Arithmetic Operations and Algebra Problems Workshop 1

Question 1

What are the classifications of the number 2?

Answer 1

N, W, Z, Q, R

N: Natural numbers, W: Whole numbers, Z: Integers, Q: Rational numbers, R: Real numbers

Question 2

Evaluate the expression 10 + 24 ÷ 6 − 8 − 3 × 2.

Answer 2

0

Question 3

What is the lowest common multiple (LCM) of 6 and 9?

Answer 3

18

Question 4

Calculate the simplest form of 1/6 + 4/9.

Answer 4

11/18

Question 5

What is the result of 3/4 × 8/9?

Answer 5

2/3

Question 6

Simplify the expression 12x + 3y − 7x + 11y − 2.

Answer 6

5x + 14y − 2

Question 7

Expand and simplify 10(2a − 5).

Answer 7

20a − 50

Question 8

Expand and simplify 7(3x − 5) + 2(x − 4).

Answer 8

23x − 43

Question 9

What is the expansion of (x − 8)²?

Answer 9

x² − 16x + 64

Question 10

What row corresponds to n = 6 in Pascal’s triangle?

Answer 10

1 6 15 20 15 6 1

Question 11

Use Pascal’s triangle to expand (a + b)⁴.

Answer 11

a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

Question 12

Factor the expression 15y + 10y².

Answer 12

5y(3 + 2y)

Question 13

Evaluate the expression 3 + 6 × 2 ÷ 4 − 1.

Answer 13

5

Question 14

What is the result of 21/5 ÷ 7/30?

Answer 14

18

Question 15

Simplify the expression 5a² + 4a + 2a² − 9a.

Answer 15

7a² − 5a

Question 16

Expand and simplify −5(3g − 8).

Answer 16

−15g + 40

Question 17

Use Pascal’s triangle to expand (x + y)³.

Answer 17

x³ + 3x²y + 3xy² + y³

Question 18

Rearrange the Ideal Gas Law to express pressure (p) in terms of volume (V), number of moles (n), temperature (T), and the ideal gas constant (R).

Answer 18

p = nRT / V

Question 19

Rearrange the Ideal Gas Law to express volume (V).

Answer 19

V = nRT / p

Question 20

Rearrange the Ideal Gas Law to express temperature (T).

Answer 20

T = pV / nR

Question 21

Rearrange the Ideal Gas Law to express number of moles (n).

Answer 21

n = pV / RT