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






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






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






4. Add the exponents and keep the same base






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






6. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






7. 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)






8. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get






9. 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






10. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






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






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






13. 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






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






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






16. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






17. 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






18. Volume of a Cylinder = pr^2h






19. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






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






21. 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






22. 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






23. 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






24. Combine like terms






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






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






27. 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






28. The whole # left over after division






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






30. Subtract the smallest from the largest and add 1






31. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






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






33. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






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






35. To solve a proportion - cross multiply






36. 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






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






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






39. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






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






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






42. 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






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






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






45. The median is the value that falls in the middle of the set - the mode is the value that appears most often






46. 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)






47. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






48. Multiply the exponents






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






50. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign