Ghana · Grade 12 · Practice Sheet 45

1. 1.

   Find the sum of the first 8 terms of a geometric series with first term a = 4 and common ratio r = 4.

   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 = 15 cm with an included angle C = 120°. 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.

   Find the population standard deviation of: 15, 16, 5, 15, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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4. 4.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 4 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A force of 94 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the force needed to accelerate a 9 kg mass at 6.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   GH₵ 3,600 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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8. 8.

   Find the gravitational potential energy of a 7 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Find the momentum of a 6 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    A 10 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    Solve using the quadratic formula: x² + 7x + 6 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    Find the population standard deviation of: 7, 16, 4, 2, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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14. 14.

    In a triangle, a = 6, b = 13 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 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    A current of 5.8 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    Find the force needed to accelerate a 11 kg mass at 5.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 100 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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19. 19.

    A current of 1.3 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A population of 7,400 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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