Thailand · Grade 10 · Practice Sheet 19

1. 1.

   A cone has base radius 9 cm and height 10 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 momentum of a 13 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A body starts at 17 m/s and accelerates at 2 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   An object with initial velocity 1 m/s accelerates at 2.1 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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5. 5.

   A 37 kg object moves at 4 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   Find the gravitational potential energy of a 50 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Solve for x: 9x + 3 = 75.

   Formula:Solving a Linear Equation

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

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8. 8.

   An object with initial velocity 14 m/s accelerates at 4.8 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 cone has base radius 4 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A right-angled triangle has legs of 17 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    ฿4,000 is invested at 7.5% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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12. 12.

    A population of 8,800 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the force needed to accelerate a 17 kg mass at 4.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A bag has 15 equally likely marbles, of which 8 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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15. 15.

    A wave has frequency 604 Hz and wavelength 3.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Find the momentum of a 32 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    Find the force needed to accelerate a 55 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    An object with initial velocity 8 m/s accelerates at 2.3 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A population of 7,000 grows 5% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    A force of 474 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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