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MassachusettsMaths

Geometry

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you find arc length, sector area, and circle measures on the MCAS?

Find circumference and area of circles, compute arc length and sector area as fractions of the whole, and apply the central-angle and inscribed-angle relationships.
A Grade 10 Math MCAS answer on circles: circumference and area, arc length and sector area as fractions of the circle, and the central-angle and inscribed-angle relationships.
9 min answer →

What are the rigid motions, and how do they define congruence on the MCAS?

Identify and apply rigid motions (translations, reflections, rotations), describe their effect on coordinates, and use them to explain why two figures are congruent.
A Grade 10 Math MCAS answer on rigid motions (translations, reflections, rotations), their effect on coordinates, and how a sequence of rigid motions establishes that two figures are congruent.
9 min answer →

How do the distance, midpoint, and slope formulas let you analyze figures on the coordinate plane?

Use the distance formula, the midpoint formula, and slope to find lengths and midpoints, classify figures, and verify properties such as parallel and perpendicular sides on the coordinate plane.
A Grade 10 Math MCAS answer on coordinate geometry: the distance and midpoint formulas, using slope to test parallel and perpendicular sides, and classifying figures such as parallelograms and right triangles on the coordinate plane.
9 min answer →

How do the Pythagorean theorem and the trig ratios solve right triangles on the MCAS?

Apply the Pythagorean theorem and the sine, cosine, and tangent ratios to find missing sides and angles in right triangles, including in real-world contexts such as angles of elevation.
A Grade 10 Math MCAS answer on right triangle trigonometry: the Pythagorean theorem, the sine, cosine, and tangent ratios with SOH-CAH-TOA, finding missing sides and angles, and angle-of-elevation problems.
10 min answer →

What makes two figures similar, and how do dilations and scale factors work on the MCAS?

Use dilations and scale factors to establish similarity, set up proportions between corresponding sides of similar figures, and relate the scale factor to changes in perimeter and area.
A Grade 10 Math MCAS answer on similarity and dilations: scale factors, proportions between corresponding sides of similar figures, the angle-angle criterion, and how a scale factor affects perimeter and area.
9 min answer →

How do you find the volume and surface area of solids using the reference sheet formulas?

Compute the volume and surface area of prisms, cylinders, cones, spheres, and pyramids using the reference sheet formulas, and solve real-world problems involving capacity and material.
A Grade 10 Math MCAS answer on volume and surface area of prisms, cylinders, cones, spheres, and pyramids, using the reference sheet formulas, and applying them to capacity and material problems with appropriate units.
9 min answer →