Greece · Grade 10 · Practice Sheet 19

1. 1.

   A wave has frequency 146 Hz and wavelength 4.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A cone has base radius 12 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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3. 3.

   A population of 4,700 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   An object has mass 84 g and volume 40 cm³. Find its density.

   Formula:Density

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

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5. 5.

   Find the force needed to accelerate a 11 kg mass at 3.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   €2,100 is invested at 8% 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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7. 7.

   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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8. 8.

   In a triangle, a = 6, b = 6 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   Find the force needed to accelerate a 47 kg mass at 6.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A triangle has sides a = 7 cm and b = 17 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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11. 11.

    In a triangle, a = 13, b = 5 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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12. 12.

    €4,700 is invested at 10% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

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

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13. 13.

    A current of 5.3 A flows through a 9 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the momentum of a 57 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    An object with initial velocity 11 m/s accelerates at 2.7 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

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

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    Solve for x: 9x + 18 = 36.

    Formula:Solving a Linear Equation

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

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18. 18.

    Find the volume of a sphere of radius 9 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 22 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A cylinder has radius 6 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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