In my previous post this month, I explored some ACT® testing taking tips and using the __Casio fx-9750GIII__ graphing calculator strategically when taking the assessment. In this follow-up post, I want to explore some key concepts that are almost always included on the assessment, and provide you with some practical advice and tips for studying, using your calculator as a tool for learning.

There are several topics on a typical ACT® that tend to show up pretty consistently, and practicing and preparing ahead of time will be really important. Below is a list of topics and quick videos on how to use the calculator to help you study and deepen your understanding of these topics so that when you see them on the test, you can quickly eliminate answers that are wrong and focus on using what you know to get to a solution - either without the calculator or choosing the most efficient method (see above) based on what you already know.

__Matrices__

Understanding Matrix operations will help you when you see problems like the one below - i.e. knowing what the 'results' look like and being able to interpret quickly will be a time saver. You can practice matrix operations very quickly and easily on the graphing calculator to get a sense of what the resulting values represent in context.

In* the 2 × 2 matrix below, b1 and b2 are the costs per pound of bok choy (Chinese greens) at Market 1 and Market 2, respectively; r1 and r2 are the costs per pound of rice flour at these 2 markets, respectively. In the following matrix product, what does q represent?* *(Source:** *__ACT® Released Items Set Four__*)*

__Triangles & Trig Relationships__

The examples below are problems that involve triangles and trig functions. Take some time to study triangle properties, particularly right triangles. Focus on the following:

Triangle Sum

Congruency theorems for Triangles (ASA, SAS, SSS, etc.)

Trig Ratios - i.e. tan, sin, cos

Using Trig Ratios to find missing angles measures in triangles

Calculating using trig functions (see video below)

Sample Problems:

*Which of the following is the sine of angle A in the right triangle below?**(Source:*__ACT® Released Items Set Two__*)*

*Taher plans to cut the 3 pieces of lumber for the flower bed border from a single piece of lumber. Each cut takes inch of wood off the length of the piece of lumber. Among the following lengths, in inches, of pieces of lumber, which is the shortest piece that he can use to cut the pieces for the flower bed border?**(Source:*__ACT® Released Items Set Four__*)**Which of the following expressions is the closest approximation to the height h, in feet, of the roof truss shown below?(Source:*__ACT® Released Items Set Four__*)*15 tan 20°

15 sin 20°

30 tan 20°

30 sin 20°

__Conic Equations__

*Which of the following is an equation of the circle with its center at (0,0) that passes through (3,4) in the standard (x,y) coordinate plane?(Source:**ACT® Released Items Set Three)**x - y = 1**x - y = 25**x2 + y = 25**x2 + y2 = 5**x2 + y2 = 25*

Problems like the one above require an understanding of the conic equations. If you know the equation of a circle, you can immediately eliminate the first 3 choices, since the x and y variables both need to be squared to form a circle. Then, understanding that the 5 and 25 in the R^2 position means the radius is the square root of 5 or the square root of 25, you can easily graph these (using the Conic Menu) or, just in thinking, if r=5, there is no way the circle itself will pass through (3,4), so the only logical solution is the fourth one - *x*2 + *y*2 = 5.

The video below shows you ways to practice and explore trig functions, matrices and conic graphs to help deepen your understanding of these concepts.

__Function Transformations__

Understanding how coefficients/constants impact the graph of an equation is something that will serve you well. This is all connected to transformations of parent functions. In the example above, the graph is that of a parabola - recognizing that and understanding how a negative constant multiplier will impact the original graph will allow you to quickly answer without having to actually perform any calculations.

Example problem:

*If g(x) = −1/2 f(x), for all values of x, which of the following is a true statement describing the graph of g in comparison with the graph of f, shown below?*

If you understand parent function of a parabola and how transformations impact the parent function graph, then you could, without graphing, already know the negative should tell Gyou that g(x) opens upward, because it is ‘inversing’ f(x) and the 1/2 should tell you that it will open wider.

The **Dyna-Graph Menu o**n the __fx-9750GIII__ is a great place to explore and experiment and look for those relationships and prepare ahead of time for these types of transformation questions. As you will see in the video below, graphing the parent function first and then exploring the different forms of the equation and modifying the coefficients/constants will help you to analyze a graph/situation and determine the impact of change quickly.

__GOOD LUCK STUDYING!__

Hopefully some of these strategies and ideas will help you be better prepared to take the math portion of the ACT®. But, more importantly, will provide you ways to practice and deepen your own understanding and applications of different mathematical concepts and be prepared for math class and any other standardized math assessments.

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