United States · Grade 10 · Practice Sheet 49

1. 1.

   A force of 35 N acts on an area of 1.9 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A wave has frequency 185 Hz and wavelength 0.96 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   An object with initial velocity 10 m/s accelerates at 1.5 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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4. 4.

   A population of 1,000 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   $3,700 is invested at 4% 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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6. 6.

   Solve using the quadratic formula: x² − 7x + 6 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A force of 5 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the momentum of a 26 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A triangle has sides a = 15 cm and b = 16 cm with an included angle C = 45°. 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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10. 10.

    A 6 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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11. 11.

    Solve for x: 8x + 8 = 96.

    Formula:Solving a Linear Equation

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

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12. 12.

    An object with initial velocity 2 m/s accelerates at 2.3 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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13. 13.

    A current of 7.8 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A 40 kg object moves at 17 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    A force of 253 N acts on an area of 5.9 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the gravitational potential energy of a 13 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    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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18. 18.

    In a triangle, a = 12, b = 16 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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19. 19.

    Find the gravitational potential energy of a 27 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Find the force needed to accelerate a 60 kg mass at 3.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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