Australia · Year 10 · Practice Sheet 27

1. 1.

   A wave has frequency 883 Hz and wavelength 1.22 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A body starts at 18 m/s and accelerates at 5.5 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A bag has 21 equally likely marbles, of which 13 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.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 8 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   $3,300 is invested at 6% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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6. 6.

   A population of 7,900 grows 8% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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8. 8.

   An object with initial velocity 1 m/s accelerates at 4.5 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   A wave has frequency 628 Hz and wavelength 3.27 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Solve for x: 8x + 7 = 23.

    Formula:Solving a Linear Equation

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

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11. 11.

    An object has mass 176.8 g and volume 26 cm³. Find its density.

    Formula:Density

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

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12. 12.

    $2,900 is invested at 6% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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13. 13.

    A wave has frequency 366 Hz and wavelength 4.06 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    In a triangle, a = 14, b = 10 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    A value changes from 55 to 114. 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.

    A current of 7.3 A flows through a 46 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    Find the force needed to accelerate a 35 kg mass at 1.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A population of 7,200 grows 5% 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.

    A value changes from 126 to 229. 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.

    A force of 322 N acts on an area of 1.2 m². Find the pressure.

    Formula:Pressure

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

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