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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 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)

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

3. 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)

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

5. 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

6. 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

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

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

9. 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

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

11. 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

12. 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

13. 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

14. Volume of a Cylinder = pr^2h

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

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

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

18. pr^2

19. The whole # left over after division

20. 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

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

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

23. 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

24. 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

25. 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

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

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

28. 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

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

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

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

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

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

34. 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

35. 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

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

37. To solve a proportion - cross multiply

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

39. Factor out the perfect squares

40. 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.

41. Add the exponents and keep the same base

42. 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

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

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

45. Probability= Favorable Outcomes/Total Possible Outcomes

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

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

48. 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

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

50. 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