Netherlands · Year 10 · Practice Sheet 26

1. 1.

   In a triangle, a = 7, b = 11 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   A current of 6 A flows through a 54 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A bag has 23 equally likely marbles, of which 12 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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4. 4.

   A force of 327 N acts on an area of 3.4 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A body starts at 7 m/s and accelerates at 2 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A bag has 9 equally likely marbles, of which 8 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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7. 7.

   An object has mass 89.7 g and volume 23 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A 27 kg object moves at 16 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A body starts at 1 m/s and accelerates at 4.6 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    Find the force needed to accelerate a 43 kg mass at 4.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 115 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    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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13. 13.

    A wave has frequency 596 Hz and wavelength 3.94 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A right-angled triangle has legs of 7 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Find the momentum of a 3 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A population of 6,300 grows 5% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    In a triangle, a = 12, b = 10 and the included angle C = 40°. 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 momentum of a 1 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A bag has 16 equally likely marbles, of which 4 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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20. 20.

    Find the gravitational potential energy of a 49 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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