18 Questions
What does the exponent represent in a power?
The number of times the base appears as a factor in the multiplication.
What is the result of any number to the exponent 1?
The number itself.
What is the value of any number (except 0) to the exponent 0?
1
What is the value of $15 - (6 + 1) + 30 ÷ (3 imes 2)$ without using brackets?
30
In the expression (8 - (5 + 1)) × 3, how do you evaluate it?
First evaluate the inner brackets, then apply the multiplication.
What is the result of $(-2)^3$?
-8
Explain the strategy for evaluating expressions with nested brackets.
Evaluate what's inside the inner-most brackets first.
What rule governs the order of operations when dealing with brackets in an expression?
BEDMAS (Brackets, Exponents, Division and Multiplication, Addition and Subtraction)
Evaluate the expression: 17 - 23 + 4 × 5.
8
Solve the equation: 72 ÷ (3 × 2) - (10 + 1).
10
Evaluate the expression: (14 - 6) × ((30 + 5) ÷ 5).
24
What are variables used for in math?
To represent unknown quantities.
What is the importance of following the reverse BEDMAS order when undoing operations?
To correctly undo operations in algebra
What is the rule that must always be followed when manipulating equations?
Whatever you do to one side of the equation, you must also do to the other side
In algebra, why is it important to represent unknown quantities with variables in word problems?
To set up equations based on the relationships given in the problem
What is the 4-step process for solving word problems with algebra?
- Represent unknown quantities with variables. 2. Use relationships to set up equations. 3. Solve the equations. 4. Answer the question.
How can negative exponents and negative integers be involved in algebraic expressions?
They can appear in calculations and solutions of algebraic equations
Explain the significance of using the two-step method to solve algebraic equations.
It simplifies the process by breaking down the solution into manageable steps
Study Notes
Exponents
- The base is the number being multiplied repeatedly, and the exponent is the number of times it appears as a factor.
- Any number to the exponent 1 is equal to itself.
- Any number (except 0) to the exponent 0 is equal to 1.
Brackets
- Brackets are used to group parts of an expression into sub-expressions.
- We commonly use parentheses (), but can also use square brackets [] or curly brackets {}.
- Brackets are evaluated first in an expression, according to BEDMAS.
- Nested brackets can be used, and the inner-most brackets are evaluated first.
Solving Equations
- Variables are symbols used to represent unknown quantities.
- To solve an equation, we must undo operations in a reverse BEDMAS order.
- Whatever operation is done to one side of the equation must also be done to the other side.
- Important rules to remember:
- Addition and subtraction are opposite operations.
- Multiplication and division are opposite operations.
Solving Word Problems with Algebra
- To solve a word problem with algebra, follow these steps:
- Represent unknown quantities with variable(s).
- Use relationships given in the problem to set up equation(s) with the variable(s).
- Solve the equation(s) for the variable(s).
- Answer the question.
Examples and Exercises
- Evaluate the following expressions:
- 17 − 23 + 4 × 5 = ?
- (a) 72 ÷ (3 × 2) − (10 + 1) = ?
- ...
- Solve the following algebraic equations for x:
- (a) x − 4 = 5
- (e) 2x − 3 = 5
- ...
- Solve the word problem: In eight years from now, Sally will be four years younger than three times her current age. How old will she be in two years from now?
Test your knowledge on exponents and bases with this quiz. Understand how a base is multiplied over and over again by the exponent, and how any number to the exponent 1 equals itself while any number (except 0) to the exponent 0 equals 1.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
