Kuwait · Grade 10 · Practice Sheet 27

1. 1.

   A triangle has sides a = 11 cm and b = 7 cm with an included angle C = 45°. 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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2. 2.

   A device runs at 234 V drawing 4.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A population of 4,600 grows 5% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   A device runs at 57 V drawing 9.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A cone has base radius 9 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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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 gravitational potential energy of a 41 kg object raised 40 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A body starts at 16 m/s and accelerates at 1 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A cylinder has radius 8 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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11. 11.

    A wave has frequency 629 Hz and wavelength 1.09 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A device runs at 24 V drawing 1.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    An object with initial velocity 4 m/s accelerates at 2.9 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.

    In a triangle, a = 14, b = 14 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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16. 16.

    Find the gravitational potential energy of a 2 kg object raised 11 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    KD 3,000 is invested at 3% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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18. 18.

    A bag has 29 equally likely marbles, of which 22 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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19. 19.

    A cylinder has radius 2 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A force of 58 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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