Russia · Grade 10 · Practice Sheet 21

1. 1.

   A bag has 16 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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2. 2.

   A value changes from 128 to 215. 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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3. 3.

   An object has mass 21 g and volume 10 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A force of 410 N acts on an area of 2.3 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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5. 5.

   In a triangle, a = 10, b = 15 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   A cylinder has radius 9 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   In a triangle, a = 17, b = 16 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   A wave has frequency 481 Hz and wavelength 0.6 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 11 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    ₽1,200 is invested at 3% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

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

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11. 11.

    ₽4,000 is invested at 8% 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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12. 12.

    A cylinder has radius 10 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    A population of 1,100 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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14. 14.

    Find the gravitational potential energy of a 41 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    An object has mass 220.4 g and volume 29 cm³. Find its density.

    Formula:Density

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

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16. 16.

    A current of 7.6 A flows through a 43 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A triangle has sides a = 5 cm and b = 6 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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18. 18.

    A body starts at 1 m/s and accelerates at 1.1 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A value changes from 20 to 29. 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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20. 20.

    A cone has base radius 8 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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