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Mathematical Operations - Intermediate Level: symbolic operations INTERMEDIATE

Comprehensive weakness targeting worksheet covering 20 intermediate-level mathematical operations problems. Worksheet 18 of 30 emphasizes symbolic operations. Master arithmetic operations, mathematical reasoning, operation rules 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 Mathematical Operations
Worksheet 18 of 30 (60% complete)

Question 1

If @ means +, # means ×, $ means -, find 5 @ (9 # 4) $ 4
Step 1: (9 × 4) = 36
Step 2: 5 + 36 - 4 = 37
bodmas, brackets

Question 2

Given # means -, $ means ×, % means ÷, @ means +, which symbols should be interchanged to make 4 # 6 $ 9 @ 13 = 35?
The equation is already correct or no single interchange works
interchange, complex

Question 3

Given: S < P, Q < R, P < Q. Which of the following is definitely true?
From S < P and Q < R, we can deduce S < R
inequality, logic

Question 4

Given % means ÷, @ means +, $ means ×, # means -, which symbols should be interchanged to make 7 % 14 @ 11 # 4 = 46?
The equation is already correct or no single interchange works
interchange, complex

Question 5

A value increases by 20% and then increases by 39%. What is the net percentage change?
Step 1: increase by 20% → multiply by 1.2
Step 2: increase by 39% → multiply by 1.3900000000000001
Net change = 66.8%
percentage, reasoning

Question 6

If # means -, $ means ×, @ means +, % means ÷, then find the value of 3 % 19 $ 6
Substitute symbols: 3 ÷ 19 × 6 = 0.96
substitution, basic

Question 7

If # means ×, @ means +, $ means -, find 10 @ (7 # 10) $ 8
Step 1: (7 × 10) = 70
Step 2: 10 + 70 - 8 = 72
bodmas, brackets

Question 8

Find the missing number in the sequence: 8, 13, 18, 23, 28, ?
The pattern: Each term increases by 5. Therefore, the missing number is 33
pattern, sequence

Question 9

Simplify: 5/12 + (1/12 × 2/9)
Following BODMAS, calculate step by step to get 47/108
fractions, bodmas

Question 10

A value increases by 50% and then decreases by 36%. What is the net percentage change?
Step 1: increase by 50% → multiply by 1.5
Step 2: decrease by 36% → multiply by 0.64
Net change = -4.0%
percentage, reasoning

Question 11

If # means ×, $ means -, @ means +, find 9 @ (3 # 12) $ 3
Step 1: (3 × 12) = 36
Step 2: 9 + 36 - 3 = 42
bodmas, brackets

Question 12

What operator should replace '?' to make 8 ? 6 + 9 = 65?
The correct operator is None because 8 None 6 + 9 = 65
operator, reasoning

Question 13

If # means -, $ means ×, % means ÷, @ means +, then find the value of 10 % 19 $ 3
Substitute symbols: 10 ÷ 19 × 3 = 1.59
substitution, basic

Question 14

If % means ÷, $ means ×, # means -, @ means +, then find the value of 18 # 10 % 5
Substitute symbols: 18 - 10 ÷ 5 = 16
substitution, basic

Question 15

Given $ means ×, % means ÷, @ means +, # means -, which symbols should be interchanged to make 10 % 15 # 7 @ 4 = 26?
The equation is already correct or no single interchange works
interchange, complex

Question 16

If $ means ×, % means ÷, @ means +, # means -, then find the value of 16 @ 20 % 10
Substitute symbols: 16 + 20 ÷ 10 = 18
substitution, basic

Question 17

If @ means +, % means ÷, $ means ×, # means -, then find the value of 15 @ 3 # 18
Substitute symbols: 15 + 3 - 18 = 0
substitution, basic

Question 18

If # means -, % means ÷, $ means ×, @ means +, then find the value of (2 @ 12) % 11 $ 10
Step 1: (2 + 12) = 14
Step 2: 14 ÷ 11 × 10 = 12.7
substitution, brackets

Question 19

Simplify: (6/8 + 2/4) - 6/9
Following BODMAS, calculate step by step to get 7/12
fractions, bodmas

Question 20

Simplify: (1/7 + 4/8) + 6/8
Following BODMAS, calculate step by step to get 39/28
fractions, bodmas
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