Ireland · Year 10 · Practice Sheet 15

1. 1.

   An object with initial velocity 4 m/s accelerates at 2.9 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   Solve for x: 7x + 9 = 65.

   Formula:Solving a Linear Equation

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

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3. 3.

   An object has mass 354.2 g and volume 46 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A value changes from 196 to 172. 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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5. 5.

   A population of 6,800 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   An object with initial velocity 12 m/s accelerates at 3.9 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

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

   Formula:Quadratic Formula

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

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8. 8.

   €3,300 is invested at 6% 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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9. 9.

   In a triangle, a = 17, b = 10 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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10. 10.

    A body starts at 10 m/s and accelerates at 2 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A bag has 25 equally likely marbles, of which 21 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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12. 12.

    A population of 3,400 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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13. 13.

    Solve for x: 7x + 11 = 25.

    Formula:Solving a Linear Equation

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

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14. 14.

    A force of 22 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    Find the gravitational potential energy of a 20 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 12 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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17. 17.

    A value changes from 159 to 182. 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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18. 18.

    A bag has 8 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 cone has base radius 5 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    An object has mass 6 g and volume 6 cm³. Find its density.

    Formula:Density

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

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