Morocco · Grade 10 · Practice Sheet 37

1. 1.

   Find the momentum of a 51 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A triangle has sides a = 14 cm and b = 13 cm with an included angle C = 60°. 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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3. 3.

   Solve using the quadratic formula: x² + 2x − 8 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A triangle has sides a = 9 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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5. 5.

   A population of 8,200 grows 10% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A right-angled triangle has legs of 3 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A wave has frequency 185 Hz and wavelength 2.85 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   An object has mass 170.2 g and volume 37 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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9. 9.

   A device runs at 150 V drawing 1.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A wave has frequency 581 Hz and wavelength 0.89 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A cone has base radius 11 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    A force of 63 N moves an object 28 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    MAD 1,800 is invested at 6% 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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14. 14.

    Find the sum of the first 11 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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15. 15.

    A cylinder has radius 3 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    A value changes from 80 to 76. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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17. 17.

    A device runs at 62 V drawing 8.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A wave has frequency 697 Hz and wavelength 3.33 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    MAD 3,300 is invested at 3% 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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20. 20.

    A force of 358 N acts on an area of 6.1 m². Find the pressure.

    Formula:Pressure

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

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