Portugal · Ano 10 · Practice Sheet 20

1. 1.

   A force of 42 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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2. 2.

   An object has mass 42 g and volume 21 cm³. Find its density.

   Formula:Density

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

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3. 3.

   Solve for x: 8x + 6 = 62.

   Formula:Solving a Linear Equation

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

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4. 4.

   A triangle has sides a = 17 cm and b = 12 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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5. 5.

   A right-angled triangle has legs of 16 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A bag has 14 equally likely marbles, of which 11 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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7. 7.

   A force of 79 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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8. 8.

   An object has mass 83.6 g and volume 19 cm³. Find its density.

   Formula:Density

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

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9. 9.

   Find the force needed to accelerate a 52 kg mass at 0.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A device runs at 69 V drawing 9.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A cone has base radius 10 cm and height 17 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 population of 3,500 grows 8% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A force of 97 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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14. 14.

    €3,700 is invested at 3% 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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15. 15.

    A force of 404 N acts on an area of 3.7 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Solve using the quadratic formula: x² − 8x + 15 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 11 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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18. 18.

    Find the force needed to accelerate a 47 kg mass at 7.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    An object with initial velocity 7 m/s accelerates at 4.3 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    Find the force needed to accelerate a 43 kg mass at 1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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