China · Grade 10 · Practice Sheet 5

1. 1.

   A wave has frequency 397 Hz and wavelength 0.27 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   An object has mass 107.8 g and volume 14 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A device runs at 223 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A value changes from 179 to 89. 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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5. 5.

   Find the momentum of a 39 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A value changes from 21 to 184. 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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7. 7.

   A device runs at 163 V drawing 4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   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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9. 9.

   Find the momentum of a 4 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A body starts at 13 m/s and accelerates at 1.5 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A force of 418 N acts on an area of 6.6 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    ¥500 is invested at 4% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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13. 13.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 4 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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14. 14.

    In a triangle, a = 17, b = 15 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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15. 15.

    A force of 107 N moves an object 31 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    In a triangle, a = 15, b = 12 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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17. 17.

    A cone has base radius 7 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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18. 18.

    A bag has 17 equally likely marbles, of which 3 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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19. 19.

    In a triangle, a = 5, b = 18 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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20. 20.

    A right-angled triangle has legs of 12 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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