If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

- Common Core MathK - 8High School

517 questions26 skills

36 questions2 skills

Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., *v*, |*v*|, ||*v*||, *v*).

30 questions1 skill

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

12 questions1 skill

Solve problems involving velocity and other quantities that can be represented by vectors.

56 questions3 skills

Add and subtract vectors.

86 questions4 skills

Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

96 questions5 skills

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

40 questions2 skills

Understand vector subtraction *v* – *w* as *v* + (–*w*), where –*w* is the additive inverse of *w*, with the same magnitude as *w* and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

40 questions2 skills

Multiply a vector by a scalar.

46 questions2 skills

Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as *c*(*v*_{x}, *v*_{y}) = (*cv*_{x}, *cv*_{y}).

20 questions1 skill

Compute the magnitude of a scalar multiple *c**v* using ||*c**v*|| = |*c*|*v*. Compute the direction of *c**v* knowing that when |*c*|*v* ≠ 0, the direction of *c**v* is either along *v* (for *c* > 0) or against *v* (for *c* < 0).

20 questions1 skill

Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

36 questions2 skills

Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

124 questions6 skills

Add, subtract, and multiply matrices of appropriate dimensions.

Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

Skills for this standard are coming soon.

30 questions1 skill

Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

28 questions2 skills

Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

31 questions2 skills

Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.