United Arab Emirates · Grade 12 · Practice Sheet 47

1. 1.

   Find the population standard deviation of: 17, 3, 8, 7, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A current of 3.9 A flows through a 52 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the gravitational potential energy of a 40 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 3 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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5. 5.

   A force of 10 N moves an object 9 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A triangle has sides a = 17 cm and b = 20 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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7. 7.

   Find the momentum of a 16 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Find the population standard deviation of: 16, 3, 6, 12, 11 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A triangle has sides a = 17 cm and b = 9 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.

    AED 3,300 is invested at 8% 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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11. 11.

    A population of 1,900 grows 3% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    A body starts at 16 m/s and accelerates at 1.3 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 11 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    A 20 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    A force of 42 N acts on an area of 6 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the momentum of a 42 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A device runs at 208 V drawing 3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    In a triangle, a = 15, b = 15 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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19. 19.

    A cone has base radius 4 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A device runs at 135 V drawing 6.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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