Mongolia · Grade 11 · Practice Sheet 48

1. 1.

   A cone has base radius 3 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   A triangle has sides a = 15 cm and b = 14 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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3. 3.

   A device runs at 31 V drawing 8.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A right-angled triangle has legs of 15 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   A force of 326 N acts on an area of 1.4 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   In a triangle, a = 18, b = 6 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   Find the momentum of a 24 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A triangle has sides a = 20 cm and b = 11 cm with an included angle C = 60°. 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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9. 9.

   A right-angled triangle has legs of 15 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    A force of 10 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A 3 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A wave has frequency 501 Hz and wavelength 0.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    An object with initial velocity 11 m/s accelerates at 1.7 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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14. 14.

    A wave has frequency 164 Hz and wavelength 0.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the momentum of a 7 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A force of 63 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A population of 4,400 grows 5% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Find the force needed to accelerate a 41 kg mass at 5.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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20. 20.

    A population of 7,600 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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