Iraq · Grade 10 · Practice Sheet 3

1. 1.

   Solve using the quadratic formula: x² + 1x − 2 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   Find the momentum of a 12 kg object moving at 22 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A wave has frequency 183 Hz and wavelength 2.72 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Solve for x: 3x + 13 = 19.

   Formula:Solving a Linear Equation

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

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5. 5.

   A right-angled triangle has legs of 12 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Find the momentum of a 30 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A force of 32 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   IQD 1,100 is invested at 6% 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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9. 9.

   A cone has base radius 12 cm and height 20 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.

    An object has mass 120 g and volume 20 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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11. 11.

    A cone has base radius 10 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    Solve using the quadratic formula: x² − 6x + 8 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    Find the force needed to accelerate a 12 kg mass at 2.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A force of 78 N acts on an area of 6.2 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    An object with initial velocity 6 m/s accelerates at 1.8 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    A force of 339 N acts on an area of 6.1 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A current of 5.1 A flows through a 13 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Solve using the quadratic formula: x² − 5x − 6 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Find the gravitational potential energy of a 31 kg object raised 3 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Find the momentum of a 37 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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