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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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. What is an exterior angle of a triangle?
For any integer n: 1^n = 1.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Set x = 0 - and solve.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

2. What is true about the slopes of parallel lines?
V = lwh
Equal slopes.
A = s^2 or A =d^2/2 where d is the diagonal
An equation that states that two ratios are equivalent. 4/6 = 10/15

3. What is the triangle inequality?
Then the quotient y/x is a constant.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = pr^2
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.

4. Law of exponents 5
A^m/b^m = (a/b)^m
Equal slopes.
A = 2(lw + lh + hw)
Then the quotient y/x is a constant.

5. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
0 is the only number that is neither positive nor negative.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Equal slopes.

6. What is special formula for the area of an equilateral triangle?
An integer greater than one that is not prime.
A = [(s^2*v3)/4]
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
Arc = (x°/360)(2pr) where x is the central angle.

7. How do you convert a percent to a fraction or a decimal?
A = (1/2)bh.
They are both the same. A divisor or factor of an integer leaves no remainder.
No matter how many angles there are - the sum around the point is 360°.
Write the percent over 100 and reduce.

8. What is a proportion?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
An equation that states that two ratios are equivalent. 4/6 = 10/15
1 is the smallest positive odd integer.
Set y = 0 - and solve.

9. What is an integer?
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
All positive and negative whole numbers - and zero.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
They are both the same. A divisor or factor of an integer leaves no remainder.

10. What is a composite number?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
An integer greater than one that is not prime.
The two pairs of opposite angles formed are equal to each other.

11. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted down 2 units.

12. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
(b^m)^n = b^mn
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any number a: a * 1 = a and a / 1 = a.

13. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Then the product xy is a constant.
For any number b: b = -b if and only if b = 0.
Cannot is 0 - must is 1 - all others are in between.

14. What is the area of a square?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An angle formed by extending the side of the polygon.
Is a right triangle with a ratio of sides x:xv3:2x.
A = s^2 or A =d^2/2 where d is the diagonal

15. Important binomial 2
Then the product xy is a constant.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

16. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
0 is a multiple of every integer.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
0 is the only number that is neither positive nor negative.

17. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted left 2 units.
0 is a multiple of every integer.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

18. What is p?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
M = (y2 - y1)/(x2 - x1)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(Circumference/diameter) of a circle - or approximately 3.14.

19. In a circle of radius r - what is the formula for the area?
A = pr^2
No matter how many angles there are - the sum around the point is 360°.
For any number n: x^-n means 1/x^n.
Set x = 0 - and solve.

20. What are the quotient and the remainder?

21. Properties of zero 1
Then the quotient y/x is a constant.
0 is the only number that is neither positive nor negative.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

22. How do you find the area of a sector of a circle?
Cannot is 0 - must is 1 - all others are in between.
Area = (x°/360)(pr^2) where x is the central angle.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = lw

23. What is true about the measures of the three angles in a triangle?
(x + y)(x - y) = x^2 - y^2
Their sum is 180°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted left 2 units.

24. What is the midpoint formula?
For any number a: a * 1 = a and a / 1 = a.
[(x1 + x2)/2] -[(y1 + y2)/2]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.

25. How you convert a fraction or a decimal to a percent?
Their sum is 180°.
The ratio of corresponding sides of similar triangles.
Divide - then multiply by 100.
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.

26. What is the formula for the area of a triangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = (1/2)bh.

27. How do you find the slope of a line?
(Circumference/diameter) of a circle - or approximately 3.14.
M = (y2 - y1)/(x2 - x1)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

28. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Arc = (x°/360)(2pr) where x is the central angle.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

29. Law of exponents 4
Write the percent as a decimal - and multiply.
1 is the smallest positive odd integer.
An integer greater than one that is not prime.
A^m*b^m = (ab)^m

30. Important binomial 1
(x + y)(x - y) = x^2 - y^2
(Circumference/diameter) of a circle - or approximately 3.14.
A = 6(l^2)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

31. What formula is used for an average?
At least one of the factors is 0.
Avg = sum of n numbers/n
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
An equation that states that two ratios are equivalent. 4/6 = 10/15

32. What are the properties of a parallelogram?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted up 2 units.
Shifted down 2 units.

33. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
A = pr^2
Corresponding sides of similar triangles are in proportion.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

34. How do you find the x-intercept of a graph?
A = (1/2)bh.
1 is a divisor (or factor) of every integer.
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
Set y = 0 - and solve.

35. What is a percent?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
D = 2r
At least one of the factors is 0.
A fraction whose denominator is 100 i.e. 17% = 17/100

36. What is true about the slopes of perpendicular lines?
If a is negative and b is positive - then a < 0 < b.
Shifted left 2 units.
A = lw
The product of their slopes is -1 (negative reciprocal).

37. Properties of zero 4
V = pr^2h
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
[(x1 + x2)/2] -[(y1 + y2)/2]

38. What is the sum of the measures of the four angles in a quadrilateral?
360°
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = l^3
A^m/b^m = (a/b)^m

39. What is a negative exponent?
V = l^3
For any number n: x^-n means 1/x^n.
(b^m)^n = b^mn
B^m/b^n = b^m-n

40. What is the formula for the volume of a rectangular solid?
180°. If two or more angles form a straight angle - their sum is 180°.
Their sum is 180°.
They are both the same. A divisor or factor of an integer leaves no remainder.
V = lwh

41. What is the measure of a straight angle?
Shifted left 2 units.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
180°. If two or more angles form a straight angle - their sum is 180°.
C = p2r

42. In a circle of radius r - what is the formula for the diameter?
D = 2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
1 is the smallest positive odd integer.
Corresponding sides of similar triangles are in proportion.

43. If the product of two or more numbers is 0 - what do you know about the numbers?
Write the percent over 100 and reduce.
1 is the smallest positive odd integer.
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
At least one of the factors is 0.

44. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Cannot is 0 - must is 1 - all others are in between.
360°
At least one of the factors is 0.
B^m*b^n = b^m+n

45. What is the distance formula?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
They are both the same. A divisor or factor of an integer leaves no remainder.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

46. What is the formula for the surface area of a cube?
An angle formed by extending the side of the polygon.
Arc = (x°/360)(2pr) where x is the central angle.
For any number b: b = -b if and only if b = 0.
A = 6(l^2)

47. How do you calculate a weighted average?
Write the percent over 100 and reduce.
An integer greater than one that is not prime.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Set x = 0 - and solve.

48. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
B^m/b^n = b^m-n
Shifted left 2 units.
All positive and negative whole numbers - and zero.

49. Law of exponents 2
Shifted right 2 units.
Write the percent over 100 and reduce.
B^m/b^n = b^m-n
Arc = (x°/360)(2pr) where x is the central angle.

50. What is a multiple of an integer?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
360°
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.