Ratio Patterns

About This Worksheet

This worksheet helps twelfth-grade Pre-Calculus students practice using ratios between consecutive values to decide whether a table represents an exponential function. Students work through ten tables and calculate how each output compares with the one before it.

If the same ratio appears each time, the table shows a constant multiplicative pattern and can be classified as exponential. If the ratios change, the relationship is not exponential. This gives students a clear numerical test instead of relying only on visual pattern recognition.

What Students Practice

Students practice dividing consecutive output values to find the common ratio. They record those ratios and then decide whether they stay constant across the table.

The worksheet includes both increasing and decreasing patterns. Students see that exponential functions do not always grow. A ratio smaller than one can create exponential decay, while a ratio greater than one creates growth.

Why This Skill Matters

The constant ratio is one of the most important features of an exponential function. Understanding it helps students move from a table to an equation and gives them a way to verify whether an exponential model really fits.

This skill also prepares students for writing exponential functions from data. Once they know the first value and the common ratio, they have the two main pieces needed to build the function.

Common Challenges

Students may subtract consecutive values instead of dividing them. Remind them that differences are useful for linear patterns, while ratios are used for exponential patterns.

Another common mistake is dividing in different directions. Students should consistently divide each new value by the one before it so the ratios are easy to compare.

How To Use It

Teachers can use this worksheet immediately after introducing exponential patterns. It works well for independent practice, partner work, homework, or a quick pattern-analysis activity.

Parents and homeschool teachers can say, “Take each new value and divide it by the previous value.” If the answer stays the same each time, the table is exponential.

Grade Alignment

This Grade 12 Pre-Calculus worksheet supports identifying exponential functions from tables and constant ratios. It also prepares students for writing equations from data.

Students should already understand basic division and ratio concepts. After this practice, they can move into identifying growth and decay rates.