## Test your basic knowledge |

# SAT Math: Concepts And Tricks

**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. 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.**

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

**3. 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**

**4. 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**

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

**6. 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**

**7. Multiply the exponents**

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

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

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

**11. 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**

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

**13. 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**

**14. (average of the x coordinates - average of the y coordinates)**

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

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

**17. 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**

**18. 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**

**19. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS**

**20. Combine like terms**

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

**22. To multiply fractions - multiply the numerators and multiply the denominators**

**23. 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**

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

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

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

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

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

**29. Surface Area = 2lw + 2wh + 2lh**

**30. 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)**

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

**32. 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**

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

**34. 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**

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

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

**38. Factor out the perfect squares**

**39. 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**

**40. pr^2**

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

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

**43. 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**

**44. 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**

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

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

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

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

**49. 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**

**50. 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**