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Symbol Notation - Intermediate-Advanced Level: notation systems INTERMEDIATE-ADVANCED

Intensive strategic solving 🎯 drill: 20 intermediate-advanced-level symbol notation questions. Worksheet 20 of 30 hones your notation systems abilities. Practice symbol relationships, logical symbols, notation decoding under timed conditions. Best for advanced developing students seeking advanced concepts with increasing complexity.

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

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 20 of 30 (66% complete)

Question 1

In the notation system where ☆ means x², what is the value of ☆(8)?
Applying ☆ to 8:
8² = 64
complex, systems

Question 2

If ⊕ = +, ∇ = - (standard order of operations applies), then evaluate: 2 ⊕ 14 ∇ 15
Substituting symbols: 2 + 14 - 15
Applying order of operations: = 1
arithmetic, basic

Question 3

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(q(4)))
Evaluate from innermost outward:
r(p(q(4)))
= 1
nested, functions, advanced

Question 4

In the notation system where ☾ means x/3, what is the value of ☾(3)?
Applying ☾ to 3:
3/3 = 1
complex, systems

Question 5

If k(x) = x² - 1, then find k(5)
Substituting x = 5:
5² - 1 = 24
functions, substitution

Question 6

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

[-1 0]
[-4 3]
matrix, advanced

Question 7

If ⊗ = ×, ⊖ = - (standard order of operations applies), then evaluate: 11 ⊗ 3 ⊖ 10
Substituting symbols: 11 × 3 - 10
Applying order of operations: = 23
arithmetic, basic

Question 8

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

Question 9

Given: A = {4, 5, 9, 10} B = {1, 3, 4, 6, 9} C = {2, 3, 4, 5, 6, 7} Find: B ∩ A
Intersection of B and A:
{1, 3, 4, 6, 9} ∩ {4, 5, 9, 10} = {4, 9}
sets, operations

Question 10

If P = False and '!' means NOT, then evaluate: !P
Logical operation: NOT
P=False → NOT flips the value
Result: True
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: q(h(5))
Evaluate from innermost outward:
q(h(5))
= 12.50
nested, functions, advanced

Question 12

If h(x) = x³/2, then find h(10)
Substituting x = 10:
10³/2 = 500
functions, substitution

Question 13

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(r(5)))
Evaluate from innermost outward:
g(p(r(5)))
= 231
nested, functions, advanced

Question 14

Given: A = {2, 3, 7} B = {1, 4, 6, 8, 10} C = {1, 2, 3} Find: C ∩ B
Intersection of C and B:
{1, 2, 3} ∩ {1, 4, 6, 8, 10} = {1}
sets, operations

Question 15

In the notation system where ▲ means 4x, what is the value of ▲(6)?
Applying ▲ to 6:
46 = 46
complex, systems

Question 16

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: h(p(q(3)))
Evaluate from innermost outward:
h(p(q(3)))
= -2.25
nested, functions, advanced

Question 17

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

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: r(p(g(6)))
Evaluate from innermost outward:
r(p(g(6)))
= 322
nested, functions, advanced

Question 19

If ♧ = ×, ♡ = ÷ (standard order of operations applies), then evaluate: 7 ♧ 12 ♡ 2
Substituting symbols: 7 × 12 ÷ 2
Applying order of operations: = 42
arithmetic, basic

Question 20

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

[ 0 -1]
[ 1 -3]
matrix, advanced
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