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Symbol Notation - Advanced Level: notation decoding ADVANCED

Exam-focused holistic practice ★ worksheet: 20 advanced-level symbol notation questions. Worksheet 23 of 30 targets notation decoding. Build proficiency in notation puzzles, symbol interpretation, symbolic representation with detailed solutions. Ideal for advanced competitive exam preparation.

📝 Worksheet 23 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 23 of 30 (76% complete)

Question 1

If ☆ = -, ⊘ = ÷ (standard order of operations applies), then evaluate: 1 ☆ 4 ⊘ 10
Substituting symbols: 1 - 4 ÷ 10
Applying order of operations: = 1
arithmetic, basic

Question 2

If '≈' means '≈', then determine: 5 ≈ 14
≈ = ≈
5 ≈ 14 (approximately equal) is False
inequality, comparison

Question 3

If ∇ = -, ♡ = ÷ (standard order of operations applies), then evaluate: 3 ∇ 11 ♡ 7
Substituting symbols: 3 - 11 ÷ 7
Applying order of operations: = 2
arithmetic, basic

Question 4

In the notation system where ★ means 2x², what is the value of ★(2)?
Applying ★ to 2:
22² = 484
complex, systems

Question 5

If '≼' means '≤', then determine: 13 ≼ 1
≼ = ≤
13 ≤ 1 is False
inequality, comparison

Question 6

Given matrices: A = [ 5 2] [ 1 1] B = [ 4 3] [ 3 3] Compute: A × B
Matrix multiplication:
A × B =

[26 21]
[ 7 6]
matrix, advanced

Question 7

If ★ = +, ♢ = + (standard order of operations applies), then evaluate: 2 ★ 8 ♢ 11
Substituting symbols: 2 + 8 + 11
Applying order of operations: = 21
arithmetic, basic

Question 8

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

Question 9

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

Question 10

If h(x) = x - x/2, then find h(6)
Substituting x = 6:
6 - 6/2 = 3
functions, substitution

Question 11

Given matrices: A = [ 4 2] [ 5 4] B = [ 4 3] [ 3 4] Compute: A × B
Matrix multiplication:
A × B =

[22 20]
[32 31]
matrix, advanced

Question 12

In the notation system where ♣ means x/2, what is the value of ♣(8)?
Applying ♣ to 8:
8/2 = 4
complex, systems

Question 13

If P = True, Q = True, and 'xor' means XOR, then evaluate: P xor Q
Logical operation: XOR
P=True, Q=True → XOR is True when inputs differ
Result: False
logic, boolean

Question 14

Given: A = {2, 7, 8} B = {2, 4, 5, 6, 8} C = {3, 4, 10} Find: C ∪ A
Union of C and A:
{3, 4, 10} ∪ {2, 7, 8} = {2, 3, 4, 7, 8, 10}
sets, operations

Question 15

If '≻' means '>', then determine: 8 ≻ 5
≻ = >
8 > 5 is True
inequality, comparison

Question 16

In the notation system where ☽ means x - 5, what is the value of ☽(6)?
Applying ☽ to 6:
6 - 5 = 1
complex, systems

Question 17

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(h(g(6)))
Evaluate from innermost outward:
f(h(g(6)))
= 678
nested, functions, advanced

Question 18

Given: A = {2, 3, 4, 7, 8, 9} B = {2, 4, 10} C = {1, 3, 5, 7, 9, 10} Find: C − A
Difference of C and A:
{1, 3, 5, 7, 9, 10} − {2, 3, 4, 7, 8, 9} = {1, 5, 10}
sets, operations

Question 19

In the notation system where ☾ means x/3, what is the value of ☾(4)?
Applying ☾ to 4:
4/3 = 1.33
complex, systems

Question 20

Given matrices: A = [ 4 4] [ 4 1] B = [ 5 1] [ 5 1] Compute: A × B
Matrix multiplication:
A × B =

[40 8]
[25 5]
matrix, advanced
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