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Mathematical Operations - Intermediate-Advanced Level: arithmetic operations INTERMEDIATE-ADVANCED

Strategic expert challenge ★ for mathematical operations: 20 intermediate-advanced-level problems. Worksheet 19 of 30 - Focus: arithmetic operations. Develop expertise in mathematical reasoning, operation rules, calculation puzzles with step-by-step solutions. Ideal for advanced developing learners targeting advanced concepts with increasing complexity.

📝 Worksheet 19 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Mathematical Operations
Worksheet 19 of 30 (63% complete)

Question 1

If % means ÷, $ means ×, # means -, @ means +, then find the value of (12 @ 11) % 14 $ 14
Step 1: (12 + 11) = 23
Step 2: 23 ÷ 14 × 14 = 22.959999999999997
substitution, brackets

Question 2

What operator should replace '?' to make 7 ? 20 × 20 = 67?
The correct operator is None because 7 None 20 × 20 = 67
operator, reasoning

Question 3

Simplify: 2/7 - (8/4 + 2/5)
Following BODMAS, calculate step by step to get -74/35
fractions, bodmas

Question 4

If % means ÷, @ means +, $ means ×, # means -, then find the value of 12 # 18 $ 16
Substitute symbols: 12 - 18 × 16 = -276
substitution, basic

Question 5

Which two numbers should be interchanged to make the equation 4 - 7 + 12 = 43 correct?
balance, interchange

Question 6

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

Question 7

If # means -, $ means ×, % means ÷, @ means +, then find the value of (3 $ 8) @ 2 % 14
Step 1: (3 × 8) = 24
Step 2: 24 + 2 ÷ 14 = 1.86
substitution, brackets

Question 8

If $ means -, @ means +, # means ×, find 7 @ (11 # 4) $ 11
Step 1: (11 × 4) = 44
Step 2: 7 + 44 - 11 = 40
bodmas, brackets

Question 9

A value decreases by 16% and then decreases by 23%. What is the net percentage change?
Step 1: decrease by 16% → multiply by 0.84
Step 2: decrease by 23% → multiply by 0.77
Net change = -35.3%
percentage, reasoning

Question 10

Find the missing number in the sequence: 2, 4, 8, ?, 32
The pattern: Each term increases by 2. Therefore, the missing number is 16
pattern, sequence

Question 11

If $ means -, @ means +, # means ×, find 8 @ (7 # 11) $ 6
Step 1: (7 × 11) = 77
Step 2: 8 + 77 - 6 = 79
bodmas, brackets

Question 12

If $ means -, @ means +, # means ×, find 5 @ (10 # 2) $ 9
Step 1: (10 × 2) = 20
Step 2: 5 + 20 - 9 = 16
bodmas, brackets

Question 13

Simplify: 4 × (3 + 2) ÷ 2 × 7
Apply BODMAS: brackets first, then multiplication/division, then addition/subtraction to get 70
bodmas, complex

Question 14

Simplify: 8 ÷ (4 × (8 + 14) + 7)
Apply BODMAS: brackets first, then multiplication/division, then addition/subtraction to get 8
bodmas, complex

Question 15

Given: Q < P, P > S, Q > P. Which of the following is definitely true?
From Q < P and P > S, we can deduce Cannot determine
inequality, logic

Question 16

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

Question 17

Find the missing number in the sequence: 9, 11, 13, 15, ?
The pattern: Each term increases by 2. Therefore, the missing number is 17
pattern, sequence

Question 18

If $ means ×, # means -, @ means +, % means ÷, then find the value of 14 % 9 @ 20
Substitute symbols: 14 ÷ 9 + 20 = 21.56
substitution, basic

Question 19

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

Question 20

If $ means ×, % means ÷, # means -, @ means +, then find the value of (7 % 13) @ 9 # 7
Step 1: (7 ÷ 13) = 0.54
Step 2: 0.54 + 9 - 7 = 2.539999999999999
substitution, brackets
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