Singapore · Grade 12 · Practice Sheet 7

1. 1.

   Find the force needed to accelerate a 23 kg mass at 7.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 8 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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3. 3.

   Find the gravitational potential energy of a 44 kg object raised 38 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   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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5. 5.

   Two masses 5,500 kg and 860 kg are 13 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 gravitational potential energy of a 36 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Two masses 2,700 kg and 600 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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8. 8.

   Find the momentum of a 50 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A force of 455 N acts on an area of 7.6 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    In a triangle, a = 10, b = 8 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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11. 11.

    Find the momentum of a 10 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 3 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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13. 13.

    Find the gravitational potential energy of a 48 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A device runs at 180 V drawing 7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    $3,200 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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16. 16.

    Solve using the quadratic formula: x² − 11x + 30 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    A triangle has sides a = 17 cm and b = 9 cm with an included angle C = 120°. 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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18. 18.

    A cone has base radius 7 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A triangle has sides a = 19 cm and b = 8 cm with an included angle C = 120°. 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.

    Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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