Portugal · Ano 10 · Practice Sheet 6

1. 1.

   A bag has 20 equally likely marbles, of which 14 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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2. 2.

   Solve for x: 5x + 2 = 32.

   Formula:Solving a Linear Equation

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

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3. 3.

   A cylinder has radius 11 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   €4,300 is invested at 7.5% 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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5. 5.

   Find the force needed to accelerate a 51 kg mass at 5.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A cone has base radius 11 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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7. 7.

   A right-angled triangle has legs of 20 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   In a triangle, a = 17, b = 18 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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9. 9.

   Find the momentum of a 57 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A force of 139 N acts on an area of 3.6 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    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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12. 12.

    In a triangle, a = 17, b = 12 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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13. 13.

    €4,000 is invested at 8% 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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14. 14.

    An object has mass 68 g and volume 34 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A current of 7.1 A flows through a 51 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 6 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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17. 17.

    A value changes from 166 to 184. 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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18. 18.

    In a triangle, a = 18, b = 15 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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19. 19.

    A wave has frequency 343 Hz and wavelength 0.21 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Solve for x: 4x + 18 = 62.

    Formula:Solving a Linear Equation

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

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