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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. 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






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






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






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






5. 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






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






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






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






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






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






11. 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






12. 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






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






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






15. 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






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






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






18. 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






19. 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






20. 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






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






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






23. 2pr






24. 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






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






26. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






27. The smallest multiple (other than zero) that two or more numbers have in common.






28. 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






29. pr^2






30. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






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






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






33. 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






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






35. 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.






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






37. Add the exponents and keep the same base






38. To solve a proportion - cross multiply






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






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






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. 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






43. 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






44. Subtract the smallest from the largest and add 1






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






46. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






47. Probability= Favorable Outcomes/Total Possible Outcomes






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






49. 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






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