Tunisia · Grade 12 · Practice Sheet 21

1. 1.

   A cone has base radius 5 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   Find the gravitational potential energy of a 14 kg object raised 24 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A force of 183 N acts on an area of 1.4 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Solve using the quadratic formula: x² + 2x − 15 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   DT 2,600 is invested at 5% compound interest per annum for 2 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.

   Find the force needed to accelerate a 23 kg mass at 6.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   DT 1,800 is invested at 3% compound interest per annum for 2 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.

   In a triangle, a = 14, 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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9. 9.

   A current of 5.6 A flows through a 49 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A 24 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    Find the population standard deviation of: 2, 9, 14, 6, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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12. 12.

    DT 2,700 is invested at 3% compound interest per annum for 2 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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13. 13.

    Find the sum of the first 7 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

    A force of 80 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A triangle has sides a = 18 cm and b = 7 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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16. 16.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 10 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    Find the population standard deviation of: 14, 3, 18, 9, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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18. 18.

    Find the force needed to accelerate a 42 kg mass at 6.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A cone has base radius 4 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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20. 20.

    A force of 12 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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