Tunisia · Grade 10 · Practice Sheet 15

1. 1.

   Solve for x: 2x + 11 = 31.

   Formula:Solving a Linear Equation

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

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2. 2.

   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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3. 3.

   A 3 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   DT 2,600 is invested at 4% 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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5. 5.

   A value changes from 152 to 63. 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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6. 6.

   Find the gravitational potential energy of a 14 kg object raised 27 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A device runs at 230 V drawing 6.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   DT 2,200 is invested at 3% compound interest per annum for 2 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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9. 9.

   A bag has 8 equally likely marbles, of which 1 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.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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11. 11.

    A wave has frequency 62 Hz and wavelength 4.6 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A device runs at 131 V drawing 9.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A wave has frequency 116 Hz and wavelength 4.16 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 12 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    Solve for x: 5x + 2 = 12.

    Formula:Solving a Linear Equation

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

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16. 16.

    A wave has frequency 615 Hz and wavelength 3.27 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A 15 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A bag has 26 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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19. 19.

    A force of 159 N acts on an area of 5.2 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    In a triangle, a = 16, b = 7 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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