Hungary · Grade 10 · Practice Sheet 24

1. 1.

   Solve using the quadratic formula: x² + 0x − 1 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   A population of 3,500 grows 2% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 1 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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4. 4.

   A force of 379 N acts on an area of 4.3 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A device runs at 188 V drawing 9.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A right-angled triangle has legs of 18 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A device runs at 24 V drawing 1.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A value changes from 22 to 92. 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 current of 7 A flows through a 34 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Ft 900 is invested at 5% 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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11. 11.

    A cone has base radius 8 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    In a triangle, a = 10, b = 5 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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13. 13.

    A device runs at 81 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A value changes from 161 to 52. 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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15. 15.

    Find the momentum of a 25 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the force needed to accelerate a 22 kg mass at 3.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Solve for x: 9x + 6 = 69.

    Formula:Solving a Linear Equation

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

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18. 18.

    Find the force needed to accelerate a 31 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A current of 7.9 A flows through a 46 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A cylinder has radius 10 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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