Mongolia · Grade 10 · Practice Sheet 22

1. 1.

   A right-angled triangle has legs of 10 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

   View formula →
2. 2.

   A body starts at 6 m/s and accelerates at 5.7 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
3. 3.

   A population of 6,300 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
4. 4.

   Solve using the quadratic formula: x² − 3x + 0 = 0.

   Formula:Quadratic Formula

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

   View formula →
5. 5.

   A cylinder has radius 6 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

   View formula →
6. 6.

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

   Formula:Volume of a Sphere

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

   View formula →
7. 7.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 2 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

   View formula →
8. 8.

   Find the force needed to accelerate a 33 kg mass at 1.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
9. 9.

   A current of 4.5 A flows through a 32 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
10. 10.

    Find the gravitational potential energy of a 21 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
11. 11.

    A wave has frequency 254 Hz and wavelength 1.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
12. 12.

    A bag has 25 equally likely marbles, of which 18 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

    View formula →
13. 13.

    A cylinder has radius 11 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
14. 14.

    Solve for x: 5x + 16 = 31.

    Formula:Solving a Linear Equation

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

    View formula →
15. 15.

    Find the force needed to accelerate a 39 kg mass at 5 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
16. 16.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 1 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

    View formula →
17. 17.

    ₮3,900 is invested at 4% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

    View formula →
18. 18.

    An object with initial velocity 10 m/s accelerates at 1.8 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
19. 19.

    In a triangle, a = 9, b = 6 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
20. 20.

    A body starts at 4 m/s and accelerates at 5.4 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.