United States · Grade 10 · Practice Sheet 4

1. 1.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 2 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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2. 2.

   A population of 4,300 grows 2% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A value changes from 29 to 96. 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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4. 4.

   $2,800 is invested at 8% compound interest per annum for 4 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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5. 5.

   Find the force needed to accelerate a 28 kg mass at 4.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   An object with initial velocity 10 m/s accelerates at 2.1 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 12 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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8. 8.

   A cylinder has radius 6 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   Solve for x: 8x + 4 = 76.

   Formula:Solving a Linear Equation

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

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10. 10.

    An object with initial velocity 7 m/s accelerates at 4.2 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    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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12. 12.

    A device runs at 22 V drawing 3.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Solve for x: 3x + 6 = 39.

    Formula:Solving a Linear Equation

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

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14. 14.

    A device runs at 164 V drawing 7.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the force needed to accelerate a 39 kg mass at 6.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A wave has frequency 742 Hz and wavelength 1.2 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the sum of the first 18 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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18. 18.

    A wave has frequency 172 Hz and wavelength 4.22 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Solve using the quadratic formula: x² − 4x − 5 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A right-angled triangle has legs of 4 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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