Hong Kong · Grade 10 · Practice Sheet 42

1. 1.

   Solve for x: 9x + 18 = 90.

   Formula:Solving a Linear Equation

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

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2. 2.

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

   Formula:Quadratic Formula

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

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3. 3.

   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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4. 4.

   A population of 1,800 grows 2% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   HK$ 4,600 is invested at 5% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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6. 6.

   HK$ 1,300 is invested at 4% 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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7. 7.

   A body starts at 0 m/s and accelerates at 1.1 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A current of 7.3 A flows through a 14 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   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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10. 10.

    A triangle has sides a = 6 cm and b = 5 cm with an included angle C = 90°. 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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11. 11.

    A force of 107 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    Find the momentum of a 18 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    An object with initial velocity 4 m/s accelerates at 2.4 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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14. 14.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    Find the force needed to accelerate a 36 kg mass at 1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A population of 2,500 grows 2% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    Solve using the quadratic formula: x² − 2x − 3 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A current of 2 A flows through a 12 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A body starts at 10 m/s and accelerates at 1 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A device runs at 234 V drawing 4.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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