Argentina · Grado 10 · Practice Sheet 10

1. 1.

   Solve for x: 7x + 1 = 29.

   Formula:Solving a Linear Equation

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

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2. 2.

   A right-angled triangle has legs of 20 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   A value changes from 88 to 167. 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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4. 4.

   A right-angled triangle has legs of 5 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   An object has mass 348 g and volume 40 cm³. Find its density.

   Formula:Density

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

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6. 6.

   A device runs at 47 V drawing 9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the momentum of a 4 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A wave has frequency 28 Hz and wavelength 0.76 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A 37 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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10. 10.

    A bag has 9 equally likely marbles, of which 3 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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11. 11.

    Solve using the quadratic formula: x² − 11x + 30 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A device runs at 90 V drawing 7.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A wave has frequency 62 Hz and wavelength 0.38 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A cylinder has radius 11 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    A cone has base radius 3 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    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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17. 17.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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18. 18.

    A cone has base radius 10 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 8 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    Solve for x: 7x + 11 = 46.

    Formula:Solving a Linear Equation

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

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