Tanzania · Grade 12 · Practice Sheet 43

1. 1.

   A force of 251 N acts on an area of 8.4 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   An object with initial velocity 11 m/s accelerates at 4.8 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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3. 3.

   A wave has frequency 323 Hz and wavelength 3.56 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   In a triangle, a = 12, b = 12 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 wave has frequency 502 Hz and wavelength 2.63 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A force of 25 N moves an object 7 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Two masses 5,300 kg and 630 kg are 20 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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8. 8.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 4 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   Find the momentum of a 21 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 8 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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11. 11.

    In a triangle, a = 7, b = 16 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.

    Two masses 6,300 kg and 830 kg are 9 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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13. 13.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 12 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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14. 14.

    Find the momentum of a 20 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Solve using the quadratic formula: x² + 4x + 3 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    A 25 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    TSh 2,300 is invested at 5% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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18. 18.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    Find the force needed to accelerate a 46 kg mass at 3.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A current of 0.9 A flows through a 29 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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