Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths open shapes of regular solids nets of a solid nets of three-dimensional shapes net of a cone

Which of the following is true for the net of a solid?

  1. A geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid.

  2. A net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure.

  3. A solid may have different nets.

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
A geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets.
Here are some steps to determine whether a net forms a solid:

1. Make sure that the solid and the net have the same number of faces and that the shapes of the faces of the solid match the shapes of the corresponding faces in the net. 
2. Visualize how the net is to be folded to form the solid and make sure that all the sides fit together properly.

Nets are helpful when we need to find the surface area of the solids.
Thus, all the statements are true.
Multiple choice combining transformations transformations vectors and transformations maths

When the axes are rotated through an angle $\dfrac{\pi}{6}$ , find the new coordinate for $(1,0)$

  1. $(\dfrac{\sqrt3}{2},\dfrac{-1}{2})$
  2. $(\dfrac{\sqrt4}{2},\dfrac{-1}{2})$
  3. $(\dfrac{\sqrt5}{2},\dfrac{-1}{2})$
  4. $(\dfrac{\sqrt3}{2},\dfrac{-1}{3})$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\\ sin(\frac{\pi}{6})=(\frac{b}{1})\\\therefore b= (\frac{1}{2})\\ so new y-coordinate wil be  = (\frac{-1}{2})\\cos(\frac{\pi}{6})=(\frac{a}{1})\\\therefore a=(\frac{\sqrt3}{2})\\\therefore new x-coordinate =(\frac{\sqrt3}{2})$

Multiple choice combining transformations transformations vectors and transformations maths

The point to which is shifted in order to remove the first degree terms in $ 2x^{ 2 }+5xy+3y^{ 2 }+6x+7y+1=0 $ is

  1. (2,1)

  2. (1,-2)

  3. (2,-1)

  4. (1,2)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To remove the first degree terms of a general conic equation, we shift the origin to (h, k) where h and k satisfy partial derivative equations with respect to x and y set to zero. Differentiating 2x^2 + 5xy + 3y^2 + 6x + 7y + 1 = 0 with respect to x gives 4x + 5y + 6 = 0, and with respect to y gives 5x + 6y + 7 = 0. Solving this system gives x = 1 and y = -2.

Multiple choice combining transformations transformations vectors and transformations maths

If the transformed equation of a curve is $9x^{2}+16y^{2}=144$ when the axes rotated through an angle of $45^{o}$ then the original equation of a curve is:

  1. $25x^{2}+14yxy+25y^{2}=228$
  2. $25x^{2}-14yxy+25y^{2}=228$
  3. $25x^{2}+14yxy-25y^{2}=228$
  4. $25x^{2}-14yxy-25y^{2}=228$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rotating axes by 45 degrees involves substituting x = (X - Y)/sqrt(2) and y = (X + Y)/sqrt(2) into the original equation. Expanding 9((X-Y)/sqrt(2))^2 + 16((X+Y)/sqrt(2))^2 = 144 leads to 9(X^2 - 2XY + Y^2)/2 + 16(X^2 + 2XY + Y^2)/2 = 144, which simplifies to 25X^2 + 14XY + 25Y^2 = 288.