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Mathematical Operations - Advanced Level: equation solving ADVANCED

Quick competitive exam prep session: 20 advanced-level mathematical operations questions. Worksheet 27 of 30 - Focus: equation solving. Practice operation rules, calculation puzzles, mathematical manipulation with instant feedback. Great for advanced students needing complex scenarios and multi-step problems practice.

📝 Worksheet 27 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Mathematical Operations
Worksheet 27 of 30 (90% complete)

Question 1

Simplify: 8 × (7 + (2 ÷ 3) - 15)
Apply BODMAS: brackets first, then multiplication/division, then addition/subtraction to get 8.67
bodmas, complex

Question 2

Given $ means ×, % means ÷, @ means +, # means -, which symbols should be interchanged to make 4 $ 15 % 14 @ 5 = 80?
The equation is already correct or no single interchange works
interchange, complex

Question 3

Simplify: (7 × 5) + (13 ÷ 8) ÷ 13
Apply BODMAS: brackets first, then multiplication/division, then addition/subtraction to get 35.12
bodmas, complex

Question 4

Given $ means ×, @ means +, % means ÷, # means -, which symbols should be interchanged to make 7 @ 8 % 5 $ 7 = 31?
The equation is already correct or no single interchange works
interchange, complex

Question 5

A value decreases by 29% and then decreases by 28%. What is the net percentage change?
Step 1: decrease by 29% → multiply by 0.71
Step 2: decrease by 28% → multiply by 0.72
Net change = -48.9%
percentage, reasoning

Question 6

A value increases by 32% and then increases by 17%. What is the net percentage change?
Step 1: increase by 32% → multiply by 1.32
Step 2: increase by 17% → multiply by 1.17
Net change = 54.4%
percentage, reasoning

Question 7

Given # means -, $ means ×, % means ÷, @ means +, which symbols should be interchanged to make 4 % 4 @ 14 # 3 = 46?
The equation is already correct or no single interchange works
interchange, complex

Question 8

If @ means +, $ means -, # means ×, find 6 @ (12 # 5) $ 10
Step 1: (12 × 5) = 60
Step 2: 6 + 60 - 10 = 56
bodmas, brackets

Question 9

What operator should replace '?' to make 17 ÷ 6 ? 17 = 28?
The correct operator is None because 17 ÷ 6 None 17 = 28
operator, reasoning

Question 10

If @ means +, % means ÷, # means -, $ means ×, then find the value of (10 % 7) # 11 @ 5
Step 1: (10 ÷ 7) = 1.43
Step 2: 1.43 - 11 + 5 = -4.57
substitution, brackets

Question 11

Find the missing number in the sequence: 1, 2, 4, ?, 16
The pattern: Each term is multiplied by 2. Therefore, the missing number is 8
pattern, sequence

Question 12

A value increases by 33% and then decreases by 29%. What is the net percentage change?
Step 1: increase by 33% → multiply by 1.33
Step 2: decrease by 29% → multiply by 0.71
Net change = -5.6%
percentage, reasoning

Question 13

What operator should replace '?' to make 17 + 15 ? 20 = 62?
The correct operator is None because 17 + 15 None 20 = 62
operator, reasoning

Question 14

If % means ÷, @ means +, # means -, $ means ×, then find the value of (7 $ 11) % 4 @ 9
Step 1: (7 × 11) = 77
Step 2: 77 ÷ 4 + 9 = 28.25
substitution, brackets

Question 15

If # means -, $ means ×, % means ÷, @ means +, then find the value of (9 # 2) $ 10 @ 4
Step 1: (9 - 2) = 7
Step 2: 7 × 10 + 4 = 74
substitution, brackets

Question 16

Which two numbers should be interchanged to make the equation 3 - 4 - 9 = 46 correct?
balance, interchange

Question 17

If % means ÷, $ means ×, # means -, @ means +, then find the value of (15 @ 13) % 2 $ 14
Step 1: (15 + 13) = 28
Step 2: 28 ÷ 2 × 14 = 196
substitution, brackets

Question 18

If @ means +, $ means -, # means ×, find 9 @ (9 # 4) $ 12
Step 1: (9 × 4) = 36
Step 2: 9 + 36 - 12 = 33
bodmas, brackets

Question 19

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

Question 20

What operator should replace '?' to make 8 × 18 ? 17 = 21?
The correct operator is None because 8 × 18 None 17 = 21
operator, reasoning
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