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Symbol Notation - Intermediate-Advanced Level: symbol relationships INTERMEDIATE-ADVANCED

This fundamentals focus worksheet contains 20 intermediate-advanced-level symbol notation problems. Worksheet 21 of 30 focuses on symbol relationships. Practice logical symbols, notation decoding, symbolic reasoning with our step-by-step solutions. Difficulty: advanced concepts with increasing complexity. Recommended for advanced developing learners.

📝 Worksheet 21 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 21 of 30 (70% complete)

Question 1

Given matrices: A = [ 1 1] [ 5 4] B = [ 3 4] [ 2 2] Compute: A - B
Matrix subtraction:
A - B =

[-2 -3]
[ 3 2]
matrix, advanced

Question 2

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(h(2))
Evaluate from innermost outward:
q(h(2))
= 2
nested, functions, advanced

Question 3

If ∆ = +, ⊘ = ÷ (standard order of operations applies), then evaluate: 13 ∆ 7 ⊘ 15
Substituting symbols: 13 + 7 ÷ 15
Applying order of operations: = 13
arithmetic, basic

Question 4

In the notation system where ★ means 2x², what is the value of ★(3)?
Applying ★ to 3:
23² = 529
complex, systems

Question 5

If ⊕ = +, ⊗ = × (standard order of operations applies), then evaluate: 6 ⊕ 8 ⊗ 5
Substituting symbols: 6 + 8 × 5
Applying order of operations: = 46
arithmetic, basic

Question 6

Given matrices: A = [ 5 2] [ 3 5] B = [ 4 3] [ 4 3] Compute: A - B
Matrix subtraction:
A - B =

[ 1 -1]
[-1 2]
matrix, advanced

Question 7

If '≻' means '>', then determine: 14 ≻ 7
≻ = >
14 > 7 is True
inequality, comparison

Question 8

If f(x) = 2x + 1, then find f(5)
Substituting x = 5:
25 + 1 = 26
functions, substitution

Question 9

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(f(g(6)))
Evaluate from innermost outward:
r(f(g(6)))
= 327
nested, functions, advanced

Question 10

If P = True and '!' means NOT, then evaluate: !P
Logical operation: NOT
P=True → NOT flips the value
Result: False
logic, boolean

Question 11

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: g(p(q(3)))
Evaluate from innermost outward:
g(p(q(3)))
= 0.50
nested, functions, advanced

Question 12

Given: A = {1, 2, 4, 6, 9} B = {2, 4, 6, 7} C = {2, 5, 6, 8, 9, 10} Find: A ∪ B
Union of A and B:
{1, 2, 4, 6, 9} ∪ {2, 4, 6, 7} = {1, 2, 4, 6, 7, 9}
sets, operations

Question 13

In the notation system where ☁ means x + 10, what is the value of ☁(7)?
Applying ☁ to 7:
7 + 10 = 17
complex, systems

Question 14

If h(x) = x - x/2, then find h(10)
Substituting x = 10:
10 - 10/2 = 5
functions, substitution

Question 15

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

Question 16

In the notation system where ♥ means 3x, what is the value of ♥(5)?
Applying ♥ to 5:
35 = 35
complex, systems

Question 17

If ∆ = +, ⊖ = - (standard order of operations applies), then evaluate: 11 ∆ 7 ⊖ 15
Substituting symbols: 11 + 7 - 15
Applying order of operations: = 3
arithmetic, basic

Question 18

If P = True, Q = True, and '&' means AND, then evaluate: P & Q
Logical operation: AND
P=True, Q=True → AND gives True only if both True
Result: True
logic, boolean

Question 19

If ♤ = -, ★ = + (standard order of operations applies), then evaluate: 9 ♤ 14 ★ 5
Substituting symbols: 9 - 14 + 5
Applying order of operations: = 0
arithmetic, basic

Question 20

If g(x) = 2x - 3, then find g(8)
Substituting x = 8:
28 - 3 = 25
functions, substitution
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