Math Questions for Tests and Worksheets

Select All Questions

Grade 12 Matrices CCSS: HSN-VM.C.12

This question is a part of a group with common instructions. View group »

How does the absolute value of the determinant of the transformation matrix relate to the area of the two quadrilaterals (the square,

$S_1$ and the transformed shape,

$S_2$ )? Choose the equation which correctly describes this relationship.

$|det(T)| = "Area"(S_1) \ "Area"(S_2)$
$"Area"(S_2) = |det(T)| \ "Area"(S_1)$
$|det(T)| = |"Area"(S_2) - "Area"(S_1)|$
There is no relationship between the absolute value of the determinant of T and the area of the shapes.

Grade 3 Place Value CCSS: 3.NBT.A.1

What is 825 rounded to the nearest 10?

Grade 12 Matrices CCSS: HSN-VM.C.9

In Leane's math homework, she has to multiply three matrices together by hand, as follows:

$[[8,2,0],[-4,7,-3]] * [[4,7,-4,-2],[1,3,8,7],[-5,-3,6,6]] * [[-6],[5],[-4],[1]]$ . She decides that if she multiplies the last two matrices together first, it will make the computation easier. Is she correct? Why or why not.

No, she cannot do this. She has to multiply the first two matrices together first, and then the third, according to normal evaluating rules.
Although she is allowed to do this, it will not make the computation easier. Regardless of how she multiplies these matrices, the answer will be a 2-by-1 matrix, and the same work will be involved either way.
Yes, she can do this, and it will make the computation easier. Multiplying the second and third matrices together first, and then the first by the product just found, will reduce the total number of arithmetic computations (multiplication and addition) to be performed.
These matrices are not able to be multiplied together, as they have incompatible dimensions.

Grade 6 Fractions and Ratios CCSS: 6.RP.A.1

2:1 What is the ratio of A's to B's in simplest form?

C A C A C A B C
A A B C B C A

Grade 12 Matrices CCSS: HSN-VM.C.10

Adrian was learning about the identity matrix and multiplicative inverses in math class, and is now working on his homework. He knows that, for a square matrix

$A$ , he can usually find another matrix

$B$ such that

$AB = I$ , where

$I$ is the identity matrix of the same size as

$A$ and

$B$ . Adrian is now considering the matrix

$A = [[3,2],[6,4]]$ . The way he has been finding the multiplicative inverse matrix is to create another matrix

$B = [[a,b],[c,d]]$ . He performs this multiplication, and it yields two systems of equations, as follows.

${{:(3a + 2c , = 1),(6a + 4c, = 0):}$

${{:(3b + 2d , = 0),(6b + 4d, = 1):}$

Adrian realizes that both these systems are inconsistent. Is Adrian's work correct? And if so, what does this imply?

No, Adrian's work is not correct. His entire method for finding multiplicative inverses is wrong.
No, Adrian's work is not correct. Although his general method is OK, he has made a mistake when multiplying the matrices.
Yes, Adrian's work is correct. This means that, in this case, no such B matrix exists, and therefore not all square matrices have a multiplicative inverse.
Yes, Adrian's work is correct. This implies that, in this case, the B matrix must be the zero matrix.

Grade 9 Sequences and Series CCSS: HSF-IF.A.3

What is the seventh term of the sequence 24, 12, 6, 3,...?

0
0.25
0.375
1.5

Grade 4 Angles CCSS: 4.MD.C.6, MP5

The measurement of this angle is 108 degrees.

True
False

Grade 4 Customary Measurement Concepts CCSS: 4.MD.A.2

Amber has a cloth that is 63 feet long. How much would this be in yards?

21 yards
189 yards
21 inches
189 inches

Grade 12 Matrices CCSS: HSN-VM.C.8

Multiply, if possible.

$[[3,2,-1],[0,9,1],[3,2,-5]] * [[1,0,1],[-2,-3,2],[5,6,-1]]$

$[[3,0,-1],[0,-27,2],[15,12,5]]$
$[[2,-14,28],[1,-25,53],[-2,-22,32]]$
$[[-5,-12,9],[-23,-22,18],[-25,-37,16]]$
$[[-6,-12,8],[-13,-21,17],[-26,-36,12]]$

Grade 12 Matrices CCSS: HSN-VM.C.8

Shane has a matrix of three ordered pairs,

$P = [[3,2],[8,-1],[5,0]]$ , where the x-coordinates are in the first column and the y-coordinates are in the second column. He wants to find a matrix A, such that the product

$A \ P$ gives a matrix that will only have the first and third ordered pairs. Which of the following matrices will give this result?

$A = [[1,1],[0,0],[1,1]]$
$A = [[1,0,0],[0,0,1]]$
$A = [[1,0,1]]$
$A = [[1,0,1],[1,0,1]]$

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

Simplify.

$(x - y)/(x^2 - 2xy + y^2)$

$x + y$
$xy$
$1/(x-y)$
$x - y$

Grade 12 Matrices CCSS: HSN-VM.C.9

Can the following matrix expression be evaluated? Why or why not?

$[[3,-4],[0,-1],[9,1]] \ * ( [[0,1],[1,0]] + [[-5,-9],[-1,4]] )$

Yes, but only as is (one cannot distribute the 3-by-2 matrix).
Yes, either as is, or if the distributive property is applied.
No, after performing the addition of the two smaller matrices, the new dimensions will not allow for multiplication with the left-most matrix.
No, all matrices must be have the same dimensions.

Grade 3 Calendar Math

If tomorrow is Monday, today is .

Sunday
Thursday
Monday
Wednesday
Tuesday

Grade 1 Basic Measurement Concepts

My friend and I would like to see who can jump the farthest. After jumping, we use a tape measure. What will this tell us?

temperature
length
weight
time

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a

$f(x) = log_4(3x-1) + 10$ , what is the inverse of this function?

$f^{-1}(x) = (4^(x-10)+1)/3$
$f^{-1}(x) = 4(x/3 + 1) - 10$
$f^{-1}(x) = 1/3 (4^x -9)$
$f^{-1}(x) = 4^((x-10)/3 + 1)$

Grade 12 Matrices CCSS: HSN-VM.C.8

Multiply.

$[[2,-1],[0,7]] * [[-1,-4],[6,1]]$

$[[-8,-9],[42,7]]$
$[[-2,4],[0,7]]$
$[[1,-5],[6,8]]$
$[[-8,-27],[12,1]]$

Grade 5 Money (USA) CCSS: 5.NBT.B.7

One pound of grapes costs $3.49. Katherine buys exactly 3 pounds of grapes. The cost of the grapes is $10.47.

True
False

Grade 3 Addition CCSS: 3.NBT.A.2

120 + 120 =

Grade 10 Quadratic Equations and Expressions

Solve.

$2a(5a-2)+3a(2a+6)+8=a(4a+1)+2a(6a-4)+50$

a = 42
a = 21
a = 4
a = 2

Grade 5 Triangles CCSS: 5.G.B.4

A scalene triangle is a triangle having three sides of different lengths.

True
False

Share/Like This Page

Filter By Grade

Browse Questions

Arithmetic and Number Concepts

Calculus

Function and Algebra Concepts

Geometry and Measurement

Mathematical Process

Statistics and Probability Concepts

Trigonometry

Math Questions - All Grades