Mongolia · Grade 10 · Practice Sheet 6

1. 1.

   A value changes from 170 to 165. 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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2. 2.

   A bag has 18 equally likely marbles, of which 8 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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3. 3.

   A force of 90 N acts on an area of 7 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A population of 8,900 grows 3% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   ₮3,100 is invested at 7.5% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

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

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6. 6.

   A value changes from 49 to 24. 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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7. 7.

   In a triangle, a = 13, b = 12 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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8. 8.

   A body starts at 12 m/s and accelerates at 3.7 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Find the force needed to accelerate a 13 kg mass at 0.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A cone has base radius 5 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    A body starts at 10 m/s and accelerates at 2 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    ₮1,500 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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13. 13.

    A cylinder has radius 9 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    ₮500 is invested at 4% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

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

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15. 15.

    A device runs at 203 V drawing 8.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A right-angled triangle has legs of 17 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    Solve for x: 9x + 14 = 104.

    Formula:Solving a Linear Equation

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

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18. 18.

    Find the force needed to accelerate a 14 kg mass at 6.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A population of 5,400 grows 8% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    A bag has 14 equally likely marbles, of which 4 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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