)$?
What is the simplified form of $(3cd)$?
The area of a rectangle with length 9 cm and width 4 cm is __________ cm².
The area of a rectangle with length 9 cm and width 4 cm is __________ cm².
To find the area of a trapezium, which formula is commonly used?
To find the area of a trapezium, which formula is commonly used?
Match the following shapes with their properties:
Match the following shapes with their properties:
Calculate the value of $2^3 \times 4^5$.
Calculate the value of $2^3 \times 4^5$.
The simplified form of $3e + 2f - e + 5f$ is $2e + 7f$.
The simplified form of $3e + 2f - e + 5f$ is $2e + 7f$.
The simplified form of $8d \times 7d$ is __________.
The simplified form of $8d \times 7d$ is __________.
Flashcards
Simplifying exponents with the same base
Simplifying exponents with the same base
To simplify an expression with exponents that have the same base, add the powers together.
Simplifying exponents with the same base divided by each other
Simplifying exponents with the same base divided by each other
To simplify an expression with exponents where the base is divided by itself, subtract the power of the denominator from the power of the numerator.
Combining like terms
Combining like terms
To simplify an algebraic expression with terms that have the same variable, add or subtract the coefficients.
Multiplying terms with variables
Multiplying terms with variables
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Area of a Trapezium
Area of a Trapezium
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Area of a Rectangle
Area of a Rectangle
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Area of a Triangle
Area of a Triangle
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Cube Root
Cube Root
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Expanding brackets
Expanding brackets
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Factorising an expression
Factorising an expression
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Simplifying an expression
Simplifying an expression
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Converting square metres to square centimetres
Converting square metres to square centimetres
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Converting metres to centimetres
Converting metres to centimetres
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Converting grams to kilograms
Converting grams to kilograms
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Simplifying exponents when dividing with the same base
Simplifying exponents when dividing with the same base
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What is the HCF?
What is the HCF?
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What is the LCM?
What is the LCM?
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How to find the mean of a set of numbers?
How to find the mean of a set of numbers?
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What is a pie chart?
What is a pie chart?
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How is the volume of a cuboid calculated?
How is the volume of a cuboid calculated?
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What are the factors of a number?
What are the factors of a number?
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What is a multiple of a number?
What is a multiple of a number?
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What is the LCM of two numbers?
What is the LCM of two numbers?
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Study Notes
Simplifying Expressions
- Combining like terms: Combine terms with the same variables and exponents.
- Multiplication: Multiply coefficients and add exponents for the same variable.
- Division: Divide coefficients and subtract exponents for the same variable.
- Powers: Raise a term to a power by multiplying the exponents of each variable.
- Parentheses: Simplify within parentheses before applying other rules.
Simplifying Algebraic Fractions
- Cancel common factors: Reduce fractions by canceling common factors in the numerator and denominator.
Area of a Trapezium
- Formula: Area = 1/2 * (sum of parallel sides) * height
- Units: Area is typically expressed in square units (e.g., cm²).
Area of a Rectangle
- Formula: Area = length x width
- Units: Area is typically expressed in square units (e.g., cm²).
Area of a Triangle
- Formula: Area = 1/2 * base * height
- Right-angled triangles: Use the sides adjacent to the right angle as base and height.
- Units: Area is typically expressed in square units (e.g., cm²).
Volume of a Cuboid
- Formula: Volume = length * width * height
- Units: Volume is typically expressed in cubic units (e.g., cm³).
Highest Common Factor (HCF)
- Prime Factorisation: Express each number as a product of its prime factors.
- Common Factors: Identify prime factors that are present in both numbers.
- Product: Multiply these common prime factors to find the HCF.
Lowest Common Multiple (LCM)
- Prime Factorisation: Express each number as a product of prime factors.
- Highest Powers: Identify the highest power of each prime factor present in either numbers.
- Product: Multiply these highest-power factors to find the LCM.
Finding Factors
- List all the numbers that divide into a given number without leaving a remainder.
Mean
- Sum all values: Total all the quantities.
- Count the number: Calculate the total count of the sample.
- Divide: Divide the sum by the count.
Converting Units
- Metric Conversions: Apply appropriate conversion factors (e.g., 1 m = 100 cm, 1 kg = 1000 g).
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