Zambia · Grade 12 · Practice Sheet 46

1. 1.

   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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2. 2.

   Find the sum of the first 10 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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3. 3.

   ZK 3,900 is invested at 6% 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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4. 4.

   A current of 4.7 A flows through a 8 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Find the force needed to accelerate a 53 kg mass at 1.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A force of 10 N moves an object 27 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A device runs at 204 V drawing 0.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A body starts at 7 m/s and accelerates at 3.6 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A 6 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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10. 10.

    ZK 1,900 is invested at 4% compound interest per annum for 4 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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11. 11.

    A triangle has sides a = 17 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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12. 12.

    In a triangle, a = 15, b = 5 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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13. 13.

    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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14. 14.

    Find the force needed to accelerate a 38 kg mass at 1.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the sum of the first 6 terms of a geometric series with first term a = 5 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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16. 16.

    In a triangle, a = 15, b = 8 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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17. 17.

    A wave has frequency 162 Hz and wavelength 4.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A triangle has sides a = 19 cm and b = 13 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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19. 19.

    Solve using the quadratic formula: x² + 0x − 1 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A wave has frequency 671 Hz and wavelength 0.43 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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