Jordan · Grade 12 · Practice Sheet 17

1. 1.

   Solve using the quadratic formula: x² − 5x − 6 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   A force of 66 N moves an object 25 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the force needed to accelerate a 16 kg mass at 4.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   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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5. 5.

   A device runs at 173 V drawing 7.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the momentum of a 56 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   JD 2,600 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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8. 8.

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

   Formula:Quadratic Formula

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

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9. 9.

   Two masses 6,700 kg and 480 kg are 14 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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10. 10.

    A triangle has sides a = 15 cm and b = 17 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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11. 11.

    A force of 493 N acts on an area of 8.9 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Two masses 3,800 kg and 270 kg are 18 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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13. 13.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 7 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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14. 14.

    Find the momentum of a 7 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A body starts at 19 m/s and accelerates at 5.4 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    An object with initial velocity 13 m/s accelerates at 1.6 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    In a triangle, a = 15, b = 12 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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18. 18.

    Find the force needed to accelerate a 37 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Find the momentum of a 38 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 11 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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