Generalization, model comparison, proof, and technology-assisted validation.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u09-l06', 'number': 6, 'title': 'Velocity, Direction and Projectile Models', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Eliminate t from x=2t+1, y=3t−4.
2. {'id': 'u09-l06', 'number': 6, 'title': 'Velocity, Direction and Projectile Models', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
For x=cos t, y=sin t, identify the curve.
3. {'id': 'u09-l06', 'number': 6, 'title': 'Velocity, Direction and Projectile Models', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
At t=2, find the point for x=t², y=3t.
4. {'id': 'u09-l06', 'number': 6, 'title': 'Velocity, Direction and Projectile Models', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
What information is lost when eliminating a parameter?
5. {'id': 'u09-l06', 'number': 6, 'title': 'Velocity, Direction and Projectile Models', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
A projectile has x=20t, y=30t−5t². Find x at t=3.
6. {'id': 'u09-l06', 'number': 6, 'title': 'Velocity, Direction and Projectile Models', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
For x=4cos t, y=2sin t, identify the curve.
7. {'id': 'u09-l07', 'number': 7, 'title': 'Vector and Parametric Design Applications', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Eliminate t from x=2t+1, y=3t−4.
8. {'id': 'u09-l07', 'number': 7, 'title': 'Vector and Parametric Design Applications', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
For x=cos t, y=sin t, identify the curve.
9. {'id': 'u09-l07', 'number': 7, 'title': 'Vector and Parametric Design Applications', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
At t=2, find the point for x=t², y=3t.
10. {'id': 'u09-l07', 'number': 7, 'title': 'Vector and Parametric Design Applications', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
What information is lost when eliminating a parameter?
11. {'id': 'u09-l07', 'number': 7, 'title': 'Vector and Parametric Design Applications', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
A projectile has x=20t, y=30t−5t². Find x at t=3.
12. {'id': 'u09-l07', 'number': 7, 'title': 'Vector and Parametric Design Applications', 'family': 'parametric', 'week': 28, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
For x=4cos t, y=2sin t, identify the curve.