Colombia · Grado 10 · Practice Sheet 43

1. 1.

   In a triangle, a = 5, b = 14 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   A 19 kg object moves at 25 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Find the force needed to accelerate a 44 kg mass at 5.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A 13 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   $4,700 is invested at 4% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

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

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6. 6.

   A wave has frequency 446 Hz and wavelength 4.52 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A current of 0.7 A flows through a 14 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 41 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A population of 3,300 grows 2% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    $700 is invested at 3% compound interest per annum for 2 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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11. 11.

    A bag has 19 equally likely marbles, of which 4 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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12. 12.

    A force of 113 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A wave has frequency 371 Hz and wavelength 0.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 2 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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15. 15.

    A cylinder has radius 7 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    A bag has 23 equally likely marbles, of which 11 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.

    A wave has frequency 734 Hz and wavelength 0.47 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the force needed to accelerate a 11 kg mass at 2.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A force of 27 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A cylinder has radius 9 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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