Israel · Grade 12 · Practice Sheet 20

1. 1.

   In a triangle, a = 17, 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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2. 2.

   A device runs at 146 V drawing 1.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the momentum of a 8 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A body starts at 8 m/s and accelerates at 4.6 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   Find the force needed to accelerate a 49 kg mass at 8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A cone has base radius 5 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   In a triangle, a = 10, b = 7 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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8. 8.

   A triangle has sides a = 7 cm and b = 10 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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9. 9.

   Find the momentum of a 37 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A triangle has sides a = 10 cm and b = 16 cm with an included angle C = 45°. 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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11. 11.

    Find the force needed to accelerate a 38 kg mass at 6.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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13. 13.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    A device runs at 177 V drawing 5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A population of 1,700 grows 5% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A wave has frequency 240 Hz and wavelength 1.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the force needed to accelerate a 2 kg mass at 3.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A body starts at 13 m/s and accelerates at 3.1 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A force of 204 N acts on an area of 3.4 m². Find the pressure.

    Formula:Pressure

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

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