Egypt · Grade 10 · Practice Sheet 31

1. 1.

   A right-angled triangle has legs of 3 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   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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3. 3.

   A body starts at 19 m/s and accelerates at 5.8 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A bag has 22 equally likely marbles, of which 9 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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5. 5.

   A right-angled triangle has legs of 9 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A device runs at 118 V drawing 4.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A triangle has sides a = 6 cm and b = 14 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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8. 8.

   In a triangle, a = 15, b = 9 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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9. 9.

   Solve for x: 7x + 12 = 96.

   Formula:Solving a Linear Equation

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

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10. 10.

    Find the momentum of a 59 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    An object has mass 69 g and volume 10 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A cone has base radius 4 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    A cylinder has radius 14 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    A 18 kg object moves at 12 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Find the force needed to accelerate a 13 kg mass at 5.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A right-angled triangle has legs of 9 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    Find the gravitational potential energy of a 35 kg object raised 4 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A body starts at 6 m/s and accelerates at 5 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    An object has mass 118.8 g and volume 18 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A wave has frequency 41 Hz and wavelength 3.51 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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