Denmark · Grade 10 · Practice Sheet 18

1. 1.

   Solve for x: 9x + 11 = 65.

   Formula:Solving a Linear Equation

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

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2. 2.

   A device runs at 86 V drawing 5.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A body starts at 1 m/s and accelerates at 3.6 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A triangle has sides a = 7 cm and b = 7 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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5. 5.

   kr 3,000 is invested at 6% 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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6. 6.

   A bag has 15 equally likely marbles, of which 5 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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7. 7.

   A population of 7,200 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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8. 8.

   A cone has base radius 3 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   A device runs at 79 V drawing 1.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Solve using the quadratic formula: x² − 7x + 10 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    Find the force needed to accelerate a 19 kg mass at 2.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    kr 4,600 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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13. 13.

    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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14. 14.

    kr 2,400 is invested at 4% 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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15. 15.

    A triangle has sides a = 11 cm and b = 16 cm with an included angle C = 90°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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16. 16.

    An object has mass 10.8 g and volume 9 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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17. 17.

    A right-angled triangle has legs of 7 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A wave has frequency 235 Hz and wavelength 2 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Solve for x: 7x + 14 = 84.

    Formula:Solving a Linear Equation

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

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20. 20.

    kr 1,100 is invested at 6% compound interest per annum for 3 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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