Cambodia · Grade 12 · Practice Sheet 45

1. 1.

   Find the force needed to accelerate a 14 kg mass at 8.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   ៛ 3,200 is invested at 5% compound interest per annum for 4 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.

   A cone has base radius 7 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 4 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A force of 56 N acts on an area of 4.9 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Solve using the quadratic formula: x² + 0x − 36 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A body starts at 20 m/s and accelerates at 3.4 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   Find the sum of the first 14 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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9. 9.

   Find the momentum of a 37 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    In a triangle, a = 12, b = 15 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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11. 11.

    A triangle has sides a = 13 cm and b = 12 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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12. 12.

    A force of 493 N acts on an area of 5.2 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A body starts at 4 m/s and accelerates at 4.5 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    Find the force needed to accelerate a 36 kg mass at 3.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 40 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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16. 16.

    Find the momentum of a 39 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A cone has base radius 11 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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18. 18.

    A wave has frequency 310 Hz and wavelength 2.83 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    In a triangle, a = 15, b = 13 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    Find the force needed to accelerate a 33 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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