Malaysia · Year 12 · Practice Sheet 48

1. 1.

   Find the sum of the first 8 terms of a geometric series with first term a = 2 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A triangle has sides a = 15 cm and b = 19 cm with an included angle C = 90°. 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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3. 3.

   Two masses 4,300 kg and 810 kg are 12 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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4. 4.

   Find the gravitational potential energy of a 32 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   RM 500 is invested at 3% 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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6. 6.

   Find the momentum of a 38 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A cone has base radius 3 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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8. 8.

   Find the force needed to accelerate a 43 kg mass at 5.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the momentum of a 10 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A triangle has sides a = 18 cm and b = 15 cm with an included angle C = 90°. 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.

    A current of 5.1 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A triangle has sides a = 17 cm and b = 14 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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13. 13.

    A force of 23 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A triangle has sides a = 9 cm and b = 14 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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15. 15.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    Find the sum of the first 7 terms of a geometric series with first term a = 8 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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17. 17.

    Find the momentum of a 29 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A wave has frequency 662 Hz and wavelength 1.32 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A force of 60 N moves an object 15 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the force needed to accelerate a 19 kg mass at 2.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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