ACT Calculator Strategies TI-84+

Summary

In this video, the presenter shares useful calculator strategies for the ACT test, focusing on tools that may be overlooked. Topics covered include solving imaginary number problems, using graphing features to find solutions, entering and multiplying matrices, and solving logarithmic equations. The presenter demonstrates step-by-step methods to tackle challenging questions efficiently, including using the math and matrix functions on the calculator. By offering practical tips and examples, the video aims to enhance test-taking strategies and improve performance on the ACT.

Takeaways

• 😀 Use the 'i' button on your calculator to handle imaginary numbers, especially when working with powers of 'i' (the imaginary unit).
• 😀 For problems involving complex equations like 4 + i^2, use the calculator’s built-in functions to solve quickly (e.g., 'second i' and the 'i^2' function).
• 😀 When faced with imaginary number problems that don't work directly on the calculator, use the 'math' tab and select the 'I' part function for correct answers.
• 😀 Use the graphing function to find solutions for quadratic equations by locating where the graph crosses the x-axis.
• 😀 For quadratic equations, you can verify the solutions by using the table feature on your calculator, which will show you the exact x-values where the equation equals zero.
• 😀 Matrix operations are simplified with the calculator: enter matrices, edit them, and perform matrix multiplication to find results for problems involving sports awards or other ratios.
• 😀 When working with matrices, be sure to accurately input the number of rows and columns to ensure proper matrix calculations.
• 😀 The calculator allows you to solve logarithmic equations directly using the 'log base' function, which can help with complex logarithmic problems like log 2 (24) - log 2 (3) = log 5 (x).
• 😀 Use the back-solving method with the 'log base' function to test answer choices and find the correct value of x in logarithmic equations.
• 😀 Always ensure your calculator is updated with the latest software to access advanced functions such as the 'log base' feature for logarithmic calculations.
• 😀 Familiarizing yourself with your calculator's features before the test will help you use these strategies efficiently, saving time and boosting your test performance.

Q & A

How can you use the calculator to solve an imaginary number problem like 4 + i^2?

You can simply type '4 + i^2' into the calculator. Press the second button and then 'i' to access the imaginary number function. The result will be 15 + 8i, which matches one of the answer choices.

What do you do if you cannot directly type in an imaginary number equation like i^62 on the calculator?

Instead of typing directly, you use the 'math' menu, select 'num', and choose the 'i part' option. This allows you to input imaginary numbers and get the correct result, such as -1 for i^2.

What is the purpose of graphing a quadratic equation like x^2 - 5x + 6 to find its roots?

Graphing helps you visually identify where the equation crosses the x-axis, which indicates the solutions (roots) of the equation. For example, the graph of x^2 - 5x + 6 shows that the roots are x = 2 and x = 3.

How can you verify the roots of a quadratic equation using the table function on the calculator?

After graphing the quadratic equation, you can access the table by pressing 'second' then 'graph'. The table shows the x-values where the equation equals zero, confirming the roots as x = 2 and x = 3.

What is the method to solve matrix-related problems on the calculator?

You enter the matrices into the calculator under the 'Matrix' menu. Then, multiply the matrices together to get the result. For example, after entering the given matrices for sports and awards, multiplying them returns 92, which is the correct answer.

How do you enter a matrix in the calculator for a problem involving sports awards?

First, access the 'Matrix' menu and choose 'edit'. Define the matrix dimensions and input the numbers for each sport. Then, repeat the process for the second matrix and multiply the two matrices to get the final result.

How do you solve a logarithmic equation like log2(24) - log2(3) = log2(5x)?

You can use the 'log base' function on the calculator to input the logarithmic expression. After simplifying the left side, you can use back-solving with the answer choices, testing x = 125 to find the correct solution.

What is back-solving, and how can it help in solving logarithmic equations?

Back-solving involves testing each answer choice in the equation to find the one that satisfies the equation. For example, testing x = 125 in the log equation gives the correct result, confirming that the answer is J.

What should you do if you encounter a matrix multiplication problem in the ACT test?

Use the calculator’s 'Matrix' menu to input and multiply the matrices. This method allows for quick and accurate solutions to matrix problems on the test.

What key features of the calculator can help you solve complex problems on the ACT?

The calculator's ability to handle imaginary numbers, perform matrix operations, graph functions, and use log base functions provides powerful tools for solving various ACT math problems efficiently.