Taiwan · Grade 10 · Practice Sheet 44

1. 1.

   Solve for x: 2x + 14 = 36.

   Formula:Solving a Linear Equation

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

   View formula →
2. 2.

   Solve using the quadratic formula: x² − 10x + 24 = 0.

   Formula:Quadratic Formula

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

   View formula →
3. 3.

   In a triangle, a = 9, b = 17 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
4. 4.

   A force of 305 N acts on an area of 7.1 m². Find the pressure.

   Formula:Pressure

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

   View formula →
5. 5.

   Find the force needed to accelerate a 54 kg mass at 5.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
6. 6.

   A force of 158 N acts on an area of 7.9 m². Find the pressure.

   Formula:Pressure

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

   View formula →
7. 7.

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

   Formula:Volume of a Cone

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

   View formula →
8. 8.

   A right-angled triangle has legs of 11 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

   View formula →
9. 9.

   A force of 66 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
10. 10.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 1 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

    View formula →
11. 11.

    NT$ 800 is invested at 3% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

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

    View formula →
12. 12.

    A body starts at 6 m/s and accelerates at 2.7 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
13. 13.

    A bag has 23 equally likely marbles, of which 7 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 →
14. 14.

    Find the momentum of a 11 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
15. 15.

    A value changes from 152 to 206. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

    View formula →
16. 16.

    A population of 2,200 grows 8% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
17. 17.

    A wave has frequency 837 Hz and wavelength 0.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
18. 18.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 9 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

    View formula →
19. 19.

    A force of 424 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

    View formula →
20. 20.

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

    Formula:Sum of an Arithmetic Series

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

    View formula →

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