Argentina · Grado 10 · Practice Sheet 35

1. 1.

   A force of 268 N acts on an area of 8.9 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   In a triangle, a = 9, b = 14 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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3. 3.

   A cone has base radius 10 cm and height 22 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 population of 2,000 grows 10% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   Find the gravitational potential energy of a 11 kg object raised 36 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   $3,200 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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7. 7.

   A bag has 14 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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8. 8.

   A value changes from 47 to 238. 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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9. 9.

   A force of 105 N acts on an area of 4.7 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Solve for x: 7x + 5 = 68.

    Formula:Solving a Linear Equation

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

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11. 11.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    An object has mass 27.2 g and volume 8 cm³. Find its density.

    Formula:Density

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

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13. 13.

    In a triangle, a = 6, b = 11 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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14. 14.

    $1,800 is invested at 8% 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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15. 15.

    Find the momentum of a 23 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the gravitational potential energy of a 31 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A cone has base radius 12 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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18. 18.

    A force of 88 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 4 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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20. 20.

    Find the gravitational potential energy of a 34 kg object raised 32 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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