Nigeria · Grade 10 · Practice Sheet 33

1. 1.

   Find the momentum of a 26 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Solve using the quadratic formula: x² + 1x − 6 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A force of 223 N acts on an area of 3.1 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   An object with initial velocity 6 m/s accelerates at 2.9 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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5. 5.

   Find the momentum of a 58 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A right-angled triangle has legs of 20 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   Find the force needed to accelerate a 9 kg mass at 8.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A wave has frequency 132 Hz and wavelength 1.6 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A cone has base radius 4 cm and height 7 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.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 4 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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11. 11.

    A device runs at 53 V drawing 7.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A current of 0.6 A flows through a 35 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    ₦3,300 is invested at 5% 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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14. 14.

    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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15. 15.

    Find the momentum of a 46 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    An object with initial velocity 15 m/s accelerates at 3.3 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    A device runs at 26 V drawing 0.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    An object has mass 142.5 g and volume 25 cm³. Find its density.

    Formula:Density

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

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19. 19.

    A right-angled triangle has legs of 18 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    Find the force needed to accelerate a 10 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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