RPN (Reverse Polish Notation) Worksheet
Name: ____________ Date: ______
Solve the following problems using techniques learned last class.
Questions
1. Evaluate an RPN expression
Evaluate:
7 2 + 3 4 * 2 / -
Answer: ______________
2. Convert to RPN
Convert the algebraic expression (5 + 3) × 4 - 6 to RPN notation.
Answer: ______________
3. Convert to algebraic notation
Convert a b + c d * e / - to standard algebraic notation.
Answer: ______________
4. Evaluate an RPN expression
Evaluate:
8 3 2 * + 5 4 - 6 * 2 / +
Answer: ______________
5. Convert to RPN
Convert the algebraic expression ((a + b) × c - d) / (e + f × g) to RPN notation.
Answer: ______________
6. Convert to algebraic notation
Convert x y z * + w v u * - / t + to standard algebraic notation.
Answer: ______________
7. Evaluate an RPN expression
Use degrees for trigonometric functions. Evaluate:
90 sin 4 sqrt * 16 4 / 2 ^ +
Answer: ______________
8. Convert to RPN
Convert the algebraic expression $\sqrt{a^2 + b^2} \cdot \cos \theta$ to RPN notation.
Answer: ______________
Challenge 1.
Write the RPN expression 5 4 3 2 1 - - - - in standard infix notation
a. Using parenthesis b. Without parenthesis
In both cases the numbers must appear in the original order but you may use any operands needed
Answer A: ______________
Answer B: ______________
Challenge 2.
An RPN expression with $n$ operands and only binary operators $+, -, \times, \div$ will have how many operators?
Answer: ______________
Challenge 3.
By reordering operators and/or operands, how many RPN expressions are equivalent to 4 3 2 1 + + +? For example 1 2 3 4 + + + has the same value
Answer: ______________
Challenge 4.
Evaluate
1000 999 998 ... 3 2 1 - - - ... - -
Where there are the appropriate number of minus signs, and the three dots indicate missing values.
Answer: ______________
Challenge 5.
Evaluate in radians.
1 cos cos cos cos ...
Where there are infinitely many cosines.
Answer: ______________