Brazil · Ano 10 · Practice Sheet 43

1. 1.

   A wave has frequency 812 Hz and wavelength 1.82 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   An object has mass 225.5 g and volume 41 cm³. Find its density.

   Formula:Density

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

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3. 3.

   Find the force needed to accelerate a 51 kg mass at 8.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A force of 87 N moves an object 15 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A current of 2.5 A flows through a 21 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A population of 4,900 grows 8% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   Find the momentum of a 23 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   In a triangle, a = 8, b = 15 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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9. 9.

   Solve for x: 6x + 16 = 64.

   Formula:Solving a Linear Equation

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

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10. 10.

    Find the momentum of a 28 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 2 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    A value changes from 195 to 249. 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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13. 13.

    An object has mass 226.8 g and volume 36 cm³. Find its density.

    Formula:Density

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

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14. 14.

    Find the force needed to accelerate a 54 kg mass at 3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 298 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    An object with initial velocity 11 m/s accelerates at 3.1 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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17. 17.

    A force of 449 N acts on an area of 9.7 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    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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19. 19.

    A cylinder has radius 4 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A bag has 9 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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