Vietnam · Grade 11 · Practice Sheet 22

1. 1.

   Find the population standard deviation of: 11, 8, 8, 6, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A population of 7,500 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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3. 3.

   A force of 65 N acts on an area of 1.6 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A cone has base radius 3 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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5. 5.

   A triangle has sides a = 16 cm and b = 8 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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6. 6.

   Find the force needed to accelerate a 6 kg mass at 1.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A population of 1,100 grows 10% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   In a triangle, a = 13, b = 14 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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9. 9.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 10 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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10. 10.

    A body starts at 17 m/s and accelerates at 1.6 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    An object with initial velocity 8 m/s accelerates at 1 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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12. 12.

    A current of 8 A flows through a 40 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A population of 1,000 grows 3% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    A force of 56 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A wave has frequency 698 Hz and wavelength 1.56 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Find the momentum of a 24 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    Find the force needed to accelerate a 3 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A population of 4,700 grows 10% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    An object has mass 261.8 g and volume 34 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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20. 20.

    A cylinder has radius 5 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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