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GMAT Algebra: Simultaneous Linear Equations & Quadratics — practice questions

Explore 20 free Algebra: Simultaneous Linear Equations & Quadratics questions in GMAT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra: Simultaneous Linear Equations & Quadratics questions and exercises with answers

Showing questions 1–20 of 20.

$\sin(180° - \theta)$ equals:Read the answer and worked solution →Find the distance of (3, 4) from the origin.Read the answer and worked solution →Point (3, k) is the midpoint of segment joining (1, 4) and (5, 6). Find k.Read the answer and worked solution →If 2x + 5 = 17, x =Read the answer and worked solution →Solve: 3(x − 2) = 12.Read the answer and worked solution →Slope of y = 4x − 7 is:Read the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Which test applies?Read the answer and worked solution →Flip and pair: condition with conclusionRead the answer and worked solution →Tap every statement true of slopeRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Complete the angle between two linesRead the answer and worked solution →True or false: using coordinatesRead the answer and worked solution →Point (3, k) is the midpoint of segment joining (1, 4) and (5, 6). Find k.Read the answer and worked solution →Find the distance of (3, 4) from the origin.Read the answer and worked solution →If 2x + 5 = 17, x =Read the answer and worked solution →$\sin(180° - \theta)$ equals:Read the answer and worked solution →Solve: 3(x − 2) = 12.Read the answer and worked solution →Slope of y = 4x − 7 is:Read the answer and worked solution →

Worked practice questions

$\sin(180° - \theta)$ equals:

  1. $-\cos\theta$
  2. $-\sin\theta$
  3. $\sin\theta$
  4. $\cos\theta$
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Correct answer: C. $\sin\theta$

Supplementary-angle identity: $\sin(180° - \theta) = \sin\theta$. Reason: sine is positive in the second quadrant (where $180° - \theta$ lies for $0° < \theta < 180°$), and the reference angle is $\theta$. Companion identities: - $\cos(180° - \theta) = -\cos\theta$ - $\tan(180° - \theta) = -\tan\theta$

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Find the distance of (3, 4) from the origin.

  1. 3
  2. 5
  3. 7
  4. 4
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Correct answer: B. 5

√(3² + 4²) = √25 = 5. The 3–4–5 right triangle.

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Point (3, k) is the midpoint of segment joining (1, 4) and (5, 6). Find k.

  1. 5
  2. 7
  3. 6
  4. 4
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Correct answer: A. 5

Midpoint y-coordinate: (4 + 6)/2 = 5. So k = 5.

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