Morocco · Grade 11 · Practice Sheet 40

1. 1.

   A cone has base radius 7 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.

   An object with initial velocity 12 m/s accelerates at 4.8 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   A right-angled triangle has legs of 19 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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4. 4.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 6 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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5. 5.

   Find the gravitational potential energy of a 23 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   A triangle has sides a = 18 cm and b = 10 cm with an included angle C = 45°. 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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7. 7.

   Find the population standard deviation of: 4, 2, 11, 18, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   An object with initial velocity 9 m/s accelerates at 2.9 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   Find the force needed to accelerate a 11 kg mass at 8.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the momentum of a 19 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the force needed to accelerate a 52 kg mass at 8.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A triangle has sides a = 20 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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13. 13.

    Find the population standard deviation of: 11, 2, 11, 12, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A force of 221 N acts on an area of 1.6 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A body starts at 2 m/s and accelerates at 2.4 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the force needed to accelerate a 35 kg mass at 3.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 11 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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18. 18.

    MAD 1,800 is invested at 8% 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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19. 19.

    A population of 7,000 grows 5% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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20. 20.

    Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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