Hong Kong · Grade 10 · Practice Sheet 17

1. 1.

   A right-angled triangle has legs of 7 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A force of 81 N moves an object 29 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   HK$ 2,800 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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4. 4.

   Find the momentum of a 38 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   HK$ 1,200 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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6. 6.

   A value changes from 111 to 213. 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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7. 7.

   A device runs at 77 V drawing 6.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Solve for x: 3x + 9 = 27.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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9. 9.

   A population of 8,100 grows 2% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    A force of 108 N moves an object 31 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    In a triangle, a = 14, b = 14 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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12. 12.

    A value changes from 31 to 66. 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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13. 13.

    A cylinder has radius 12 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    A body starts at 9 m/s and accelerates at 1.1 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A force of 167 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A force of 111 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A body starts at 6 m/s and accelerates at 2.5 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A device runs at 108 V drawing 4.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A bag has 26 equally likely marbles, of which 8 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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20. 20.

    Solve for x: 9x + 17 = 62.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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