KSA Grade 10 Geometry. Practice it free.

Experiment with transformations in the plane, prove geometric theorems, and understand congruence, similarity, and trigonometry. This Grade 10 reporting domain maps to 5 practice skills and 8 representative questions from the playable bank.

Grade 10G5 mapped skills
What the test measures

Geometry skills

  1. Use geometric transformations to define congruence and similarity

  2. Prove and apply theorems about lines and angles, triangles, and circles

  3. Make geometric constructions

  4. Explain volume formulas and use them to solve problems

  5. Apply trigonometric ratios to right triangles

Standards basis

Kentucky Academic Standards (KAS) for Mathematics — Kentucky

How the KSA reports it

Kentucky KSA is a state summative assessment built on Kentucky Academic Standards (KAS) rather than a separate national framework. For mathematics, the assessed content closely follows Common Core–style grade-band domains in grades 3-8 and uses Kentucky high-school conceptual categories in grade 10.

Blueprint & weighting

KSA uses the Independent / state-specific framework (by grade domains structure).

Practice by skill

Topics mapped to this domain

Surface area and volume

Grade 1015 questions

Algebra and polygon angle measures (ACT)

Grade 910 questions

Right triangle trig from two ratios

Grade 1010 questions

Special right triangles

Grade 1015 questions

Volume word problems (ACT)

Grade 910 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

Find the volume of a cylinder with radius 11 and height 1010. Use π=3\pi = 3.

V=πr2h=3×1×10=30V = \pi r^2 h = 3 \times 1 \times 10 = 30.

Practice playeasy

Each interior angle of rectangle WXYZWXYZ measures (3x−12)°(3x-12)°. What is the value of xx?

Every interior angle of a rectangle measures 90°90°, so 3x−12=903x-12=90 and x=34x=34.

Practice playeasy

In a right triangle, cos⁡α=513\cos\alpha = \dfrac{5}{13} and tan⁡α=125\tan\alpha = \dfrac{12}{5}. What is sin⁡α\sin\alpha?

sin⁡α=tan⁡α⋅cos⁡α=125⋅513=1213\sin\alpha = \tan\alpha \cdot \cos\alpha = \dfrac{12}{5} \cdot \dfrac{5}{13} = \dfrac{12}{13}.

Practice playeasy

In a 3030-6060-9090 triangle the short leg is 88. What is the hypotenuse?

The hypotenuse is twice the short leg: 2×8=162 \times 8 = 16.

Practice playmedium

An ice machine makes spherical ice balls with a diameter of 66 centimeters. What is the volume of one ice ball, in cubic centimeters?

The radius is half the diameter: r=3r = 3 cm. Then V=43πr3=43π(3)3=36πV = \dfrac{4}{3}\pi r^{3} = \dfrac{4}{3}\pi (3)^{3} = 36\pi cubic centimeters.

Practice playeasy

Find the volume of a sphere with radius 33. Use π=3\pi = 3.

V=43πr3=43×3×27=108V = \dfrac{4}{3} \pi r^{3} = \dfrac{4}{3} \times 3 \times 27 = 108.

Practice playeasy

In △ABC\triangle ABC, m∠A=(x+8)°m\angle A=(x+8)°, m∠B=(2x+17)°m\angle B=(2x+17)°, and m∠C=(x+55)°m\angle C=(x+55)°. What is the value of xx?

The three interior angles sum to 180°180°: (x+8)+(2x+17)+(x+55)=180(x+8)+(2x+17)+(x+55)=180, so 4x+80=1804x+80=180 and x=25x=25.

Practice playeasy

In a right triangle, sin⁡θ=1517\sin\theta = \dfrac{15}{17} and cos⁡θ=817\cos\theta = \dfrac{8}{17}. What is tan⁡θ\tan\theta?

tan⁡θ=sin⁡θcos⁡θ=1517817=1517⋅178=158\tan\theta = \dfrac{\sin\theta}{\cos\theta} = \dfrac{\dfrac{15}{17}}{\dfrac{8}{17}} = \dfrac{15}{17} \cdot \dfrac{17}{8} = \dfrac{15}{8}.

Keep practicing

Turn geometry into game time.

The KSA placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
7.G.B.6HSG.GMD.A.3HSG.SRT.C.6HSG.SRT.C.8
Geometry in other KSA grades
Grade 5Grade 6Grade 7Grade 8
The same skills on other tests
MCAS
Source and test overview
All KSA prepOfficial test source
Reporting categories

More Grade 10 domains

Number and QuantityExtend the real number system to include irrational numbers and work with quantities in mathematical and real-world situations.8 QsPractice →AlgebraSee structure in expressions and solve equations; create equations that describe numbers or relationships; and reason with equations and inequalities.8 QsPractice →FunctionsInterpret, build, and analyze functions that describe relationships between quantities.8 QsPractice →Statistics and ProbabilitySummarize, represent, and interpret data on a single count or measurement variable; interpret linear models; make inferences and justify conclusions from sample surveys, experiments, and observational studies; and use probability to evaluate outcomes of decisions.8 QsPractice →