United States · Grade 12 · Practice Sheet 33

1. 1.

   An object with initial velocity 0 m/s accelerates at 4.8 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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2. 2.

   Solve using the quadratic formula: x² + 0x − 16 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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3. 3.

   A cone has base radius 6 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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4. 4.

   In a triangle, a = 14, b = 5 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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5. 5.

   A body starts at 17 m/s and accelerates at 4.8 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 4.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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7. 7.

   A device runs at 161 V drawing 1.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A wave has frequency 319 Hz and wavelength 4 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A device runs at 191 V drawing 7.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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11. 11.

    A device runs at 215 V drawing 5.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the force needed to accelerate a 38 kg mass at 7.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the sum of the first 6 terms of a geometric series with first term a = 4 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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14. 14.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 2 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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15. 15.

    A 32 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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16. 16.

    A triangle has sides a = 16 cm and b = 6 cm with an included angle C = 60°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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17. 17.

    A device runs at 59 V drawing 2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 3 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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19. 19.

    In a triangle, a = 15, b = 7 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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20. 20.

    Find the momentum of a 12 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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