DCAS Algebraic Reasoning 1 — Questions and Answers
Question 1: If 3x + 5 = 20, what is the value of x?
- 3
- 5 (Correct answer)
- 7
- 15
Correct answer: 5
Subtracting 5 from both sides gives 3x = 15, then dividing by 3 gives x = 5.
Question 2: Which expression represents '7 less than 4 times a number n'?
- 7 - 4n
- 4n - 7 (Correct answer)
- 4 + n - 7
- 7n - 4
Correct answer: 4n - 7
'4 times a number n' is 4n, and '7 less than' means subtract 7 from it, giving 4n - 7.
Question 3: What is the value of 3² + 4 × 2 - 6 ÷ 3?
- 15 (Correct answer)
- 17
- 19
- 21
Correct answer: 15
Using order of operations: 3² = 9, then 4×2 = 8 and 6÷3 = 2, giving 9 + 8 - 2 = 15.
Question 4: If f(x) = 2x - 3, what is f(4)?
- 5 (Correct answer)
- 8
- 11
- 14
Correct answer: 5
Substituting x = 4: f(4) = 2(4) - 3 = 8 - 3 = 5.
Question 5: Which inequality represents 'a number x is at least 12'?
- x < 12
- x > 12
- x ≤ 12
- x ≥ 12 (Correct answer)
Correct answer: x ≥ 12
'At least 12' means x can equal 12 or be greater, which is written as x ≥ 12.
Question 6: What is the next term in the arithmetic sequence: 2, 5, 8, 11, ___?
- 12
- 13
- 14 (Correct answer)
- 15
Correct answer: 14
Each term increases by 3 (the common difference is 3), so 11 + 3 = 14.
Question 7: Which of the following is a variable expression?
- 4 + 7
- 3 × 6
- 5n + 2 (Correct answer)
- 100 - 45
Correct answer: 5n + 2
5n + 2 contains the variable n, making it a variable expression; the others consist only of numbers.
DCAS Algebraic Reasoning 1
If 3x + 5 = 20, what is the value of x?