Norway · Grade 10 · Practice Sheet 11

1. 1.

   A bag has 19 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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2. 2.

   In a triangle, a = 13, b = 8 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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3. 3.

   A right-angled triangle has legs of 5 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   kr 1,700 is invested at 3% 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.

   Solve for x: 2x + 11 = 25.

   Formula:Solving a Linear Equation

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

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6. 6.

   A value changes from 144 to 192. 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.

   kr 600 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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8. 8.

   A force of 48 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A wave has frequency 558 Hz and wavelength 4.05 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A 31 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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11. 11.

    A population of 5,200 grows 8% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 8 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    Solve for x: 9x + 9 = 90.

    Formula:Solving a Linear Equation

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

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14. 14.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 3 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.

    A population of 2,900 grows 8% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    Find the momentum of a 26 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    kr 3,700 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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18. 18.

    Solve for x: 5x + 13 = 53.

    Formula:Solving a Linear Equation

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

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19. 19.

    In a triangle, a = 8, b = 15 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    A body starts at 11 m/s and accelerates at 5.1 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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