Simplifying Expressions and Number Operations

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Questions and Answers

Simplify the expression: $3x + 5y - 2x + y$

$5x + 6y$
$5x + 4y$
$x + 5y$
$x + 6y$ (correct)

Expand and simplify the expression: $2(a + 3) - (a - 1)$

$a + 7$ (correct)
$3a + 5$
$3a + 7$
$a + 5$

What is the 7th term in the sequence defined by the nth term formula: $3n - 2$?

20
23
19 (correct)
16

Calculate: $\frac{2}{5} + \frac{1}{3}$

<p>$\frac{11}{15}$ (A)</p> Signup and view all the answers

A bag contains 3 red balls and 5 blue balls. What is the probability of picking a red ball at random?

<p>$\frac{3}{8}$ (D)</p> Signup and view all the answers

Flashcards

Combining Like Terms

Terms with the same variable part can be combined to simplify expressions.

Expanding Brackets

The process of multiplying out a bracket using the distributive property. Each term inside the bracket is multiplied by the term outside.

Substitution

Replacing variables (letters) in an expression with their given numerical values and then calculating the result.

Adding/Subtracting Fractions

Fractions require a common denominator before they can be added or subtracted. Convert to equivalent fractions first.

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Venn Diagrams (Probability)

A diagram that uses overlapping circles to visually represent sets and their relationships, including probabilities.

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Study Notes

Combining like terms simplifies expressions
Terms can be multiplied and divided
Expanding and simplifying brackets involves the distributive property
Factorising expressions is the reverse of expanding brackets
Substitution replaces variables with numbers
Sequences follow a pattern to find the nth term
Fractions can be added and subtracted
Multiplying and dividing fractions requires specific steps
Fractions, decimals, and percentages are interchangeable
Probability quantifies the likelihood of events
Venn diagrams visually represent sets and probabilities
2D and 3D shapes have different properties and angles
Similar shapes have proportional sides and angles
Angle rules govern relationships between angles
Polygon angles have specific properties
Percentages represent proportions of a whole
Negative numbers can be used in all four operations
Decimal numbers can be used in all four operations

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Description

This lesson covers simplifying expressions by combining like terms, expanding and factorising brackets, and substitution. It also explores sequences, fractions, decimals, percentages, probability, and geometric shapes. The lesson includes operations with negative and decimal numbers.