Peru · Grado 12 · Practice Sheet 48

1. 1.

   Find the sum of the first 8 terms of a geometric series with first term a = 6 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.

   Find the population standard deviation of: 16, 13, 2, 8, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   A population of 3,500 grows 3% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   Solve using the quadratic formula: x² − 3x + 2 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   Two masses 1,100 kg and 430 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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6. 6.

   Find the momentum of a 35 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A cone has base radius 8 cm and height 11 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.

   A force of 172 N acts on an area of 2.1 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A triangle has sides a = 9 cm and b = 8 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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10. 10.

    Find the momentum of a 12 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    S/ 3,500 is invested at 3% compound interest per annum for 3 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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12. 12.

    A device runs at 223 V drawing 1.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A force of 111 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the force needed to accelerate a 35 kg mass at 9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    An object with initial velocity 5 m/s accelerates at 3.6 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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17. 17.

    Find the momentum of a 51 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 368 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A device runs at 178 V drawing 5.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A cone has base radius 8 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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