Philippines · Grade 12 · Practice Sheet 14

1. 1.

   A wave has frequency 253 Hz and wavelength 4.23 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   ₱3,400 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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3. 3.

   Solve using the quadratic formula: x² + 7x + 12 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 4 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   Find the force needed to accelerate a 22 kg mass at 2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the gravitational potential energy of a 39 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A body starts at 1 m/s and accelerates at 4.8 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A cone has base radius 4 cm and height 5 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 force needed to accelerate a 17 kg mass at 6.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 13 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    An object with initial velocity 8 m/s accelerates at 2 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A device runs at 39 V drawing 6.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the gravitational potential energy of a 16 kg object raised 11 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    In a triangle, a = 5, b = 5 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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16. 16.

    Find the momentum of a 17 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    Find the sum of the first 8 terms of a geometric series with first term a = 2 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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18. 18.

    Find the gravitational potential energy of a 23 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A cone has base radius 8 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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20. 20.

    Two masses 2,300 kg and 150 kg are 17 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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