Israel · Grade 12 · Practice Sheet 34

1. 1.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 11 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A force of 264 N acts on an area of 3.3 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A force of 31 N moves an object 33 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A body starts at 7 m/s and accelerates at 2.9 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A wave has frequency 406 Hz and wavelength 0.64 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   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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7. 7.

   A current of 7 A flows through a 10 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 1 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   A wave has frequency 266 Hz and wavelength 3.44 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    An object with initial velocity 9 m/s accelerates at 5 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    Solve using the quadratic formula: x² + 2x − 15 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A force of 136 N acts on an area of 7.5 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A population of 1,300 grows 8% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    In a triangle, a = 11, b = 14 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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15. 15.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    A force of 363 N acts on an area of 6.5 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the momentum of a 19 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A device runs at 22 V drawing 2.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A force of 438 N acts on an area of 3.7 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    An object with initial velocity 3 m/s accelerates at 1.9 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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