Ecuador · Grado 10 · Practice Sheet 7

1. 1.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 10 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   $4,000 is invested at 6% compound interest per annum for 3 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 value changes from 112 to 174. 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.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 8 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A right-angled triangle has legs of 14 cm and 13 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A cone has base radius 6 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A current of 5.8 A flows through a 7 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Find the gravitational potential energy of a 47 kg object raised 28 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A wave has frequency 127 Hz and wavelength 0.58 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the momentum of a 44 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A triangle has sides a = 17 cm and b = 19 cm with an included angle C = 30°. 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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12. 12.

    A cylinder has radius 14 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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13. 13.

    A bag has 15 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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14. 14.

    In a triangle, a = 7, b = 9 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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15. 15.

    A wave has frequency 36 Hz and wavelength 0.46 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Find the force needed to accelerate a 20 kg mass at 3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A device runs at 194 V drawing 9.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    Find the force needed to accelerate a 46 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 26 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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