Vocab: Operations
What operation gives you a "product"?
Multiplication
In the expression 3x² + 2x − 7, what are the three "terms"?
3x², 2x, and −7
Is √2 rational or irrational, and why?
Irrational, it cannot be written as a fraction; its decimal never repeats or ends
What is the rule for multiplying two terms with the same base? Give an example.
Add the exponents: x² · x³ = x⁵
What are inverse operations, and why do we use them when solving equations?
Operations that undo each other (+ and −, × and ÷). We use them to isolate the variable while keeping the equation balanced.
What do you call the answer to a subtraction problem?
The difference
What is the "degree" of the polynomial 4x⁴ + 2x² − 1?
4 (the largest exponent)
Name one example of a rational number that is NOT an integer.
Any fraction or repeating/terminating decimal, e.g. 1/2 or 0.25
Simplify (x³)²
x⁶ power of a power means multiply exponents: 3 × 2 = 6
Solve 2x + 5 = 15. Show your steps.
Subtract 5 from both sides → 2x = 10; divide both sides by 2 → x = 5
What do you call the answer to a division problem?
The quotient
In 3x² + 2x − 7, what is the "leading coefficient"?
3
Is 0.333… (one-third) rational or irrational?
Rational, it can be written as the fraction 1/3
A student writes x² · x³ = x⁶. What mistake did they make?
They multiplied the exponents instead of adding them. The correct answer is x⁵.
What does it mean for an equation to be "true"?
Both sides have the same value — e.g. 7 + 5 = 12 is true
If you are asked to 'evaluate' an expression, what must you do first?
Replace (substitute) the variable with the given value
In 3x² + 2x − 7, which term is the "constant"?
−7 (the term with no variable)
How can you use a calculator to check if a number is a perfect square?
Take the square root. If the result is a whole number, it is a perfect square.
Simplify x⁵ ÷ x². State the rule you used.
x³ when dividing same-base terms, subtract the exponents: 5 − 2 = 3
Solve A = lw for w.
Divide both sides by l: w = A/l
What does it mean to "simplify" an expression?
Make it easier to read; combine like terms or reduce until no further steps are possible
A student says the degree of 4x⁴ is 4 because 4 is the coefficient. Is the student correct, and why?
No, the degree is the exponent, not the coefficient. The degree is 4 because the exponent on x is 4.
Which is irrational: √49 or √50?
√50, its decimal is non-terminating and non-repeating. √49 = 7, which is rational.
What is a polynomial? Give an example.
An expression with variables, coefficients, and exponents. Example: 3x² + 2x − 7
Solve P = 2l + 2w for w. Show all steps.
Subtract 2l: P − 2l = 2w; divide by 2: w = (P − 2l)/2