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Worksheetsalgebra
Total questions: 65
Worksheet time: 33mins
1. Given two points A(0,6) and B(4,8). Find the midpoint of the segment AB.
(7,2)
(7,7)
(2,7)
1. Given two points A(-5,4) and B(1,-2). Find the midpoint of the segment AB.
(-2,2)
(-1,2)
(-2,1)
1. Given two points A(2,3) and B(3,-3). Find the point M which divides the segment AB in the ratio 2:5.
(16/6,9/6)
(17/6,9/7)
(16/7,9/7)
1. Given two points A(-2,3) and B(4,6). Find the point M which divides the segment AB in the ratio 2:3.
(5/221/5)
(2/5,22/6)
(2/5,21/5)
1. If A is ( )-matrix and B is ( )-matrix, what is the size of the matrix X in the matrix product AXB ?
2X3
2X2
4X3
1. If a matrix В is the inverse matrix for a matrix А then
АВ=ВА=I
АВ=ВА=J
CВ=ВC=I
1. If three vectors are coplanar then …
Abc=0
Abc=1
Abc=2
1. If two straight lines with slopes and are parallel, then …
K1=K2
K1=K3
K4=K2
1. If two straight lines with slopes and are perpendicular, then …
K1k2=-1
K1k2=1
K1k2=-2
1. If two vectors lie on the same line or on parallel lines, then they are …
Collinear
Uncollinear
Vertical
1. Three vectors are said to be coplanar if …
They lie in the same plane or in the parallel unculinear
They lie in the same plane or in the parallel circles
They lie in the same plane or in the parallel planes
1. Let a=(3 -1) (0 4) and b=(2 3) (-5 1)Find the determinant of the matrix (A-B)2
287
187
277
1. Let a=2p+3q and b=p-q . Find the scalar product a*b if , p=5 q=2 and vectors p and q form the angle of 600
43
34
44
1. Show the direction vector of the straight line x-7/-5 y-1/1=z+5/4
(-5,5,4)
(-4,1,5)
(-5,1,4)
1. Show the direction vector of the straight line
(7,-5,9)
(9,-5,7)
(9,-5,0)
1. Show the equation of the yz-plane
X=1
X=0
X=2
1. Show the equation of the xz-plane
Y=0
Y=2
Y=1
1. Show the equation of the xy-plane
Z=2
Z=0
Z=1
1. Solve the equation [4 8] [-1 x]=0
-2
2
0
1. Solve the equation [x 5] [ 4 3]=4
8
6
10
1. Show the normal vector of the plane 4x – 2y + 6z + 7=0
(4,-2,0)
(6,-2,4)
(4,-2,6)
1. Show the normal vector of the plane x – 8z + 3=0
(1,0,-8)
(1,0,-1)
(1,0,-1)
1. Solve the system of equations (x-y=1)(2x+y=5)
(2,1)
(1,2)
(2,2)
1. Solve the system of equations(3x+2y=7(4x-5y=40
(5,-4)
(-5,-4)
(5,4)
1. Solve the system of equations (5x+2y=4(7x+4y=8)
(0,2)
(0,2)
(1,2)
1. Solve the system of equations (2x-y=0(x+3y=7), then find the value of x – y
1
2
0
1. Solve the system of equations (x-2y(2x+y=-16) ,then find the value of x – y
1
11
2
1. Solve the system of equations then find the value of x + y – z
0
2
1
1. The area of a parallelogram formed by two vectors and is equal to
a*b
a*c
b*a
1. The cofactor of an element of the matrix А is defined by
Aij=(-1)i+jMA
Aij=(-1)i+jMij
Mij=(-1)i+jMij
1. The determinant of the matrix A=(a11a12)(a21 a22)) is the number
a11a22-a12a21
a11a22-a12a22
a21a22-a12a12
1. The solution of the matrix equation AX=B is defined by
X=B-1B
X=A-2B
X=A-1B
1. The solution of the matrix equation XD=B is defined by
X=D-1B
X=D-1A
X=D-2B
1. The triple product of three coplanar vectors is equal to
0
1
2
1. Two matrices can be added if
They have the same line
They have the same size
They not
1. Two matrices can be multiplied if
The number of columns of the first matrix is equal to the number of rows of the second matrix
The number of columns of the first matrix is equal to the number of rows of the second vector
The number of columns of the first matrix is equal to the number of rows of the second equinor
1. Which of the following planes is parallel to the xy-plane ?
o Z=4
o Z=2
o Z=6
1. Which of the following planes is parallel to the xz-plane ?
o Y=1
o Y=-1
o Y=3
1. Which of the following planes is parallel to the yz-plane ?
X=2
X=6
X=3
1. Which of the following points belongs to the plane 3x – 5y + 2z – 17=0?
(2,-1,2)
(2,-1,3)
(2,-2,3)
1. Which of the following points belongs to the plane x – 7y – 3z +5=0?
(8,1,2)
(8,1,1)
(2б1,2)
1. Which of the following vectors is collinear to the vector ? a=i+2j-k?
(2,4,-6)
(4,4,-6)
(2,4,-2)
1. Which of the following vectors is collinear to the vector ? a=-2+j-k
(2,-41)
(2,-1,1)
(2,-1,-2)
1. Which of the following points belongs to the straight line y = 3x + 13 ?
(-1,13)
(-1,12)
(-14,1)
1. Which of the following points belongs to the straight line x = 4 ?
(4,5)
(5,5)
(4,4)
1. Which of the following statements is true?
Every homogeneous system of equations is consistent
Every homogeneous system of equations is coplinent
Every homogeneous system of equations is paralell
1. Which of the following statements is false?
Every homogeneous system of equations is inconsistent
Every homogeneous system of equations is irreguler
Every homogeneous system of equations is finaly
1. Which of the following straight lines is parallel to the line 2x + y – 7=0 ?
2x+y-4=0
2x+y-4=1
2x+y-4=4
1. Which of the following straight lines is parallel to the line x + 5y – 3=0 ?
2x+10y-7=0
2x+10y-4=0
3x+10y-7=0
1. Which of the following straight lines is perpendicular to the line 3x – 5y = 0 ?
3y+5-1=0
4y+5-1=2
3y+6-1=0
1. Write the equations of asymptotes of the hyperbola x2/9-y2/25=1
Y=+-4/3x
Z=+-5/3x
Y=+-5/3x
1. Write the equations of asymptotes of the hyperbola x2/4-y2=1
Y=+-0,5x
Z=+-0,6x
Y=+-1,5x
1. Write the equation of the plane which passes through the point M(3,0,3) and is parallel to the plane
2x+6y-5z+9=0
2x+6y-5z+7=1
2x+3y-5z+8=0
1. Write the equation of the plane which passes through the points (7,6, 7), (5, 10, 5), (-1, 8, 9)
3x+5y+5z=110
3x+5y+7z=100
3x+3y+7z=100
1. Write the equation of the plane which passes through the points (1, -1, 0), (6, 1, -2), (0, 2, 0)
6x+2y+17z+4
6x+3y+11z+4
4x+2y+17z+4
1. Write the equation of a straight line which passes through the point (0,3) and is parallel to the x-axis
Y=2
Y=3
Z=3
1. Write the equation of a straight line which passes through the point (-5,0) and is parallel to the y-axis
Y=-4
Y=-5
Y=-10
1. Write the equation of a straight line which passes through the points (-1,-4) and (0,5)
9x-y+5=1
9x-y+5=0
5x-y+5=0
1. Write the equation of a straight line which passes through the points (2,0) and (1,3)
3x+y-6=0
3x+y-4=1
6x+y-3=0
Write the equation of a straight line which passes through the point (1, - 2) and is parallel to the straight line 2x-3y+7=0
2x-3y-8=0
4x-3y-8=1
1x-9y-8=0
1. Write the equation of a straight line which passes through the point (2, 3) and is parallel to the straight line 3x-2y+2=0
3x-2y-12=0
9x-4y-12=2
1x-2y-11=3
Write the equation of a straight line which passes through the point (-3, 2) and is perpendicular to the straight line 7x+4y-11=0
4x-7+26=0
2x-7+26=2
4x-9+26=6
1. Write the equation of a straight line which passes through the point (1, -4) and is perpendicular to the straight line x-2y+5=0
2x+y+2=0
3x+y+4=1
6x+y+2=0
1. Write the equation of a straight line with the slope k which passes through the point M0(X0Y0)
y=y0+k(x-x0)
z=y0+k(z-x0)
a=a0+k(x-x0)
1. Write the equation of a straight line with the slope k = 1 which passes through the point (1,1)
Y=z
A=z
Q=z
