Start learning →

GMAT Straight Lines and Conic Sections — practice questions — page 2

Explore 52 free Straight Lines and Conic Sections questions in GMAT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Straight Lines and Conic Sections with Quill →

Straight Lines and Conic Sections questions and exercises with answers

Showing questions 31–52 of 52.

Two sides of a triangle are 10 cm and 8 cm long and the sine of the angle between them is 0.5. What is the area?Read the answer and worked solution →Two sides of a triangle and the angle opposite the shorter of them are given. What does this produce?Read the answer and worked solution →Why does a trigonometric equation have infinitely many solutions unless the domain is restricted?Read the answer and worked solution →When solving a trigonometric equation, what is the CAST diagram used for?Read the answer and worked solution →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: convert degrees to radiansRead the answer and worked solution →Flip and pair: identity with its valueRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Tap every correct identityRead the answer and worked solution →

Worked practice questions

Two sides of a triangle are 10 cm and 8 cm long and the sine of the angle between them is 0.5. What is the area?

  1. 20 square centimetres
  2. 40 square centimetres
  3. 80 square centimetres
  4. 18 square centimetres
Show answer and solution

Correct answer: A. 20 square centimetres

1. The area rule works in any triangle and needs no perpendicular height. 2. It gives half the product of two side lengths multiplied by the sine of the angle between them. 3. Multiply the two sides: 10 cm times 8 cm is 80 square centimetres. 4. Multiply by the sine of the included angle: 80 times 0.5 is 40 square centimetres. 5. Take half of that: half of 40 is 20 square centimetres. 6. The area of the triangle is therefore 20 square centimetres. 7. Answering 80 square centimetres uses neither the sine value nor the halving. 8. Answering 40 square centimetres forgets the halving, and 18 square centimetres adds the sides instead. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 6: Trigonometry_

Open this question →

Two sides of a triangle and the angle opposite the shorter of them are given. What does this produce?

  1. One possible triangle
  2. Two possible triangles
  3. No possible triangle
  4. Four possible triangles
Show answer and solution

Correct answer: B. Two possible triangles

1. Two sides and an interior angle have been given, so the sine rule is the tool to use. 2. The side opposite the given angle is the shorter of the two given sides. 3. In that situation two different triangles can be drawn on the same given dimensions. 4. This is called the ambiguous case, because the given information can be read in two ways. 5. The sine rule gives one angle, and a second angle with the same sine also fits. 6. Both of those answers are correct, so two possible triangles exist. 7. Answering one possible triangle misses the second angle with the same sine value. 8. Answering no possible triangle would need the given sides to be too short to close a triangle at all. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 6: Trigonometry_

Open this question →

Why does a trigonometric equation have infinitely many solutions unless the domain is restricted?

  1. The functions are always positive
  2. The functions repeat periodically
  3. The functions have no maximum
  4. The functions are not continuous
Show answer and solution

Correct answer: B. The functions repeat periodically

1. Sine, cosine and tangent all repeat their values after a fixed interval of angle. 2. So once one angle satisfies an equation, adding whole periods to it gives more angles that also satisfy it. 3. Subtracting whole periods works in the same way and gives negative angles. 4. That is why a general solution is written with a whole number of periods added on. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 4: Trigonometry_

Open this question →

How to practise

  1. Choose a Straight Lines and Conic Sections question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Straight Lines and Conic Sections practice for GMAT. Read explanations as you go. No signup form needed to start.

Practise Straight Lines and Conic Sections →

More Mathematics topics

Statistics and ProbabilityPermutations and CombinationsProbabilityArithmetic ProgressionRelations, Functions & Inverse TrigonometryProbability & StatisticsAlgebra: LogarithmsLinear Programming