How to make a study sheet: a worked example you can follow

You've finished a page of notes. Can you use the ideas on it with the page covered? Build that check into your study sheet from the start. Leave room for questions, short explanations and a worked example. The amount of space depends on the topic. Aim for a sheet that lets you find a method quickly and then practise using it on your own.

What belongs on my study sheet when the chapter is long?

Check your teacher's learning goals and the questions you have already worked through in class. List the tasks you are expected to do: define a term, calculate a value, explain a choice or read a graph. Select the information that helps you complete those tasks. Keep any conditions attached to a rule. A shorter formula is no help if you forget when it applies.

Set aside space for the main ideas, a method and mistakes you want to avoid. One page can be a useful starting limit for a small topic. If everything needs tiny writing, split the topic across two sheets. Colour can make corrections easier to find, but the explanation should still make sense without it. Finish the content before spending time on the layout.

What does a finished sheet for straight-line graphs look like?

Start with this short lesson: a function of the form f(x) = mx + b has a straight-line graph. The fixed number m is its slope, also called the gradient, and b is its vertical intercept. To calculate an output, substitute an input for x. To find an input that gives a particular output, set f(x) equal to that output and solve the equation.

Here is a study sheet for f(x) = 3x - 2, with real numbers allowed as inputs. Write the question on the left of your paper and the explanation on the right. Keep enough space between them to cover the answers with another sheet.

• What do the numbers mean? The slope is 3 and the vertical intercept is -2. The line crosses the vertical axis at (0, -2).
• How do I find an output? For an input of 4, substitute x = 4: f(4) = 3 × 4 - 2 = 10.
• How do I find an input? For an output of 10, solve 3x - 2 = 10. Then 3x = 12, so x = 4.
• How do I draw the graph? Calculate two distinct points: f(0) = -2 and f(1) = 1. Plot (0, -2) and (1, 1), then draw the straight line through them.
• What might I mix up? The input is the number substituted for x. The output is the value after calculating f(x). Read which one the question gives you.

Add a small graph with labelled axes and a consistent scale on each axis. On this line, an increase of 1 in x gives an increase of 3 in f(x). That connects the slope to something you can see. If your class is studying increasing and decreasing functions, note that this function is increasing because its slope is positive.

How can I check that my sheet is accurate?

Compare each entry with your lesson and a worked classroom example. Check negative signs and the order of operations. Suppose you wrote f(4) = 3 × (4 - 2) = 6. The extra brackets changed the rule. In 3x - 2, you multiply the input by 3 before subtracting 2. Correct the line, cover it and try an input of 5. The output should be 13.

Keep claims about the example separate from general rules. This function gives exactly one input for each chosen real output because its slope is nonzero. A constant function such as g(x) = -2 behaves differently: every real input gives -2, and no input gives 10. Include this distinction if constant functions are part of your course.

How do I study with the sheet once it is finished?

Cover the answers and explain each method without reading it. Then change the numbers. For f(x) = 3x - 2, calculate f(-2) and find the input that produces 7. The answers are -8 and x = 3. Check the second answer by substitution: 3 × 3 - 2 = 7. If you needed a hint, mark that question for another attempt without help.

Dunlosky and colleagues' 2013 review rated practice testing and distributed practice as high-utility learning techniques. It did not establish that a particular study-sheet design is best. The approach here uses a sheet to support questions, checked answers and further practice over time. Put a short return to the topic in your calendar, then use your errors to choose the questions.

Which mistakes should I avoid when making a study sheet?

• Copying every sentence from the chapter: select the information needed for the tasks you will be assessed on.
• Removing the conditions of a rule to save space: keep the details that determine when you can use it.
• Recording only the final answer: show enough working to reconstruct the method.
• Spending the whole session decorating: leave time to solve a fresh problem with the sheet covered.

Graduo can help you prepare a study sheet from your course material. Compare the result with your teacher's explanations, add a checked example and hide the answers when you test yourself. Make a study sheet