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Strange symbols in S.A.T. Math problems may confuse test-takers, but they can be mastered with practice. This guide offers essential tactics for interpreting and evaluating these unique symbols effectively. It provides clear examples, such as evaluating expressions with custom operations like "☺" and "▼," ensuring you understand the mathematical patterns involved. Follow the instructions diligently, and apply your math skills to succeed. By familiarizing yourself with these symbols, you'll boost your confidence and performance on test day.
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S.A.T. Math Testing Tactics Tactic 16: Handle Strange Symbols Properly
Strange Symbols • On the S.A.T. you will encounter problems with strange symbols and instructions on how to evaluate them. • These problems are designed to test your ability to read, understand, and apply a mathematical pattern or algorithm. • Follow the instructions carefully!!!
Example 16.1 • If a ☺b = , what is the value of 25☺15 ? Obviously, our “a” is 25 and our “b” is 15. Substitute these into the equation and evaluate. 25☺15 = 4
Example 16.2 For any numbers x and y, x▼y = xy – (x + y) a) Find -2▼3 We can see that our “x” is -2 and our “y” is 3. Substitute these values in and evaluate. -2▼3 = (-2)(3) – (-2 +3) = -6 – 1 = -7 -7
Example 16.2 For any numbers x and y, x▼y = xy – (x + y) b) For what value of x does x▼5=x▼10? Set up each side of this equation using our strange symbol rule. On the left side, our “y” is 5. On the right side, our “y” is 10. x(5) –(x+5) = x(10) – (x +10) 5x – x – 5 = 10x – x – 10 4x – 5 = 9x – 10 1 5 = 5x 1 = x
Example 16.2 For any numbers x and y, x▼y = xy – (x + y) How many positive numbers are the solutions of the equation: y ▼ y = y ? A) None B) 1 C) 2 D) 3 E) More than 3 Set up the left side of the equation using our rule. The “x” will be y. y(y) –(y + y) = y 0 is not positive or negative 3 is positive y2 – 2y = y y2 – 3y = 0 B y(y – 3) =0 y = 0 or y = 3
Example 16.3 • For any real number c and d, c♥d = cd + dc . What is the value of 1♥ (2 ♥ 3) ? Since there are two special characters in this expression, we need to follow the order of operations. So, complete the computation inside parenthesis first. 1♥ (2 ♥ 3) 1♥ (23+ 32 ) 1♥ (8 + 9) 1♥ 17 117+ 171 18 1 + 17 18
In Conclusion When you see a strange symbol, don’t worry! Just follow the instructions provided very carefully and evaluate using familiar mathematical skills.