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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Multiply the exponents






2. 2pr






3. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






4. The largest factor that two or more numbers have in common.






5. Sum=(Average) x (Number of Terms)






6. To multiply fractions - multiply the numerators and multiply the denominators






7. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex






8. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






9. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520






10. The whole # left over after division






11. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides






12. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






13. 1. Re-express them with common denominators 2. Convert them to decimals






14. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






15. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees






16. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






17. Surface Area = 2lw + 2wh + 2lh






18. A square is a rectangle with four equal sides; Area of Square = side*side






19. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






20. To add or subtract fraction - first find a common denominator - then add or subtract the numerators






21. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






22. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)






23. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






24. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






25. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






26. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






27. (average of the x coordinates - average of the y coordinates)






28. Volume of a Cylinder = pr^2h






29. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides






30. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






31. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional






32. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common






33. Factor out the perfect squares






34. To find the reciprocal of a fraction switch the numerator and the denominator






35. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






36. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






37. For all right triangles: a^2+b^2=c^2






38. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






39. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3






40. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive






41. To solve a proportion - cross multiply






42. Subtract the smallest from the largest and add 1






43. Part = Percent x Whole






44. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






45. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






46. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






47. you can add/subtract when the part under the radical is the same






48. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






49. Combine equations in such a way that one of the variables cancel out






50. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12