Mathematics
Grade 10
15 min
Input/output tables with addition, subtraction, multiplication, and division
Input/output tables with addition, subtraction, multiplication, and division
What you'll learn
- Identify the real and imaginary components of a complex number expressed in standard form (a + bi) with 100% accuracy.
- Explain the relationship between complex numbers and the imaginary unit 'i', including its definition (i² = -1) and its role in expanding the number system, in a written paragraph demonstrating comprehension.
- Apply the rules of addition, subtraction, and multiplication to simplify expressions involving complex numbers, achieving at least 80% accuracy on a problem set.
- Represent complex numbers graphically on the complex plane, correctly plotting at least 4 out of 5 given complex numbers.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Analyze input/output tables to determine the underlying single-operation or multi-operation rule.
Express the rule for an input/output table using formal function notation (e.g., f(x) = mx + b).
Calculate the constant rate of change (slope) from table values to determine the multiplicative component of a rule.
Algebraically solve for the constant (y-intercept) in a two-operation linear rule.
Generate output values for given inputs and determine input values for given outputs using the derived rule.
Prove that a derived rule is correct by verifying it against all data pairs in the table.
Model a real-world linear scenario by creating an input/output table and its corresponding function.
How does a concert ticket app instantly calculate the total cost for...
2
Key Concepts & Vocabulary
TermDefinitionExample
Input (Independent Variable)The value that is provided to a rule or function. It is the variable that is intentionally changed or manipulated. In a table, it is typically the 'x' column.In a table showing temperature conversion, the input could be degrees in Celsius.
Output (Dependent Variable)The value that results from applying a rule or function to an input. Its value depends on the input. In a table, it is typically the 'y' or 'f(x)' column.In a temperature conversion table, the output would be the corresponding degrees in Fahrenheit.
Rule (Function)The specific mathematical relationship that consistently transforms each input value into its corresponding output value. For Grade 10, this is often a linear function.The rule to convert...
3
Core Formulas
Rate of Change Formula
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
Use this formula to find the constant rate of change, 'm', for a linear relationship. Select any two pairs of (input, output) values, (x₁, y₁) and (x₂, y₂), from the table and substitute them into the formula.
Linear Function Form (Slope-Intercept)
y = mx + b
This is the general equation for a linear rule. Once you have calculated 'm' (the rate of change), substitute 'm' and any (x, y) pair from the table into this equation to solve for 'b' (the y-intercept).
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Challenging
A streaming service charges a monthly membership fee plus a fee for each movie rented. In January, a user rented 5 movies and paid $27.50. In March, they rented 12 movies and paid $48.50. What would be the total cost for a month in which 20 movies are rented?
A.$60.00
B.$72.50
C.$68.50
D.$75.00
Challenging
A linear function is described by the rule f(x) = -4x + 11. An input/output table for this function contains the pair (k, 31). What is the value of the missing input, k?
A.-5
B.5
C.-113
D.10.5
Challenging
An input/output table represents a linear function. The inputs are not sequential: (2, 13), (7, 33), (10, 45), (18, 77). What is the rule for this table?
A.f(x) = 3x + 7
B.f(x) = 5x + 3
C.f(x) = 4x + 5
D.f(x) = 6x + 1
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Frequently asked questions
What grade level is "Input/output tables with addition, subtraction, multiplication, and division"?
Input/output tables with addition, subtraction, multiplication, and division is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Input/output tables with addition, subtraction, multiplication, and division?
You'll be able to: Identify the real and imaginary components of a complex number expressed in standard form (a + bi) with 100% accuracy; Explain the relationship between complex numbers and the imaginary unit 'i', including its definition (i² =….
Is "Input/output tables with addition, subtraction, multiplication, and division" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Input/output tables with addition, subtraction, multiplication, and division?
This lesson includes 26 practice questions across multiple difficulty levels, each with instant feedback and explanations.