ReasoningAbility.com

Symbol Notation - Beginner-Intermediate Level: mathematical notation BEGINNER-INTERMEDIATE

Intensive quick response training 🎯 drill: 20 beginner-intermediate-level symbol notation questions. Worksheet 10 of 30 hones your mathematical notation abilities. Practice symbol interpretation, symbolic representation, notation systems under timed conditions. Best for developing students seeking building on fundamentals with moderate challenges.

📝 Worksheet 10 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 10 of 30 (33% complete)

Question 1

If ◇ = ÷, ⊘ = ÷ (standard order of operations applies), then evaluate: 14 ◇ 14 ⊘ 14
Substituting symbols: 14 ÷ 14 ÷ 14
Applying order of operations: = 14
arithmetic, basic

Question 2

If '≽' means '≥', then determine: 19 ≽ 2
≽ = ≥
19 ≥ 2 is True
inequality, comparison

Question 3

Given: A = {1, 5, 9} B = {5, 7, 9} C = {3, 4, 6, 8, 10} Find: A − B
Difference of A and B:
{1, 5, 9} − {5, 7, 9} = {1}
sets, operations

Question 4

In the notation system where ☾ means x/3, what is the value of ☾(7)?
Applying ☾ to 7:
7/3 = 2.33
complex, systems

Question 5

If k(x) = x - 8, then find k(8)
Substituting x = 8:
8 - 8 = 0
functions, substitution

Question 6

If ♢ = +, ★ = + (standard order of operations applies), then evaluate: 5 ♢ 4 ★ 4
Substituting symbols: 5 + 4 + 4
Applying order of operations: = 13
arithmetic, basic

Question 7

If P = False, Q = False, and '<->' means IFF, then evaluate: P <-> Q
Logical operation: IFF
P=False, Q=False → IFF is True when both are same
Result: True
logic, boolean

Question 8

In the notation system where ▼ means x² - 1, what is the value of ▼(3)?
Applying ▼ to 3:
3² - 1 = 8
complex, systems

Question 9

If h(x) = 2x², then find h(10)
Substituting x = 10:
210² = 44100
functions, substitution

Question 10

In the notation system where ◆ means 2x + 1, what is the value of ◆(4)?
Applying ◆ to 4:
24 + 1 = 25
complex, systems

Question 11

Given: A = {1, 3, 4} B = {4, 6, 8, 10} C = {4, 5, 7, 9, 10} Find: C △ A
Symmetric Difference of C and A:
{4, 5, 7, 9, 10} △ {1, 3, 4} = {1, 3, 5, 7, 9, 10}
sets, operations

Question 12

If k(x) = x - 8, then find k(8)
Substituting x = 8:
8 - 8 = 0
functions, substitution

Question 13

If '≠' means '≠', then determine: 7 ≠ 5
≠ = ≠
7 ≠ 5 is True
inequality, comparison

Question 14

Given: A = {1, 2, 4, 9, 10} B = {1, 3, 8, 10} C = {2, 4, 6} Find: A − C
Difference of A and C:
{1, 2, 4, 9, 10} − {2, 4, 6} = {1, 9, 10}
sets, operations

Question 15

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: r(p(h(3)))
Evaluate from innermost outward:
r(p(h(3)))
= 35
nested, functions, advanced

Question 16

In the notation system where ♣ means x/2, what is the value of ♣(2)?
Applying ♣ to 2:
2/2 = 1
complex, systems

Question 17

Given: A = {3, 4, 6, 7, 8, 10} B = {5, 7, 8, 9} C = {3, 5, 8, 9, 10} Find: B △ C
Symmetric Difference of B and C:
{5, 7, 8, 9} △ {3, 5, 8, 9, 10} = {3, 7, 10}
sets, operations

Question 18

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: f(q(g(3)))
Evaluate from innermost outward:
f(q(g(3)))
= 13.50
nested, functions, advanced

Question 19

If '≺' means '<', then determine: 17 ≺ 17
≺ = <
17 < 17 is False
inequality, comparison

Question 20

If ♢ = +, ⊘ = ÷ (standard order of operations applies), then evaluate: 6 ♢ 3 ⊘ 13
Substituting symbols: 6 + 3 ÷ 13
Applying order of operations: = 6
arithmetic, basic
Previous Worksheet Next Worksheet