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Symbol Notation - Advanced Level: mathematical notation ADVANCED

Boost your speed and accuracy with this high difficulty set 📈 worksheet. Worksheet 25 of 30 presents 20 advanced-level symbol notation problems. Focus on mathematical notation while practicing symbolic representation, notation systems, symbol relationships. Difficulty: complex scenarios and multi-step problems. Perfect for advanced test takers.

📝 Worksheet 25 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 25 of 30 (83% complete)

Question 1

If □ = ÷, ♢ = + (standard order of operations applies), then evaluate: 4 □ 4 ♢ 8
Substituting symbols: 4 ÷ 4 + 8
Applying order of operations: = 9
arithmetic, basic

Question 2

If '≻' means '>', then determine: 18 ≻ 15
≻ = >
18 > 15 is True
inequality, comparison

Question 3

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

Question 4

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(r(h(2)))
Evaluate from innermost outward:
f(r(h(2)))
= 35
nested, functions, advanced

Question 5

If ♧ = ×, □ = ÷ (standard order of operations applies), then evaluate: 4 ♧ 15 □ 4
Substituting symbols: 4 × 15 ÷ 4
Applying order of operations: = 12
arithmetic, basic

Question 6

Given: A = {2, 3, 4, 5, 7, 10} B = {1, 3, 7, 8} C = {3, 5, 6, 8} Find: B △ A
Symmetric Difference of B and A:
{1, 3, 7, 8} △ {2, 3, 4, 5, 7, 10} = {1, 2, 4, 5, 8, 10}
sets, operations

Question 7

In the notation system where ▶ means x - 2, what is the value of ▶(6)?
Applying ▶ to 6:
6 - 2 = 4
complex, systems

Question 8

Given: A = {1, 4, 6, 8, 10} B = {4, 5, 6, 8, 10} C = {8, 9, 10} Find: A ∩ B
Intersection of A and B:
{1, 4, 6, 8, 10} ∩ {4, 5, 6, 8, 10} = {4, 6, 8, 10}
sets, operations

Question 9

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

Question 10

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

Question 11

If ♡ = ÷, ⊘ = ÷ (standard order of operations applies), then evaluate: 4 ♡ 2 ⊘ 12
Substituting symbols: 4 ÷ 2 ÷ 12
Applying order of operations: = 4
arithmetic, basic

Question 12

In the notation system where ◆ means 2x + 1, what is the value of ◆(7)?
Applying ◆ to 7:
27 + 1 = 28
complex, systems

Question 13

Given matrices: A = [ 4 1] [ 2 1] B = [ 4 2] [ 2 1] Compute: A + B
Matrix addition:
A + B =

[ 8 3]
[ 4 2]
matrix, advanced

Question 14

If P = True, Q = True, and 'nand' means NAND, then evaluate: P nand Q
Logical operation: NAND
P=True, Q=True → NAND is True except when both are True
Result: False
logic, boolean

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: q(r(p(4)))
Evaluate from innermost outward:
q(r(p(4)))
= 15
nested, functions, advanced

Question 16

If k(x) = x² - 1, then find k(2)
Substituting x = 2:
2² - 1 = 3
functions, substitution

Question 17

In the notation system where ● means x + x, what is the value of ●(8)?
Applying ● to 8:
8 + 8 = 16
complex, systems

Question 18

If P = False, Q = True, and '->' means IMPLIES, then evaluate: P -> Q
Logical operation: IMPLIES
P=False, Q=True → IMPLIES is False only when P=True and Q=False
Result: True
logic, boolean

Question 19

If '≺' means '<', then determine: 15 ≺ 13
≺ = <
15 < 13 is False
inequality, comparison

Question 20

If ⊗ = ×, ⊕ = + (standard order of operations applies), then evaluate: 13 ⊗ 2 ⊕ 8
Substituting symbols: 13 × 2 + 8
Applying order of operations: = 34
arithmetic, basic
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