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: ______________