Applications - Rate of Change, Tangents & Normals

Grade 12 Maths Higher — Applications - Rate of Change, Tangents & Normals: 25 practice questions with instant scoring and explanations.

1. The rate of change of a quantity with respect to time is represented by:
2. For a curve y = f(x), the slope of tangent at (a, f(a)) is:
3. The equation of tangent to y = f(x) at (a, f(a)) is:
4. The slope of normal to a curve at a point is:
5. If tangent slope is m, then normal slope is:
6. For y = x² at (2, 4), the tangent slope is:
7. The normal to y = √x at (1, 1) has equation:
8. If water flows out of tank at rate 5 L/min, then dV/dt =
9. For a spherical balloon with radius r, the rate of volume change dV/dr =
10. Related rates problems use:
11. A ladder against wall: if dx/dt is horizontal speed, the dy/dt is:
12. For a growing circle, if dr/dt = 2 cm/s, then dA/dt at r = 5 =
13. The normal vector direction is:
14. For y = sin(x) at x = π/2, the tangent line is:
15. The angle between two curves is the angle between their:
16. If f'(x) = 0 at x = a, the tangent at a is:
17. The equation of normal to y = e^x at (0, 1) is:
18. For population growth P(t), the rate dP/dt represents:
19. A particle's velocity v = dx/dt and acceleration a = d²x/dt² = dv/dt =
20. For velocity v = t² - 3t + 2, acceleration a = dv/dt =
21. Orthogonal trajectories are curves that:
22. Finding orthogonal trajectories uses:
23. The angle of inclination θ of tangent line relates to slope m by:
24. If two curves are perpendicular at intersection, m₁·m₂ =
25. Slope of tangent to y = x² at x = 2: