Spain · Grado 10 · Practice Sheet 42

1. 1.

   A device runs at 102 V drawing 9.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   In a triangle, a = 14, b = 14 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   A body starts at 4 m/s and accelerates at 3 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   €2,000 is invested at 5% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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5. 5.

   Solve for x: 5x + 12 = 52.

   Formula:Solving a Linear Equation

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

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6. 6.

   A cylinder has radius 13 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   A right-angled triangle has legs of 11 cm and 15 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   A wave has frequency 44 Hz and wavelength 0.86 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A value changes from 84 to 58. 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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10. 10.

    A device runs at 186 V drawing 4.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A wave has frequency 162 Hz and wavelength 4.13 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A bag has 15 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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13. 13.

    A force of 72 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A wave has frequency 707 Hz and wavelength 1.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A value changes from 181 to 112. 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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16. 16.

    A bag has 10 equally likely marbles, of which 6 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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17. 17.

    €2,200 is invested at 4% compound interest per annum for 5 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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18. 18.

    A cylinder has radius 13 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A triangle has sides a = 17 cm and b = 12 cm with an included angle C = 120°. 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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20. 20.

    Find the force needed to accelerate a 6 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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