Denmark · Grade 10 · Practice Sheet 34

1. 1.

   A body starts at 3 m/s and accelerates at 2.4 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A bag has 18 equally likely marbles, of which 15 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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3. 3.

   Find the momentum of a 19 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Solve using the quadratic formula: x² + 11x + 30 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   Find the force needed to accelerate a 60 kg mass at 4.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A device runs at 8 V drawing 8.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A wave has frequency 175 Hz and wavelength 3.56 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A current of 3.9 A flows through a 9 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A right-angled triangle has legs of 3 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    A bag has 12 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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11. 11.

    Solve using the quadratic formula: x² − 8x + 12 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    An object with initial velocity 12 m/s accelerates at 5 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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13. 13.

    A population of 1,400 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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14. 14.

    An object has mass 110 g and volume 25 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A value changes from 142 to 159. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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16. 16.

    Solve for x: 4x + 4 = 44.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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17. 17.

    Find the momentum of a 35 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 260 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A value changes from 148 to 130. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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20. 20.

    Find the gravitational potential energy of a 39 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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