Practice evaluating, converting to RPN, and converting from RPN before the quiz. Work each one out on paper, then click to check your answer. This is NOT an exhaustive review of quiz material – just some helpful practice.

Question

1. Evaluate: 6 2 / 3 + 4 *

$6/2=3$, $3+3=6$, $6\times4=24$.

24

Question

2. Convert to RPN: (7 - 2) × 3 + 8

7 2 - 3 * 8 +

Question

3. Convert to algebraic notation: a b - c d + *

$(a - b)(c + d)$

Question

4. Evaluate: 9 4 - 5 2 * +

$9-4=5$, $5\times2=10$, $5+10=15$.

15

Question

5. Convert to RPN: (p + q) × (r - s)

p q + r s - *

Question

6. Convert to algebraic notation: x y * z w - /

$\dfrac{xy}{z - w}$

Question

7. Evaluate: 30 sin 2 * 9 3 / 2 ^ -

$\sin 30^\circ = 0.5$, $0.5\times2=1$, $9/3=3$, $3^2=9$, $1-9=-8$.

-8

Question

8. Convert to RPN: 12 / (4 + 2) - 1

12 4 2 + / 1 -

Question

9. Convert to algebraic notation (do not evaluate): 15 3 / 4 +

$\dfrac{15}{3} + 4$

Question

10. Evaluate: 18 3 / 4 - 2 ^

$18/3=6$, $6-4=2$, $2^2=4$.

4

Question

11. Convert to RPN: $\sqrt{m^2 + n^2}$

m 2 ^ n 2 ^ + sqrt

Question

12. Convert to algebraic notation: p q r * + s t - /

$\dfrac{p + qr}{s - t}$

Question

13. Evaluate: 60 cos 4 * 25 sqrt +

$\cos 60^\circ = 0.5$, $0.5\times4=2$, $\sqrt{25}=5$, $2+5=7$.

7

Question

14. Convert to RPN: (9 + 3) / (2 × 2)

9 3 + 2 2 * /

Question

15. Convert to algebraic notation: a b c + * d -

$a(b + c) - d$

Question

16. Evaluate: 7 3 + 2 * 4 -

$7+3=10$, $10\times2=20$, $20-4=16$.

16

Question

17. Convert to RPN: (u - v)(w + z) / y

u v - w z + * y /

Question

18. Evaluate: 8 3 2 * - 2 /

$3\times2=6$, $8-6=2$, $2/2=1$.

1

Question

19. Convert to RPN: $\dfrac{a+b}{c-d} \times e$

a b + c d - / e *

Question

20. Convert to algebraic notation: m n + p / q r * -

$\dfrac{m+n}{p} - qr$