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Symbol Notation - Intermediate Level: symbol interpretation INTERMEDIATE

Comprehensive weakness targeting worksheet covering 20 intermediate-level symbol notation problems. Worksheet 18 of 30 emphasizes symbol interpretation. Master symbolic representation, notation systems, symbol relationships through detailed explanations. Difficulty: moderate complexity with mixed patterns. Tailored for mid-level preparation.

📝 Worksheet 18 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 18 of 30 (60% complete)

Question 1

If h(x) = 2x², then find h(4)
Substituting x = 4:
24² = 576
functions, substitution

Question 2

If '≺' means '<', then determine: 15 ≺ 12
≺ = <
15 < 12 is False
inequality, comparison

Question 3

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

[ 6 6]
[ 2 4]
matrix, advanced

Question 4

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

Question 5

If ◊ = ×, ∇ = - (standard order of operations applies), then evaluate: 2 ◊ 5 ∇ 5
Substituting symbols: 2 × 5 - 5
Applying order of operations: = 5
arithmetic, basic

Question 6

In the notation system where ▲ means 4x, what is the value of ▲(2)?
Applying ▲ to 2:
42 = 42
complex, systems

Question 7

If '≼' means '≤', then determine: 4 ≼ 10
≼ = ≤
4 ≤ 10 is True
inequality, comparison

Question 8

If ★ = +, ♤ = - (standard order of operations applies), then evaluate: 9 ★ 15 ♤ 14
Substituting symbols: 9 + 15 - 14
Applying order of operations: = 10
arithmetic, basic

Question 9

Given matrices: A = [ 3 4] [ 1 3] B = [ 5 1] [ 5 1] Compute: A + B
Matrix addition:
A + B =

[ 8 5]
[ 6 4]
matrix, advanced

Question 10

If ☆ = -, ⊖ = - (standard order of operations applies), then evaluate: 13 ☆ 15 ⊖ 15
Substituting symbols: 13 - 15 - 15
Applying order of operations: = -17
arithmetic, basic

Question 11

In the notation system where ☀ means x³, what is the value of ☀(3)?
Applying ☀ to 3:
3³ = 27
complex, systems

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: h(r(q(5)))
Evaluate from innermost outward:
h(r(q(5)))
= 992.25
nested, functions, advanced

Question 13

If '≠' means '≠', then determine: 2 ≠ 17
≠ = ≠
2 ≠ 17 is True
inequality, comparison

Question 14

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

[ 0 3]
[ 0 -2]
matrix, advanced

Question 15

If ♤ = -, ◊ = × (standard order of operations applies), then evaluate: 9 ♤ 5 ◊ 12
Substituting symbols: 9 - 5 × 12
Applying order of operations: = -51
arithmetic, basic

Question 16

If h(x) = x + 10, then find h(8)
Substituting x = 8:
8 + 10 = 18
functions, substitution

Question 17

If ♧ = ×, ∆ = + (standard order of operations applies), then evaluate: 4 ♧ 4 ∆ 3
Substituting symbols: 4 × 4 + 3
Applying order of operations: = 19
arithmetic, basic

Question 18

If '≻' means '>', then determine: 3 ≻ 4
≻ = >
3 > 4 is False
inequality, comparison

Question 19

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

Question 20

If ⊘ = ÷, ⊖ = - (standard order of operations applies), then evaluate: 5 ⊘ 13 ⊖ 4
Substituting symbols: 5 ÷ 13 - 4
Applying order of operations: = -4
arithmetic, basic
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