Argentina · Grado 10 · Practice Sheet 20

1. 1.

   A cylinder has radius 13 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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2. 2.

   In a triangle, a = 18, b = 18 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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3. 3.

   $500 is invested at 4% compound interest per annum for 3 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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4. 4.

   A force of 87 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A body starts at 0 m/s and accelerates at 5.9 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   $3,900 is invested at 6% compound interest per annum for 3 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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7. 7.

   Find the momentum of a 33 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A force of 475 N acts on an area of 5.8 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A current of 4.4 A flows through a 16 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    $4,400 is invested at 8% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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11. 11.

    A wave has frequency 529 Hz and wavelength 3.74 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    In a triangle, a = 6, b = 10 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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13. 13.

    Solve using the quadratic formula: x² + 2x − 8 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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14. 14.

    A population of 3,900 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A wave has frequency 126 Hz and wavelength 4.19 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A device runs at 12 V drawing 6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A bag has 11 equally likely marbles, of which 2 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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18. 18.

    Find the gravitational potential energy of a 36 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A triangle has sides a = 14 cm and b = 6 cm with an included angle C = 120°. 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 12 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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