Jordan · Grade 10 · Practice Sheet 15

1. 1.

   A body starts at 6 m/s and accelerates at 5.9 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A wave has frequency 124 Hz and wavelength 1.41 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 5 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   Solve using the quadratic formula: x² − 6x + 5 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   An object with initial velocity 8 m/s accelerates at 3.5 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A cylinder has radius 11 cm and height 26 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   Solve using the quadratic formula: x² + 6x + 5 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   JD 4,000 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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9. 9.

   A 12 kg object moves at 6 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    A population of 8,900 grows 3% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A current of 6.5 A flows through a 34 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A force of 372 N acts on an area of 5.5 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A value changes from 161 to 39. 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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14. 14.

    In a triangle, a = 15, b = 9 and the included angle C = 60°. 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.

    A force of 5 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    JD 1,600 is invested at 8% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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17. 17.

    Solve for x: 7x + 10 = 66.

    Formula:Solving a Linear Equation

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

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18. 18.

    A cylinder has radius 11 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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19. 19.

    A 36 kg object moves at 12 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A body starts at 2 m/s and accelerates at 2 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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