Spain · Grado 10 · Practice Sheet 38

1. 1.

   A cone has base radius 4 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   A right-angled triangle has legs of 16 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   A cone has base radius 11 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   A wave has frequency 621 Hz and wavelength 4.5 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A current of 6.8 A flows through a 6 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A value changes from 109 to 45. 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.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 1 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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8. 8.

   In a triangle, a = 14, b = 11 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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9. 9.

   Find the force needed to accelerate a 47 kg mass at 1.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the gravitational potential energy of a 42 kg object raised 32 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    An object has mass 256 g and volume 32 cm³. Find its density.

    Formula:Density

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

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12. 12.

    Find the momentum of a 49 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A device runs at 182 V drawing 4.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    €3,600 is invested at 10% 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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15. 15.

    A bag has 29 equally likely marbles, of which 10 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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16. 16.

    A current of 7.1 A flows through a 48 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    Solve using the quadratic formula: x² + 7x + 6 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A device runs at 100 V drawing 2.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Solve for x: 5x + 20 = 30.

    Formula:Solving a Linear Equation

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

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20. 20.

    An object with initial velocity 11 m/s accelerates at 4.1 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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