Free Printable WorksheetMathPre-CalculusMath CurriculumHSG-GPE.A.1-3(+)

Pre CAL.123 Model Motion Applications with Parametric Equations Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.123 Model Motion Applications with Parametric Equations. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.123 Model Motion Applications with Parametric Equations - Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given a parametric motion model, determine positions at stated times and select the interpretation that matches the motion described. Associated standards listed with this skill in this prompt cell: CCSS HSG-GPE.A.1-3(+); CCSS HS-Modeling; SMP 1,2,4,5,7,8; AP Precalculus CED Units 3-4; TX §111.42(c)(3)(D-H); FL MA.912.GR.7.1-7.9, MA.912.T.4.5-4.7; VA MA.AG.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.123 Model Motion Applications with Parametric Equations skill assessments:

Problem 1Difficulty: Mastery
A moving point has x(t)=2t2-4t+5 and y(t)=-t2+4t+1. Which statement correctly compares t=1 and t=3?
AAt t=1 it is at (4, 3), and at t=3 it is at (4, 11); the coordinates are swapped.
BAt t=1 it is at (3, 4), and at t=3 it is also at (3, 4); it returns to the same point.
CAt t=1 it is at (7, 4), and at t=3 it is at (11, 16); the signs in the quadratics were changed.
DAt t=1 it is at (3, 4), and at t=3 it is at (11, 4); it returns to the same height at a different x-position.
Solution & Explanation:At t=1, x=2-4+5=3 and y=-1+4+1=4. At t=3, x=18-12+5=11 and y=-9+12+1=4, so only the height is the same.
Problem 2Difficulty: Mastery
A point on a circle is x(t)=1+6cos(t), y(t)=1+6sin(t). Which comparison is correct for t=pi/4 and t=5pi/4?
AThe positions are (1+6sqrt(2), 1+6sqrt(2)) and (1-6sqrt(2), 1-6sqrt(2)); the cosine and sine factors were not halved.
BThe positions are (1+3sqrt(2), 1-3sqrt(2)) and (1-3sqrt(2), 1+3sqrt(2)); the sine signs were swapped.
CThe positions are (1+3sqrt(2), 1+3sqrt(2)) and (1-3sqrt(2), 1-3sqrt(2)); they are opposite ends of a diameter.
DThe positions are (1, 7) and (1, -5); they are top and bottom points.
Solution & Explanation:At pi/4, cos and sin are sqrt(2)/2, so 6 times each is 3sqrt(2). At 5pi/4 both are negative, giving the opposite point through the center.
Problem 3Difficulty: Mastery
A shifted circular model is x(t)=9-4cos(pi t/2) and y(t)=2+4sin(pi t/2). Which statement is true at t=2?
A(5, 2); the negative cosine coefficient was ignored.
B(13, 2); because of the negative cosine coefficient, the point is on the right side of the circle at this time.
C(9, 6); the point is at the top of the circle.
D(9, -2); the point is at the bottom of the circle.
Solution & Explanation:At t=2, the angle is pi. Since cos(pi)=-1, x=9-4(-1)=13; since sin(pi)=0, y=2. The negative cosine flips the usual left-right position.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard HSG-GPE.A.1-3(+) (Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given a parametric motion model, determine positions at stated times and select the interpretation that matches the motion described. Associated standards listed with this skill in this prompt cell: CCSS HSG-GPE.A.1-3(+); CCSS HS-Modeling; SMP 1,2,4,5,7,8; AP Precalculus CED Units 3-4; TX §111.42(c)(3)(D-H); FL MA.912.GR.7.1-7.9, MA.912.T.4.5-4.7; VA MA.AG.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.).

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