Algebra Class: Simplifying Expressions and Areas

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Questions and Answers

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?

2^2 × 3^3 × 5 × 7

The factorization of y^3 - 4y results in (y - 2)(y^2 + 2y).

False

What is the lowest common multiple (LCM) of 3780 and 3240 expressed as a product of prime factors?

2^3 × 3^3 × 5 × 7 × 13 Signup and view all the answers

Simplify 8e + 2f - 11e + 3f.

-3e + 5f Signup and view all the answers

The area of the floor of the room is 12 m². Change 12 m² into ______ cm².

120000 Signup and view all the answers

The factors of 9 are ______.

1, 3, 9 Signup and view all the answers

What is the lowest common multiple (LCM) of 15 and 70?

210 Signup and view all the answers

Match the following expressions to their simplifications:

a × 5 × b × c = 5abc q^5 + q^5 + q^5 = 3q^5 7m + 6n - 2m - 9n = 5m - 3n Signup and view all the answers

The mean of a set of numbers is always greater than the median.

False Signup and view all the answers

What is the factorization of t² - 10t?

t(t - 10) Signup and view all the answers

4500 grams is equivalent to 4.5 kilograms.

True Signup and view all the answers

If a pie chart indicates that 16 buses went past a school, how many bicycles went past if 50 vehicles went by in total?

34 bicycles Signup and view all the answers

How much fruit juice does Lauren have left after making as many cups of drinks as possible, if each cup contains 225 millilitres?

75 Signup and view all the answers

What is the mean number of matches if Becky counted 50 boxes with a total of 300 matches?

10 Signup and view all the answers

Match the following quantities with their respective calculations:

Volume of the cuboid = 806 cm³ Mean number of matches = Total matches ÷ Number of boxes Factors of 9 = 1, 3, 9 Highest common factor of 3780 and 3240 = Product of prime factors Signup and view all the answers

What is the simplified form of $g^6 \times g^4$?

$g^{10}$ Signup and view all the answers

The expression $k^4 \div k^2$ simplifies to $k^2$.

True Signup and view all the answers

What is the simplified form of $(3cd)$?

3cd Signup and view all the answers

The area of a rectangle with length 9 cm and width 4 cm is __________ cm².

36 Signup and view all the answers

To find the area of a trapezium, which formula is commonly used?

$\frac{1}{2} \times (b_1 + b_2) \times h$ Signup and view all the answers

Match the following shapes with their properties:

Trapezium = Has one pair of parallel sides Rectangle = All angles are right angles Triangle = Has three sides Circle = Has no corners or edges Signup and view all the answers

Calculate the value of $2^3 \times 4^5$.

2048 Signup and view all the answers

The simplified form of $3e + 2f - e + 5f$ is $2e + 7f$.

False Signup and view all the answers

The simplified form of $8d \times 7d$ is __________.

$56d^2$ Signup and view all the answers

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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Description

This quiz covers essential concepts in algebra, including simplifying expressions and understanding the area formulas for trapeziums, rectangles, and triangles. Test your knowledge on combining like terms, multiplication, division, and proper unit measures for area calculations. Perfect for students looking to strengthen their algebra skills.