Israel · Grade 12 · Practice Sheet 42

1. 1.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   A cone has base radius 11 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A body starts at 20 m/s and accelerates at 2.3 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 5 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   Find the gravitational potential energy of a 31 kg object raised 11 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   A force of 30 N moves an object 13 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A population of 5,800 grows 2% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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8. 8.

   Find the population standard deviation of: 16, 6, 4, 17, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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9. 9.

   A triangle has sides a = 20 cm and b = 9 cm with an included angle C = 120°. 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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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.

    In a triangle, a = 12, b = 8 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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12. 12.

    Solve using the quadratic formula: x² + 3x − 18 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    Find the population standard deviation of: 18, 14, 6, 16, 17 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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14. 14.

    Find the momentum of a 28 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    An object with initial velocity 14 m/s accelerates at 4.9 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    A device runs at 129 V drawing 9.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A triangle has sides a = 13 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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18. 18.

    A force of 412 N acts on an area of 6 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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19. 19.

    Find the momentum of a 22 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A force of 92 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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