SAT Math: Practice Questions-Passport to advanced mathematics-Structure in expressions

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Question

Crawford County, Iowa, is shaped like a rectangle. The length of the county is 6 miles longer than the width of the county. If \(A(x)\) is the area of the county, in square miles, and \(x\) is the width, in miles, which equation best models the area of the county? 

  1. \(A(x) = x(6x)\)
  2. \(A(x) = x(6 – x)\)
  3. \(A(x) = x(x – 6)\)
  4. \(A(x) = x(x + 6)\)
Answer/Explanation

Ans: D

Question

Which of the following expressions is equivalent to \(x^2+ 10x + 21\) ? 

  1. \( (x+ 1)(x+ 9) + 12 \)
  2. \((x + 1)(x + 9) + 12x\)
  3. \( (x+3)(x+ 7) + 5\)
  4. \((x + 3)(x + 7) + 5x\)
Answer/Explanation

Ans: A

Question

Which of the following is an equivalent form of the expression \((2x — 2)^2 — (2x — 2)\) ? 

  1. \(2x^2 — 6x + 6\)
  2. \(4x^2 — 10x + 2\)
  3. \((2x — 2)(2x — 2)\)
  4. \( (2x — 3)(2x — 2)\)
Answer/Explanation

Ans: D

Question

\((3x+2)(2x+3)\)

Which of the following is equivalent to the expression above? 

  1. \(3x^2 + 10x+5\)
  2. \(5x^2 + 13x+ 5\)
  3. \(6x^2 + 13x+6\)
  4. \(6x^2 +15x+9\)
Answer/Explanation

Ans: C

Question

Which of the following is equivalent to \((2x + 4)^2 – 4x^2\) ? 

  1. \(16(x+1)\)
  2. \(8(x+ 2)\)
  3. \(4(4x + 1)\)
  4. \(2(8x + 1) \)
Answer/Explanation

Ans: A

Question

If \(3x-6y=9z\), which of the following expressions is equivalent to \(x^2-4xy+4y^2\)? 

  1. \(9z\)
  2. \(3z^2\)
  3. \(9z^2\)
  4. \(81z^2\)
Answer/Explanation

Ans: C

Question

\(x(x + 1) + 2(x + 1) = ax^2 +bx+ c\)

In the equation above, \(a, b\), and \(c\) are constants. If the equation is true for all values of \(x\), what is the value of \(a + b + c \)? 

  1. 6
  2. 5
  3. 4
  4. 3
Answer/Explanation

Ans: A

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