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Advanced Algebra Foundations

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Advanced Algebra Foundations

Show clear working for calculation questions. Simplify answers where possible.

Algebraic language

1.Match each algebra term to its definition.

Variable
Coefficient
Constant
Expression
Equation
Like terms

The numerical factor multiplying a variable
A combination of terms and operations, without an equals sign
A term with no variable
A letter or symbol whose value can vary
A statement that two expressions have equal value
Terms with the same variable part and powers

2.In the expression 8p − 3q + 11, identify all variables.

3.In −6m² + 4m − 9, what is the coefficient of m²?

4.Which statement about 5a + 2 is correct?

It is an equation because it contains a variable.
It is an expression with coefficient 5 and constant 2.
It is an expression with coefficient 2 and constant 5.
It has no variable.

Simplifying and expanding

5.Simplify 9x − 4x + 6x.

6.Simplify 6y + 8 − 3y − 12.

7.Simplify 5r − 2s + 7r + 6s − 3.

8.Expand 7(x − 4).

9.Expand and simplify 3(2t + 5) − 4t.

10.Expand −2(3n − 8).

Substitution

11.Evaluate 4x − 9 when x = 4.

12.Evaluate 3y² + 2 when y = −3.

13.Find 2a − 3b + 5 when a = −2 and b = 4.

14.A rectangle has length (2w + 3) cm and width (w − 2) cm. Calculate its perimeter when w = 6.

Solving linear equations

15.Solve x − 9 = 14.

16.Solve 5y = −35.

17.Solve 3x + 8 = 29.

18.Solve 6z − 5 = 31.

19.Substitute your solution into the equation above to verify it. State the value of each side.

Writing and using algebra

20.Georgia has n stickers. Her cousin has four fewer than three times Georgia’s number. Write an expression for the cousin’s stickers.

21.A bike tour charges a fixed $18 fee plus $0.25 for each kilometre travelled. Write an expression for the total cost in dollars for k kilometres.

22.A streaming service charges $14 per month plus $2 for each extra film rental. If the bill is $30, how many extra films were rented? Write and solve an equation.