France · Classe 10 · Practice Sheet 35

1. 1.

   In a triangle, a = 9, b = 10 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   A device runs at 102 V drawing 7.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A wave has frequency 498 Hz and wavelength 2.93 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the momentum of a 44 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A force of 475 N acts on an area of 6.9 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   A 10 kg object moves at 21 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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8. 8.

   A right-angled triangle has legs of 14 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   A value changes from 79 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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10. 10.

    A wave has frequency 616 Hz and wavelength 1.68 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A right-angled triangle has legs of 15 cm and 5 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    €2,500 is invested at 6% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

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

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13. 13.

    In a triangle, a = 14, b = 13 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    A force of 73 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    €1,400 is invested at 3% compound interest per annum for 3 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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16. 16.

    A cylinder has radius 2 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    A population of 8,600 grows 10% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Find the force needed to accelerate a 25 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    An object with initial velocity 10 m/s accelerates at 3.6 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    A force of 30 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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