Taiwan · Grade 10 · Practice Sheet 38

1. 1.

   A cone has base radius 6 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A value changes from 91 to 191. 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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4. 4.

   Find the momentum of a 38 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A wave has frequency 692 Hz and wavelength 1.23 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A force of 147 N acts on an area of 8.1 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A device runs at 18 V drawing 0.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the gravitational potential energy of a 21 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Solve for x: 5x + 6 = 21.

   Formula:Solving a Linear Equation

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

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10. 10.

    Solve using the quadratic formula: x² − 1x − 12 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    Find the gravitational potential energy of a 39 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    In a triangle, a = 5, b = 5 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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13. 13.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 10 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    A force of 291 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A wave has frequency 650 Hz and wavelength 4.76 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A 2 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    A body starts at 20 m/s and accelerates at 3.8 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A force of 67 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Solve using the quadratic formula: x² + 2x − 3 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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