Hungary · Grade 10 · Practice Sheet 22

1. 1.

   A force of 236 N acts on an area of 6.6 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A triangle has sides a = 5 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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3. 3.

   Find the momentum of a 26 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A bag has 20 equally likely marbles, of which 5 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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5. 5.

   A body starts at 4 m/s and accelerates at 2.5 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A current of 4.5 A flows through a 36 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the momentum of a 33 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Find the gravitational potential energy of a 38 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A bag has 11 equally likely marbles, of which 6 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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10. 10.

    A right-angled triangle has legs of 16 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    A value changes from 103 to 62. 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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12. 12.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 7 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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13. 13.

    A force of 390 N acts on an area of 6.7 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    In a triangle, a = 9, b = 11 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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15. 15.

    Solve using the quadratic formula: x² − 6x + 0 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    Find the force needed to accelerate a 8 kg mass at 4.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A triangle has sides a = 18 cm and b = 10 cm with an included angle C = 45°. 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 force of 61 N moves an object 8 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A triangle has sides a = 15 cm and b = 18 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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20. 20.

    Solve for x: 8x + 19 = 83.

    Formula:Solving a Linear Equation

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

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