Belgium · Year 11 · Practice Sheet 2

1. 1.

   Find the population standard deviation of: 18, 2, 3, 19, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   Find the momentum of a 3 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   Solve using the quadratic formula: x² + 8x + 15 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A population of 1,100 grows 8% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   A force of 71 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A population of 4,900 grows 2% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   A device runs at 159 V drawing 0.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the force needed to accelerate a 26 kg mass at 6.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A cone has base radius 9 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A right-angled triangle has legs of 8 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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11. 11.

    Find the momentum of a 48 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A force of 255 N acts on an area of 2.1 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A cone has base radius 8 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    A body starts at 9 m/s and accelerates at 3 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A force of 173 N acts on an area of 4 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    An object has mass 50.7 g and volume 13 cm³. Find its density.

    Formula:Density

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

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17. 17.

    In a triangle, a = 6, b = 6 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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18. 18.

    Find the gravitational potential energy of a 7 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    In a triangle, a = 7, b = 8 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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20. 20.

    A 2 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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