Russia · Grade 10 · Practice Sheet 36

1. 1.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 3 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.

   A triangle has sides a = 15 cm and b = 9 cm with an included angle C = 90°. 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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3. 3.

   A right-angled triangle has legs of 14 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   An object with initial velocity 0 m/s accelerates at 3.5 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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5. 5.

   Find the force needed to accelerate a 43 kg mass at 4.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A bag has 26 equally likely marbles, of which 7 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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7. 7.

   Find the momentum of a 29 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A cone has base radius 8 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   Solve for x: 4x + 14 = 34.

   Formula:Solving a Linear Equation

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

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10. 10.

    ₽1,700 is invested at 5% 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 force of 54 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A population of 7,300 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    ₽2,300 is invested at 5% 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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14. 14.

    A force of 368 N acts on an area of 3.8 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Find the momentum of a 12 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 2 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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17. 17.

    An object has mass 64.8 g and volume 24 cm³. Find its density.

    Formula:Density

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

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18. 18.

    ₽4,600 is invested at 5% 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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19. 19.

    Find the gravitational potential energy of a 27 kg object raised 36 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A current of 7.7 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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