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Basic Algebra Foundations

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Basic Algebra Foundations

Show working where space is provided. Simplify expressions by combining like terms, and check equations by substituting your answer.

Algebraic language

Identify key parts of expressions and connect algebra vocabulary to its meaning.

1.Match each algebra word to the best description.
  • Variable
  • Coefficient
  • Constant
  • Expression
  • Term
  • Equation
  • One part of an expression separated from other parts by + or −
  • The numerical factor multiplying a variable
  • A mathematical combination of numbers, variables and operations, without an equals sign
  • A mathematical statement showing that two expressions have equal value
  • A number in an expression that has no variable attached
  • A letter standing for a number that can vary or is not yet known
2.For the expression 7m − 4, state the variable, coefficient and constant.

Simplifying expressions

Combine like terms and recognise expressions that are already in simplest form.

3.Simplify 6p + 2p.
4.Simplify 5q + 3 + 4q.
5.Simplify 8r − 2 + 3r + 7.
6.Which expressions are already simplified? Select every correct option.
  • 4a + 9
  • 6b + 2b
  • 3c − 5 + c
  • 12 − 2d
  • 7e + 1 + 4

Substitution and everyday algebra

Replace variables with given values, then apply an expression to a practical situation.

7.Evaluate 4x + 3 when x = 5.
8.Evaluate 3y − 8 when y = 7.
9.Find the value of 5k + 2 when k = 4.
  • 22
  • 18
  • 26
  • 14
10.A community pool charges a $9 entry fee plus $4 for each hour of lane hire. Write an expression for the total cost in dollars for h hours, then calculate the cost for 3 hours.

Solving equations

Use inverse operations to find unknown values, then check a solution and model a word problem.

11.Solve n + 8 = 19.
12.Solve t − 6 = 17.
13.Solve w + 12 = 31.
14.Is a = 9 a solution to a + 7 = 16?
  • Yes, because 9 + 7 = 16.
  • No, because 9 + 7 = 15.
  • No, because 9 + 7 = 17.
  • Yes, because 9 − 7 = 16.
15.Finn has some marbles. After she gives 8 away, she has 17 left. Write an equation for the starting amount m and solve it.

3 printable pages

  • Basic Algebra Foundations, page 1 of 3: Algebraic language

    Page 1

  • Basic Algebra Foundations, page 2 of 3: Simplifying expressions, Substitution and everyday algebra

    Page 2

  • Basic Algebra Foundations, page 3 of 3: Solving equations

    Page 3

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