Geometry Final Exam with Answer Key (Spring)

Apply the Pythagorean theorem and right-triangle trigonometric ratios to find an unknown side length.

Calculate the volume and surface area of cones, cylinders, spheres, and pyramids from given dimensions.

Solve proportions involving similar figures to find an unknown side length.

Factor polynomial expressions and identify their correct factors.

Find the equation, area, or probability associated with a circle from given measurements.

Assign Form A and Form B to different class periods, or use one as a makeup version, since both cover the same topics with different numbers and figures.

Review right-triangle trigonometry, the Pythagorean theorem, and 3D volume/surface-area formulas before the exam, since these recur across multiple questions in both forms.

Because the file is an editable Word document, reorder, remove, or renumber questions before printing if a shorter or customized version is needed.

Preview each form's diagrams ahead of time, since several problems (the cone, the cylinder, the composite circle-in-square figure) are reused with new numbers across both forms.

Right-triangle trigonometry — students use trigonometric ratios and the Pythagorean theorem to solve for unknown sides, as in "Use trigonometry to approximate the length of x."

3D volume and surface area — students calculate volume and surface area for cones, cylinders, spheres, and pyramids from labeled dimensions.

Proportional reasoning with similar figures — students write and solve proportions to find an unknown side in similar-figure problems.

Polynomial factoring — students factor quadratic and higher-degree expressions and identify the correct factor from multiple-choice options.

Circle geometry — students find circle equations, areas of composite shapes involving circles, and probability from circular target regions.