United Arab Emirates · Grade 10 · Practice Sheet 44

1. 1.

   Find the force needed to accelerate a 13 kg mass at 8.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A triangle has sides a = 19 cm and b = 5 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 body starts at 11 m/s and accelerates at 4.7 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A cone has base radius 12 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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5. 5.

   A wave has frequency 219 Hz and wavelength 4.99 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the force needed to accelerate a 20 kg mass at 8.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A force of 314 N acts on an area of 1.2 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 6 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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9. 9.

   A cylinder has radius 8 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A right-angled triangle has legs of 16 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    An object with initial velocity 1 m/s accelerates at 3.5 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 3 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    An object has mass 81.4 g and volume 22 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A value changes from 120 to 24. 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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15. 15.

    A triangle has sides a = 7 cm and b = 17 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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16. 16.

    Solve for x: 5x + 15 = 45.

    Formula:Solving a Linear Equation

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

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17. 17.

    Find the force needed to accelerate a 31 kg mass at 8.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A wave has frequency 695 Hz and wavelength 3.34 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A device runs at 91 V drawing 5.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A cone has base radius 5 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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