Peru · Grado 10 · Practice Sheet 19

1. 1.

   A current of 1.5 A flows through a 43 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   Solve using the quadratic formula: x² + 4x − 5 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A wave has frequency 735 Hz and wavelength 1.22 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the momentum of a 1 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Solve using the quadratic formula: x² + 4x + 0 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   An object has mass 161 g and volume 23 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A bag has 15 equally likely marbles, of which 13 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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8. 8.

   S/ 2,900 is invested at 3% 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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9. 9.

   A population of 6,300 grows 10% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    In a triangle, a = 17, b = 17 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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11. 11.

    Find the force needed to accelerate a 37 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A population of 8,200 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the force needed to accelerate a 49 kg mass at 6.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A device runs at 128 V drawing 6.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    An object has mass 243.2 g and volume 38 cm³. Find its density.

    Formula:Density

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

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16. 16.

    Solve using the quadratic formula: x² + 7x + 10 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    A wave has frequency 338 Hz and wavelength 4.1 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A value changes from 128 to 140. 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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19. 19.

    A wave has frequency 621 Hz and wavelength 0.82 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 4 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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