Lebanon · Grade 10 · Practice Sheet 31

1. 1.

   A right-angled triangle has legs of 20 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.

   A wave has frequency 314 Hz and wavelength 2.2 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A population of 7,500 grows 8% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   A current of 6.7 A flows through a 55 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   LL 2,500 is invested at 8% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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6. 6.

   A bag has 14 equally likely marbles, of which 6 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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7. 7.

   A device runs at 192 V drawing 7.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A cone has base radius 6 cm and height 7 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.

   Find the gravitational potential energy of a 22 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A device runs at 73 V drawing 7.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A force of 120 N moves an object 39 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A body starts at 11 m/s and accelerates at 5.2 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    In a triangle, a = 10, b = 10 and the included angle C = 110°. 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 force needed to accelerate a 22 kg mass at 5.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    LL 2,800 is invested at 8% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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17. 17.

    In a triangle, a = 7, b = 6 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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18. 18.

    A wave has frequency 299 Hz and wavelength 0.68 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A triangle has sides a = 13 cm and b = 12 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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20. 20.

    A body starts at 12 m/s and accelerates at 5.8 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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