Math worksheets

Math worksheets give students in every grade focused practice in math. This page has 1 free printable sets, grouped by grade, and every set includes a computed answer key that is never wrong. Print them or save as a PDF, no login needed.

How to teach it

For a curve that stays above the x-axis, the area between it and the axis from a to b is exactly the definite integral. Sketch the region first, then evaluate F(b) - F(a). Give the area in square units.

Worked example

Find the exact area of the shaded region between the curve y = 3x^2 + 5x + 5 and the x-axis, from x = 0 to x = 3. (The curve stays above the x-axis on this interval.)

Answer: 129/2 square units

Why: Area = definite integral of (3x^2 + 5x + 5) dx from 0 to 3 = F(3) - F(0) where F(x) = x^3 + (5/2)x^2 + 5x; = 129/2 - (0) = 129/2.

Common mistake

Assuming the definite integral always equals the area, it only does so where the curve is above the axis; below the axis the integral is negative (a signed area), which is why this introduction keeps the curve positive.

What's inside

Find the exact area of the shaded region between the curve y = 3x^2 + 5x + 5 and the x-axis, from x = 0 to x = 3. (The curve stays above the x-axis on this interval.)
Find the exact area of the shaded region between the curve y = 4x^2 + 2x + 3 and the x-axis, from x = 0 to x = 2. (The curve stays above the x-axis on this interval.)
Find the exact area of the shaded region between the curve y = 3x^2 + 4x + 1 and the x-axis, from x = 0 to x = 3. (The curve stays above the x-axis on this interval.)
Find the exact area of the shaded region between the curve y = x + 1 and the x-axis, from x = 0 to x = 1. (The curve stays above the x-axis on this interval.)
Find the exact area of the shaded region between the curve y = 3x^3 + x^2 + 5x + 2 and the x-axis, from x = 2 to x = 5. (The curve stays above the x-axis on this interval.)
Find the exact area of the shaded region between the curve y = 4x^2 + 4x + 1 and the x-axis, from x = 2 to x = 3. (The curve stays above the x-axis on this interval.)

Sample questions. Each set (A, B, C…) has fresh numbers and a computed answer key.

Year 11-12 Math

All Year 11-12 worksheets →

Set A

PDF · answer key with Pro

Frequently asked questions

Are these math worksheets free?

Yes. Every worksheet on ChalkBee is free to view and print or save as a PDF, with no login required. Pro unlocks the printable answer key and removes the watermark.

Do the worksheets have answer keys?

The answers are computed in code from the exact questions on each sheet. The printable answer key is available with Pro.

What grades do math worksheets cover?

Math worksheets on this page cover every grade. There are 1 printable sets in total, grouped by grade so you can pick the right level.

How do I print or download them?

Open any set, then use your browser's print option to print it or to save it as a PDF. The pages are laid out to print cleanly on standard letter or A4 paper.