Philippines · Grade 12 · Practice Sheet 8

1. 1.

   An object with initial velocity 15 m/s accelerates at 2.6 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   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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3. 3.

   A body starts at 3 m/s and accelerates at 4.1 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A cone has base radius 9 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   Two masses 2,500 kg and 570 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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6. 6.

   Find the sum of the first 8 terms of a geometric series with first term a = 6 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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7. 7.

   In a triangle, a = 15, b = 17 and the included angle C = 80°. 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.

   A body starts at 19 m/s and accelerates at 1.2 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 8 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    A population of 6,700 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A wave has frequency 649 Hz and wavelength 0.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Solve using the quadratic formula: x² + 3x − 18 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A cone has base radius 2 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    A body starts at 12 m/s and accelerates at 3.9 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A current of 3 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    ₱1,900 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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17. 17.

    An object with initial velocity 7 m/s accelerates at 1.3 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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18. 18.

    A triangle has sides a = 7 cm and b = 7 cm with an included angle C = 90°. 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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19. 19.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 6 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    A 38 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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