Algebra Class Overview

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which method is used to combine terms that have the same variable and exponent in algebra?

  • Substituting
  • Collecting like terms (correct)
  • Solving
  • Expanding

What is the solution for $2x + 3 = 7 - x$?

  • x = 1
  • x = 3
  • x = 2 (correct)
  • x = 0

When graphing a linear inequality, which part of the inequality is represented by a dashed line?

  • Less than (correct)
  • Greater than or equal to
  • Less than or equal to
  • Greater than

Which technique would you use to solve $x^2 + 5x + 6 = 0$?

<p>Factoring (B)</p> Signup and view all the answers

Which equation represents a system of simultaneous equations with one linear and one quadratic?

<p>$y = 2x + 3$ and $y = x^2 - 4$ (B)</p> Signup and view all the answers

How would you go about factorising the quadratic expression $x^2 + 7x + 10$?

<p>To factorise it, look for two numbers that multiply to 10 and add to 7, which are 2 and 5. Thus, it can be expressed as $(x + 2)(x + 5)$.</p> Signup and view all the answers

What is the significance of collecting like terms in algebraic expressions?

<p>Collecting like terms simplifies expressions by consolidating similar variables and their coefficients. This makes equations easier to manipulate and solve.</p> Signup and view all the answers

Describe how to interpret the solution of the inequality $3x - 4 > 2$ on a number line.

<p>First, solve for $x$ to get $x &gt; 2$. On the number line, represent this with an open circle at 2 and shade the region to the right.</p> Signup and view all the answers

When faced with the simultaneous equations $2x + y = 10$ and $x - y = 2$, what method can be used to find the solution?

<p>You can use the substitution method or elimination method to solve for $x$ and $y$. For instance, rearranging the second equation to $y = x - 2$ and substituting it into the first.</p> Signup and view all the answers

Explain how you would solve the equation $5(x - 3) = 2(x + 4)$ and show the steps involved.

<p>First, expand both sides to get $5x - 15 = 2x + 8$. Then, rearrange the equation to isolate $x$, leading to $3x = 23$, thus $x = rac{23}{3}$.</p> Signup and view all the answers

Flashcards

Evaluating algebraic expressions

Substituting numbers for letters in an expression to find its value.

Solving linear equations

Finding the value of an unknown variable in an equation.

Simplifying algebraic expressions

Combining 'like terms' to make an expression shorter and clearer.

Solving simultaneous equations

Finding the values of two unknowns using two equations.

Signup and view all the flashcards

Factorising quadratic expressions (a=1)

Writing a quadratic expression as the product of two linear factors.

Signup and view all the flashcards

Expand

To multiply out brackets and simplify a mathematical expression.

Signup and view all the flashcards

Factorise

To rewrite an expression as a product of its factors.

Signup and view all the flashcards

Like terms

Terms with the same variable(s) raised to the same power. They can be added or subtracted.

Signup and view all the flashcards

Multiply a single term over a bracket

To distribute the single term to each term inside the bracket by multiplying.

Signup and view all the flashcards

Factorise into a single bracket

To rewrite an expression as a product of a single term and a bracket.

Signup and view all the flashcards

Study Notes

Algebraic Expressions

  • Evaluating expressions by substituting numerical values for letters
  • Understanding mathematical terms: simplify, expand, factorise, base, index, and power
  • Collecting like terms
  • Multiplying a single term over a bracket
  • Factorising into a single bracket
  • Expanding the product of two linear expressions
  • Rearranging formulas

Linear Equations

  • Solving equations with unknowns on both sides and with brackets
  • Solving equations with fractions
  • Solving word problems using algebra

Inequalities

  • Understanding how inequalities are represented on a number line
  • Solving linear and quadratic inequalities
  • Representing solutions on a number line

Quadratic Equations

  • Factorising and solving quadratic expressions where a=1
  • Factorising and solving quadratic equations where a > 1
  • Solving quadratic equations using the formula
  • Solving problems by forming and solving quadratic equations

Simultaneous Equations

  • Solving linear simultaneous equations
  • Solving problems by formulating and solving simultaneous equations
  • Solving simultaneous equations where one is linear and the other is quadratic

Algebraic Fractions

  • Simplifying algebraic fractions by addition/subtraction
  • Multiplying/dividing algebraic fractions
  • Factorising numerators/denominators and cancelling algebraic fractions (including quadratic expressions)

Graphs

  • Plotting linear graphs (recap) and recognising key properties of straight lines

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser