United States · Grade 12 · Practice Sheet 47

1. 1.

   A force of 61 N moves an object 2 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   In a triangle, a = 12, b = 17 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   A device runs at 34 V drawing 2.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A wave has frequency 846 Hz and wavelength 3.38 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Two masses 1,600 kg and 410 kg are 3 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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6. 6.

   A force of 240 N acts on an area of 0.6 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A body starts at 4 m/s and accelerates at 1.9 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A current of 2.1 A flows through a 6 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A 16 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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10. 10.

    A population of 8,000 grows 10% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    An object with initial velocity 5 m/s accelerates at 1.6 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    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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13. 13.

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

    Formula:Quadratic Formula

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

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14. 14.

    A population of 4,000 grows 10% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A current of 4.1 A flows through a 21 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 10 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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17. 17.

    Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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18. 18.

    A force of 319 N acts on an area of 4.1 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A cone has base radius 7 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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