Portugal · Ano 10 · Practice Sheet 50

1. 1.

   In a triangle, a = 13, b = 11 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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2. 2.

   €3,900 is invested at 4% 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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3. 3.

   A current of 3.1 A flows through a 33 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the gravitational potential energy of a 6 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A wave has frequency 56 Hz and wavelength 2.04 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A value changes from 51 to 136. 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.

   An object with initial velocity 3 m/s accelerates at 1.4 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   Find the force needed to accelerate a 59 kg mass at 4.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   €3,100 is invested at 6% 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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10. 10.

    A value changes from 148 to 148. 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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11. 11.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 11 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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12. 12.

    Find the gravitational potential energy of a 43 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A wave has frequency 682 Hz and wavelength 3.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    €4,000 is invested at 5% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

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

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15. 15.

    A device runs at 111 V drawing 1.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A cone has base radius 3 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    A wave has frequency 521 Hz and wavelength 4.03 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the force needed to accelerate a 6 kg mass at 0.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    An object with initial velocity 5 m/s accelerates at 4.7 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    Solve for x: 2x + 7 = 15.

    Formula:Solving a Linear Equation

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

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