Peru · Grado 12 · Practice Sheet 19

1. 1.

   Find the force needed to accelerate a 19 kg mass at 2.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A current of 4.5 A flows through a 6 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Solve using the quadratic formula: x² − 9x + 18 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A force of 33 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A cone has base radius 7 cm and height 9 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.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 10 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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7. 7.

   A cone has base radius 7 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   Find the force needed to accelerate a 16 kg mass at 5.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A device runs at 40 V drawing 5.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    S/ 2,200 is invested at 3% 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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11. 11.

    A force of 348 N acts on an area of 6.1 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A wave has frequency 395 Hz and wavelength 1.21 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Two masses 5,700 kg and 240 kg are 20 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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14. 14.

    A body starts at 3 m/s and accelerates at 1.4 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A force of 71 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A current of 0.9 A flows through a 39 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    An object with initial velocity 2 m/s accelerates at 1.9 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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18. 18.

    Find the sum of the first 3 terms of a geometric series with first term a = 5 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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19. 19.

    Find the gravitational potential energy of a 16 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Find the force needed to accelerate a 39 kg mass at 8.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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