Expressions and Substitution in Algebra

What expression represents '1 more than x'?

How would you represent 'the sum of k and 5' as an expression?

Write the expression for 'double the value of u'.

What expression would represent '4 lots of y'?

Describe the expression 'it is subtracted from 10' if the variable is t.

How many lollies does Nicholas buy in total if there are 7 lollies in each bag and he buys 10 bags?

If there are n lollies in each bag and Nicholas buys 10 bags, what expression represents the total number of lollies?

What expression represents Mikayla's earnings if she works 8 hours and is paid $x per hour?

If Mikayla receives a pay rise of $3 per hour, what is her new hourly wage if her current wage is $x?

What expression shows how much Mikayla earns for 8 hours of work at her new hourly rate?

Expressions and Substitution

Expressions are mathematical phrases which can include numbers and letters.
Letters in an expression represent unknown numbers and are called variables.
An expression is composed of one or more terms separated by a plus or minus sign.
When a value is substituted for a variable, we can evaluate the expression.
To evaluate an expression, follow the order of operations (PEMDAS):
- Parentheses
- Exponents
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)

Substitution with Powers and Roots

Powers in expressions are written as the base number followed by the power, for example, x^2.
When evaluating expressions with powers, the power is applied to the base number.
Roots in expressions are written as a radical sign followed by the number, for example, √9.
When evaluating expressions with roots, find the number that, when multiplied by itself (the same number of times as the index of the root), equals the original number.
The index of the root is the small number written in the left corner of the radical sign. (If no index is written, it means it is 2)

Equivalent Expressions

Equivalent expressions represent the same value for the same variable values.
To determine if expressions are equivalent, evaluate them with the same variable values.

Substitution with Powers and Roots

Expressions containing powers can be evaluated by applying the power to the base number.
Expressions containing roots can be evaluated by finding the number that, when multiplied by itself the same number of times as the index, equals the original number.

This quiz covers the fundamentals of expressions and substitution in algebra, focusing on the evaluation of expressions using the order of operations (PEMDAS). It also addresses the concepts of powers and roots within expressions. Test your understanding of how to manipulate variables and evaluate mathematical phrases effectively.