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Symbol Notation - Expert Level: comparative symbols EXPERT

Intensive progress check 🎯 drill: 20 expert-level symbol notation questions. Worksheet 30 of 30 hones your comparative symbols abilities. Practice notation puzzles, symbol interpretation, symbolic representation under timed conditions. Best for expert-level students seeking challenging problems and time-bound practice.

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

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 30 of 30 (100% complete)

Question 1

If P = True, Q = False, and 'nor' means NOR, then evaluate: P nor Q
Logical operation: NOR
P=True, Q=False → NOR is True only when both are False
Result: False
logic, boolean

Question 2

If k(x) = x² - 1, then find k(4)
Substituting x = 4:
4² - 1 = 15
functions, substitution

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: p(f(g(5)))
Evaluate from innermost outward:
p(f(g(5)))
= 24
nested, functions, advanced

Question 4

If ⊕ = +, ∇ = - (standard order of operations applies), then evaluate: 5 ⊕ 4 ∇ 15
Substituting symbols: 5 + 4 - 15
Applying order of operations: = -6
arithmetic, basic

Question 5

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(h(5))
Evaluate from innermost outward:
r(h(5))
= 324
nested, functions, advanced

Question 6

If ◇ = ÷, ⊘ = ÷ (standard order of operations applies), then evaluate: 10 ◇ 15 ⊘ 8
Substituting symbols: 10 ÷ 15 ÷ 8
Applying order of operations: = 10
arithmetic, basic

Question 7

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

Question 8

If '≈' means '≈', then determine: 12 ≈ 7
≈ = ≈
12 ≈ 7 (approximately equal) is False
inequality, comparison

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: h(p(f(2)))
Evaluate from innermost outward:
h(p(f(2)))
= 1
nested, functions, advanced

Question 10

In the notation system where ★ means 2x², what is the value of ★(6)?
Applying ★ to 6:
26² = 676
complex, systems

Question 11

If h(x) = x³/2, then find h(3)
Substituting x = 3:
3³/2 = 13.50
functions, substitution

Question 12

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(6))
Evaluate from innermost outward:
g(p(6))
= 23
nested, functions, advanced

Question 13

In the notation system where ● means x + x, what is the value of ●(3)?
Applying ● to 3:
3 + 3 = 6
complex, systems

Question 14

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

Question 15

If f(x) = x - 2, then find f(7)
Substituting x = 7:
7 - 2 = 5
functions, substitution

Question 16

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

[13 33]
[ 8 24]
matrix, advanced

Question 17

If h(x) = 2x², then find h(6)
Substituting x = 6:
26² = 676
functions, substitution

Question 18

If ☆ = -, ⊖ = - (standard order of operations applies), then evaluate: 10 ☆ 3 ⊖ 9
Substituting symbols: 10 - 3 - 9
Applying order of operations: = -2
arithmetic, basic

Question 19

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(g(2)))
Evaluate from innermost outward:
f(r(g(2)))
= 323
nested, functions, advanced

Question 20

In the notation system where ☀ means x³, what is the value of ☀(8)?
Applying ☀ to 8:
8³ = 512
complex, systems
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