Lebanon · Grade 10 · Practice Sheet 44

1. 1.

   Find the momentum of a 53 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A triangle has sides a = 9 cm and b = 15 cm with an included angle C = 30°. 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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3. 3.

   A right-angled triangle has legs of 16 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   Find the force needed to accelerate a 16 kg mass at 2.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A current of 5.3 A flows through a 46 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A wave has frequency 160 Hz and wavelength 3.89 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   LL 2,400 is invested at 3% 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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8. 8.

   A cone has base radius 9 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   Solve for x: 2x + 3 = 15.

   Formula:Solving a Linear Equation

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

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10. 10.

    A device runs at 145 V drawing 5.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the momentum of a 2 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Solve for x: 4x + 12 = 60.

    Formula:Solving a Linear Equation

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

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13. 13.

    Solve using the quadratic formula: x² + 3x − 4 = 0.

    Formula:Quadratic Formula

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

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14. 14.

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

    Formula:Work Done

    $W = F d$

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15. 15.

    In a triangle, a = 16, b = 18 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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16. 16.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 11 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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17. 17.

    A force of 495 N acts on an area of 7.1 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Solve using the quadratic formula: x² − 3x − 4 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    An object has mass 101.2 g and volume 22 cm³. Find its density.

    Formula:Density

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

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20. 20.

    Find the force needed to accelerate a 57 kg mass at 8.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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