Philippines · Grade 12 · Practice Sheet 48

1. 1.

   Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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2. 2.

   Two masses 5,500 kg and 640 kg are 8 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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3. 3.

   A force of 35 N moves an object 19 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A force of 76 N acts on an area of 3.2 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A 39 kg object moves at 4 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   Solve using the quadratic formula: x² + 4x − 5 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   In a triangle, a = 6, b = 6 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   Solve using the quadratic formula: x² + 8x + 12 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 1 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    ₱2,500 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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11. 11.

    A force of 35 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    An object with initial velocity 10 m/s accelerates at 4 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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13. 13.

    Find the force needed to accelerate a 52 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A device runs at 214 V drawing 6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A cone has base radius 7 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A force of 45 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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18. 18.

    A body starts at 18 m/s and accelerates at 4.1 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A triangle has sides a = 10 cm and b = 18 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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20. 20.

    Solve using the quadratic formula: x² − 3x − 10 = 0.

    Formula:Quadratic Formula

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

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