Ghana · Grade 12 · Practice Sheet 23

1. 1.

   A cone has base radius 10 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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2. 2.

   Find the sum of the first 7 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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3. 3.

   GH₵ 3,700 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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4. 4.

   A device runs at 176 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A triangle has sides a = 6 cm and b = 14 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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6. 6.

   GH₵ 500 is invested at 5% compound interest per annum for 5 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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7. 7.

   A population of 1,400 grows 5% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A current of 2.8 A flows through a 15 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A device runs at 47 V drawing 2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A 33 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    A force of 66 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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12. 12.

    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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13. 13.

    Find the force needed to accelerate a 21 kg mass at 8.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the momentum of a 18 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    An object with initial velocity 1 m/s accelerates at 2.6 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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16. 16.

    A triangle has sides a = 12 cm and b = 12 cm with an included angle C = 30°. 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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17. 17.

    A wave has frequency 31 Hz and wavelength 4.11 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A triangle has sides a = 5 cm and b = 9 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 + 9x + 18 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A current of 3.1 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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