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






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






3. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






4. 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






5. Volume of a Cylinder = pr^2h






6. Factor out the perfect squares






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






8. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9






9. Add the exponents and keep the same base






10. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






11. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






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






13. 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






14. 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






15. Domain: all possible values of x for a function range: all possible outputs of a function






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






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






18. 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






19. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






20. 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






21. 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






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






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






24. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






25. Probability= Favorable Outcomes/Total Possible Outcomes






26. The whole # left over after division






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






28. 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






29. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact






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






31. 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






32. Part = Percent x Whole






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






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






35. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






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






37. Change in y/ change in x rise/run






38. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






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






40. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4






41. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






42. To divide fractions - invert the second one and multiply






43. Subtract the smallest from the largest and add 1






44. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






45. 2pr






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






47. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






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






49. To solve a proportion - cross multiply






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