Greece · Grade 10 · Practice Sheet 50

1. 1.

   Find the momentum of a 41 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   €2,800 is invested at 7.5% 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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3. 3.

   A triangle has sides a = 13 cm and b = 14 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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4. 4.

   A force of 108 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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5. 5.

   Solve for x: 2x + 17 = 39.

   Formula:Solving a Linear Equation

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

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6. 6.

   In a triangle, a = 14, b = 9 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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7. 7.

   Find the momentum of a 21 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A population of 5,400 grows 3% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A triangle has sides a = 16 cm and b = 17 cm with an included angle C = 120°. 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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10. 10.

    An object with initial velocity 11 m/s accelerates at 3.5 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 11 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    A force of 377 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A triangle has sides a = 17 cm and b = 13 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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14. 14.

    A body starts at 7 m/s and accelerates at 5.5 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A device runs at 201 V drawing 5.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Solve using the quadratic formula: x² + 3x + 0 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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17. 17.

    Find the momentum of a 21 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Solve for x: 6x + 19 = 43.

    Formula:Solving a Linear Equation

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

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19. 19.

    A force of 296 N acts on an area of 5.4 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A right-angled triangle has legs of 12 cm and 3 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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