Senior High School Mathematics 1 - Algebra and Functions

These flashcards cover key algebra concepts including operations on sets, functions, binary operations, surds, quadratic equations, polynomial functions, rational functions, linear programming, and graphical representations, providing essential study aids for students preparing for exams.

What is the outcome of applying set theory in solving problems?

Students will be able to apply set theory to solve various mathematical problems.

What is the difference between a relation and a function?

A relation is a set of ordered pairs, while a function is a specific type of relation where each input has exactly one output.

What does the binomial theorem help with?

It helps to expand expressions of the form (a + b)^n.

What operations can be performed on rational functions?

Students learn to add, subtract, multiply, and divide rational functions.

When is a rational function considered undefined?

A rational function is undefined when the denominator equals zero.

What are De Morgan’s laws used for?

De Morgan's laws are used to relate the union and intersection of sets through complementation.

What is the significance of identifying the identity element in binary operations?

The identity element helps to find inverses in binary operations.

How does one find the domain of a function?

The domain is found by identifying all the possible input values that do not lead to undefined operations.

What are simultaneous linear inequalities used for in linear programming?

They are used to optimize a linear objective function subject to constraints.

What mathematical operations are associated with surds?

Surds can be added, subtracted, multiplied, and rationalized.

How are quadratic functions represented graphically?

Quadratic functions are represented as parabolas, which can open upwards or downwards.

What is the discriminant used for in quadratic equations?

The discriminant helps to determine the nature of the roots of a quadratic equation.

What does the addition and multiplication of polynomials involve?

It involves combining like terms and applying the distributive property.

What are binary operations?

Binary operations are operations that combine two elements to produce another element from a set.

What is an inverse in the context of binary operations?

An inverse is an element that, when combined with another element through a binary operation, results in the identity element.

How can the range of a function be determined?

The range can be determined by evaluating the function for all values within its domain.

What is the process for sketching the graph of a quadratic function?

Sketching involves identifying the vertex, axis of symmetry, and intercepts, then plotting the points accordingly.

What do rational functions look like?

Rational functions are expressed as the ratio of two polynomials.

How can students simplify a complex fraction using partial fractions?

Partial fractions allow for the decomposition of a rational function into simpler fractions.

What do inequalities represent in a graphical context?

Inequalities represent regions on a graph, indicating solutions that meet specified conditions.

How do you represent linear programming visually?

Linear programming can be represented graphically using Cartesian coordinates to illustrate feasible regions.

What is a composite function?

A composite function is formed when one function is applied to the result of another function.

What operations can be carried out on vectors?

Vectors can be added, subtracted, and multiplied by scalars or other vectors.