Jordan · Grade 10 · Practice Sheet 47

1. 1.

   A force of 255 N acts on an area of 9.7 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the momentum of a 44 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A cylinder has radius 8 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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4. 4.

   Find the gravitational potential energy of a 12 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Solve using the quadratic formula: x² + 8x + 15 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   A right-angled triangle has legs of 14 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A value changes from 171 to 208. 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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8. 8.

   A 38 kg object moves at 19 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Find the gravitational potential energy of a 43 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A population of 2,500 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A bag has 14 equally likely marbles, of which 11 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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12. 12.

    A 13 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    An object with initial velocity 15 m/s accelerates at 4.3 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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14. 14.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A right-angled triangle has legs of 15 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A triangle has sides a = 11 cm and b = 10 cm with an included angle C = 90°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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17. 17.

    Find the force needed to accelerate a 57 kg mass at 8.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Solve for x: 2x + 20 = 30.

    Formula:Solving a Linear Equation

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

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19. 19.

    A wave has frequency 710 Hz and wavelength 3.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the gravitational potential energy of a 47 kg object raised 4 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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