Singapore · Grade 10 · Practice Sheet 30

1. 1.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 11 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A value changes from 72 to 46. 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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3. 3.

   A current of 5.8 A flows through a 51 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   An object has mass 119.6 g and volume 23 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A wave has frequency 228 Hz and wavelength 2.59 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A device runs at 146 V drawing 9.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A force of 296 N acts on an area of 9.5 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the momentum of a 22 kg object moving at 23 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A force of 100 N acts on an area of 5 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A wave has frequency 800 Hz and wavelength 3.06 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A population of 2,600 grows 8% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    Solve using the quadratic formula: x² + 7x + 12 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A force of 66 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the gravitational potential energy of a 47 kg object raised 34 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A device runs at 208 V drawing 2.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A wave has frequency 840 Hz and wavelength 2.91 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the momentum of a 30 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Solve for x: 8x + 15 = 31.

    Formula:Solving a Linear Equation

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

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19. 19.

    A device runs at 156 V drawing 6.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    An object with initial velocity 12 m/s accelerates at 1.9 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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