Today, we worked on two more functions: absolute and
radical after studying more in the logarithm. All of the knowledge in
this chapter is truly a basic concepts about the special function,
domain, range, graphs, equations. More and deep things will be explored
at high school, advance Math study.
Here is the homework for today’s contents:
P.553, 19.4.5, 19.4.6, 19.4.7, 19.4.8, 19.4.9
P.562, 20.1.1, 20.1.2, 20.1.5, 20.1.6
P.568, 20.2.2, 20.2.3, 20.2.4, 20.2.5.
In today’s class, students continued to study exponential functions, equations and interest that is dealing with money. This is hard section for students because the methods that make money in different ways, such as simple interest, compounded interest and relation and difference between the interests. In solving exponential equations, basically it can be resolved with the same bases case, but for the equation with different bases, logarithm concept is used to get the solution. It is explored that logarithm and exponential are inverse function mutually. Students need to get skilled in handling the logarithmic and exponential expressions.
The two important topics, interest and logarithm are critical in Algebra studying. I hope students would digest and master the knowledge through practicing.
Here is the homework assignment:
P.532, 19.1.4, 19.1.6, 19.1.7(challenging)
P.538, 19.2.1, 19.2.2, 19.2.3, 19.2.4,
P.545, 19.3.1, 19.3.2, 19.3.3, 19.3.4
P.552, 19.4.1, 19.4.2 19.4.3, 19.4.4
Today, students studied the functions, particularly of polynomial function and exponential function. In polynomial function, function standard form, domain, degree, addition/subtraction, multiplication of polynomials were introduced and studied. In exponential function, domain, range, graph were present. Solving exponential equations from the principle of same base rule. One important key in solving equation is to have clear mind about the exponent rules which are used to simplify the exponent equations.
Here is the homework assignment:
P.516, 18.1.1, 18.1.3, 18.1.4, 18.1.5
P.521, 18.2.2, 18.2.4, 18.2.5 (a)(b)(c)
P.532, 19.1.1, 19.1.2, 19.1.3, 19.1.5
Today, students continued to study function, composition function, inverse function, solving problems by functions and graphs of function. Some of challenging questions were demonstrated to help the understanding of the conceptual and practical ideas.
Here is the homework assignment for today’s contents
P.467, 16.3.3, 16.3.4
P.472, 16.4.1, 16.4.2
P.477, 16.5.1, 16.5.3, 16.5.5
today, students studied the new concept: function, which is discribing a relation of independent variable and dependent variable. In the function topic, domain, range, evaluation, combining functions, composition, were introduced in the class.
Here is the homework assignment:
P.460, 16.1.1, 16.1.2, 16.1.3, 16.1.4, 16.1.5, 16.1.6, 16.1.7(a)
P.464, 16.2.1(a), 16.2.2
P.267, 16.3.1, 22.214.171.124
Today, students continued to work on sequence and series, geometric sequence and series. Different from arithmetic sequence, geometric sequence has the common ratio. Same as arithmetic sequence and series, geometric sequence and series has the formulas to find the nth term and sum of the terms. Particularly, in geometric series, the infinite geometric series has result as long as the |ratio|<1. This feature can be used to convert repeated decimals to fractions.
Here is the homework for today’s class.
P.604, 21.3.1, 21.3.2, 21.3.4, *21.3.5
P.616, 21.4.1, 21.4.2, 21.4.3, 21.4.4, *21.4.5
In today’s class, we changed the topic from quadratic related to number list related: sequence and series. This is the basic of sequence and series in algebra. We started with arithmetic sequence and series which has the same difference between any two consecutive terms. Formulas were derived and the meaningful methods that help in solving problems were also introduced, such as arithmetic mean, steps related to the difference.
Here is the homework for sequence and series
P.594, 21.1.1, 21.1.2, 21.1.3
P.601, 21.2.1, 21.2.2, 21.2.3, 21.2.6, and extra 21.2.5
Today, students continued to study one-variable quadratic inequality with the non-factorable quadratic expression and real solutions or with the non-factorable expression and non-real solutions. The key is how to write a quadratic expression in factor form from the roots of the equation. For non-real solution case, the quadratic is either always positive or always negative. Through this results, we can figure out whether the quadratic inequality has solution or not. In learning two-variable quadratic inequality, students recalled the two-variable linear inequality. The process of solving the inequality are exactly the same in both linear and quadratic inequality, that is, plotting graph, determining the border, choosing a point to find out whether region where the point is located is the solution or not. For advanced section of quadratic section, students learned to find out the maximum or minimum value of any quadratic expression, in addition, students learned an inequality with more than two factors in binomial form by analyzing the signs of each binomial factor to find inequality solutions.
Here is the homework for today’s class:
P.430, 15.1.3, 15.1.5, 15.1.4 (change the inequality to y<-x^2+4)
P.434, 15.2.1, 15.2.2
P.446, 15.4.1, 15.4.2, 15.4.3
Today, students studied another two methods to solve quadratic equations, “completing the square” and “quadratic formula”. In fact, quadratic formula is derived in solving standard quadratic equation, ax^2+bx+c=0, by using “completing the square”. Both methods are so powerful that all quadratic equations can be solved through them. Completing the square is a method that is not only used in solving quadratic equation, but many places that need to form a perfect square.
Here is today’s homework:
1, 2(a)(b)(f)(g), 3, 5.(b)(d)(f)(h), 11.(a)(c)(e)(h), 12.(a)(c)(g),13.(a), 14.(a)(e)(g).
Today, students studied writing quadratic equations and solving quadratic inequality with one variable. Writing equations requires at least three conditions and selects proper quadratic form to find the values that need to complete the equation, such as standard form and vertex form. In the quadratic inequality with one variable, factorization is still the major method. With the factor form, through positive and negative analysis of each binomial factor to find the values of the variable that satisfy the equality inequality. In next class, we will continue to solve quadratic inequality factorization through the roots and the case of no real roots.
Here is the homework assignment to cover today’s contents:
P.414, 14.1.5 (a), 14.1.6
P.430, 15.1.1, 15.1.2