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SAT Math: Concepts And Tricks

Subjects : sat, math
  • Answer 50 questions in 15 minutes.
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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. 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

2. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width

3. Multiply the exponents

4. pr^2

5. 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

6. Factor out the perfect squares

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

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

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

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

11. 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

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

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

14. 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

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

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

17. 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

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

19. 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

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

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

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. 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

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. To solve a proportion - cross multiply

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

27. 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

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

29. Part = Percent x Whole

30. 2pr

31. 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

32. 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

33. The whole # left over after division

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

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

36. 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

37. 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

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

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

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

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

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

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

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

45. 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

46. 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

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

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

49. Volume of a Cylinder = pr^2h

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