How to Review DAT Quantitative Reasoning Math

TL;DR

Master the DAT Quantitative Reasoning section by reviewing trigonometry, geometry, numerical calculations, algebra, conversions, word problems, probability, and statistics. For right-triangle questions, memorize common Pythagorean triples and use SOHCAHTOA to identify sine, cosine, and tangent quickly, then derive reciprocal functions and account for coordinate signs when working outside the first quadrant.

Transcript

There are seven sections that you need to be familiar with for the DAT Quantitative Reasoning Exam. And it's trig, geometry, numerical calculations, algebra, conversions, word problems, and probability and statistics. So let's start with trigonometry. Uh, let's get right into it. So let's start with trigonometry. The first thing you need to be fami... Read More

Key Insights

• The DAT Quantitative Reasoning review covers seven sections: trigonometry, geometry, numerical calculations, algebra, conversions, word problems, and probability and statistics. The listed study topics also include formulas, geometric measurements, scientific notation, linear relationships, and several equation types.
• The Pythagorean theorem is c² = a² + b² for a right triangle, where c is the hypotenuse across from the right angle. For sides 3 and 4, the calculation gives c² = 25 and therefore a hypotenuse of 5.
• Special right triangles are useful because their side ratios can reveal missing lengths without repeated squaring and subtraction. The most emphasized triples are 3-4-5 and 5-12-13, while 7-24-25 and 8-15-17 are also presented as important patterns.
• Scaled Pythagorean triples preserve their original side ratios. A triangle with a hypotenuse of 26 and another side of 10 matches 5-12-13 multiplied by 2, so its missing side is 24.
• SOHCAHTOA defines the three primary trigonometric ratios: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. The opposite and adjacent sides are identified relative to the selected angle, while the hypotenuse remains across from the right angle.
• Reciprocal trigonometric functions are obtained by flipping the corresponding primary ratios. Cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent. Tangent also equals sine divided by cosine, while cotangent equals cosine divided by sine.
• A single trigonometric ratio can determine the remaining functions by constructing a right triangle. If sine is 7/25, the 7-24-25 triangle gives cosine as 24/25 and tangent as 7/24, after which their reciprocal functions follow directly.
• Quadrant signs determine whether trigonometric ratios are positive or negative. For tangent equal to -2/5 in quadrant two, the vertical side is 2, the horizontal side is -5, and the Pythagorean theorem gives a hypotenuse of √29.

Questions & Answers

Q: What topics are covered on the DAT Quantitative Reasoning exam?

The review organizes DAT Quantitative Reasoning into seven sections: trigonometry, geometry, numerical calculations, algebra, conversions, word problems, and probability and statistics. The description further lists right triangles, trigonometric identities, special triangles, geometric area and volume, coordinate formulas, slopes, fractions, decimals, radicals, scientific notation, and linear, quadratic, and exponential equations as study topics.

Q: How do you use the Pythagorean theorem on DAT math questions?

Use c² = a² + b² when a triangle contains a right angle, with c assigned to the hypotenuse across from that angle. For legs of 3 and 4, calculate 3² + 4² = 9 + 16 = 25, then take the square root to obtain c = 5. Rearrange the equation when a leg is missing.

Q: Which Pythagorean triples should you recognize for the DAT?

The review emphasizes 3-4-5 and 5-12-13 as the two most common special right triangles. It also recommends recognizing 7-24-25 and 8-15-17. Less common examples mentioned are 9-40-41 and 11-60-61. Memorizing these patterns can save time when a problem asks for a missing side.

Q: How do scaled special triangles help solve missing-side problems?

Scaled special triangles retain the same ratio after every side is multiplied by one factor. A triangle containing sides 6 and 10 matches 3-4-5 multiplied by 2, so the missing side is 8. Likewise, sides 10 and 26 match 5-12-13 multiplied by 2, making the missing side 24.

Q: What does SOHCAHTOA mean in right-triangle trigonometry?

SOHCAHTOA summarizes the three primary trigonometric definitions. Sine equals the side opposite the chosen angle divided by the hypotenuse. Cosine equals the adjacent side divided by the hypotenuse. Tangent equals the opposite side divided by the adjacent side. The hypotenuse is always across from the right angle, but opposite and adjacent depend on theta's position.

Q: How do you find all six trig functions from sine 7/25?

Draw a right triangle and assign 7 to the side opposite theta and 25 to the hypotenuse. Recognizing the 7-24-25 triangle gives an adjacent side of 24. Therefore, cosine is 24/25, tangent is 7/24, cosecant is 25/7, secant is 25/24, and cotangent is 24/7.

Q: How do quadrant signs affect trigonometric ratios?

The coordinate signs of the triangle determine the signs of its trigonometric ratios. In quadrant two, the vertical value is positive and the horizontal value is negative. Therefore, a tangent of -2/5 can be represented by an opposite side of 2 and an adjacent side of -5, with a positive hypotenuse of √29.

Q: How do you find trig functions from tangent -2/5 in quadrant two?

Represent tangent as opposite over adjacent, using 2 for the positive vertical side and -5 for the negative horizontal side in quadrant two. The hypotenuse is √(2² + 5²), or √29. Sine is 2/√29, cosine is -5/√29, cosecant is √29/2, secant is -√29/5, and cotangent is -5/2.

Summary & Key Takeaways

• The review identifies seven areas for the DAT Quantitative Reasoning exam: trigonometry, geometry, numerical calculations, algebra, conversions, word problems, and probability and statistics. Its trigonometry section begins with right triangles, the Pythagorean theorem, common side-length patterns, SOHCAHTOA, reciprocal functions, coordinate signs, and worked practice problems.

• The Pythagorean theorem finds a missing right-triangle side through the relationship c² = a² + b², with c representing the hypotenuse. Recognizing triples such as 3-4-5, 5-12-13, 7-24-25, and 8-15-17 can avoid lengthy calculations, including when every side has been multiplied by the same factor.

• SOHCAHTOA defines sine as opposite over hypotenuse, cosine as adjacent over hypotenuse, and tangent as opposite over adjacent. Cosecant, secant, and cotangent are their respective reciprocals. A triangle can reconstruct all six functions from one ratio, while the point's quadrant determines whether horizontal and vertical side values are positive or negative.