Russia · Grade 12 · Practice Sheet 24

1. 1.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 9 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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2. 2.

   Find the force needed to accelerate a 37 kg mass at 4.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the sum of the first 8 terms of a geometric series with first term a = 7 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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4. 4.

   A force of 212 N acts on an area of 7.1 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   ₽3,200 is invested at 6% compound interest per annum for 5 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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6. 6.

   A device runs at 219 V drawing 2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 7 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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8. 8.

   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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9. 9.

   ₽600 is invested at 3% 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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10. 10.

    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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11. 11.

    Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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12. 12.

    Solve using the quadratic formula: x² + 0x − 9 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    A current of 7.3 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Solve using the quadratic formula: x² − 1x − 2 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    A body starts at 6 m/s and accelerates at 5.2 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    An object with initial velocity 4 m/s accelerates at 1.3 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    Find the force needed to accelerate a 24 kg mass at 8.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A force of 67 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A wave has frequency 635 Hz and wavelength 3.71 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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