South Korea · Grade 10 · Practice Sheet 49

1. 1.

   ₩1,200 is invested at 10% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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2. 2.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 7 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   ₩2,200 is invested at 5% 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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4. 4.

   A cone has base radius 2 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   Find the momentum of a 21 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Solve using the quadratic formula: x² − 10x + 24 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A population of 5,200 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A force of 385 N acts on an area of 1.4 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A value changes from 196 to 139. 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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10. 10.

    A force of 41 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A force of 301 N acts on an area of 3.8 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    ₩2,100 is invested at 3% compound interest per annum for 5 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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13. 13.

    A bag has 9 equally likely marbles, of which 3 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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14. 14.

    Solve for x: 2x + 9 = 33.

    Formula:Solving a Linear Equation

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

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15. 15.

    Find the force needed to accelerate a 30 kg mass at 7.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A 10 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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17. 17.

    A value changes from 73 to 189. 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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18. 18.

    A device runs at 220 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Solve using the quadratic formula: x² + 7x + 12 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A body starts at 9 m/s and accelerates at 2.5 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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