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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 true about the measures of the three angles in a triangle?
In the expression x^b - x is the base and b is the exponent.
An angle formed by extending the side of the polygon.
Their sum is 180°.
The ratio of corresponding sides of similar triangles.

2. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
V = lwh
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The two pairs of opposite angles formed are equal to each other.

3. What is the sum of the measures of the four angles in a quadrilateral?
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.
360°
Cannot is 0 - must is 1 - all others are in between.
A = (1/2)bh.

4. Properties of one 2
Corresponding sides of similar triangles are in proportion.
Then the product xy is a constant.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any integer n: 1^n = 1.

5. How do you find the slope of a line?
V = lwh
A = 6(l^2)
M = (y2 - y1)/(x2 - x1)
(b^m)^n = b^mn

6. Properties of zero 3
0 is a multiple of every integer.
A = (1/2)bh.
360°
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

7. What is p?
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
(Circumference/diameter) of a circle - or approximately 3.14.
An integer greater than one that is not prime.
Then the product xy is a constant.

8. What is the triangle inequality?
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.
C = p2r
For any integer n: 1^n = 1.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

9. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An angle formed by extending the side of the polygon.
V = pr^2h
A = pr^2

10. What is a Venn diagram?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Write the percent as a decimal - and multiply.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

11. Properties of zero 5
B^m*b^n = b^m+n
Write the percent as a decimal - and multiply.
A = pr^2
For any number b: b = -b if and only if b = 0.

12. What do we mean by the slope of the line?
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
360°
A fraction whose denominator is 100 i.e. 17% = 17/100

13. Law of exponents 3
B^m*b^n = b^m+n
(b^m)^n = b^mn
An integer greater than one that is not prime.
V = l^3

14. What is the formula for the surface area of a cube?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Corresponding sides of similar triangles are in proportion.
A = 6(l^2)
Even numbers are divisible by 2 and odd numbers are not.

15. How do you find the length of an arc of a circle?
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
Arc = (x°/360)(2pr) where x is the central angle.
For any number b: b = -b if and only if b = 0.

16. What is true about the measures of the two acute angles in a right triangle?
180°. If two or more angles form a straight angle - their sum is 180°.
A^m*b^m = (ab)^m
Their sum is 90°.
D = 2r

17. What is the formula for the surface area of a rectangular solid?
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.
M = (y2 - y1)/(x2 - x1)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = 2(lw + lh + hw)

18. What is a multiple of 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.
Then the product xy is a constant.
180°. If two or more angles form a straight angle - their sum is 180°.
For any number b: b = -b if and only if b = 0.

19. Law of exponents 5
A^m/b^m = (a/b)^m
The product of their slopes is -1 (negative reciprocal).
An integer greater than one that is not prime.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

20. How do you find the area of a sector of a circle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Area = (x°/360)(pr^2) where x is the central angle.
Divide - then multiply by 100.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

21. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
For any number b: b = -b if and only if b = 0.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
360°

22. How do you convert a percent to a fraction or a decimal?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Equal slopes.
Write the percent over 100 and reduce.
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°.

23. If you were given the graph of y = f(x) - what does f(a) represent?
A = 2(lw + lh + hw)
360°
A = (1/2)bh.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

24. What is the formula for the volume of a cylinder?
V = pr^2h
Shifted down 2 units.
A = 2(lw + lh + hw)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

25. Important binomial 2
(n - 2)(180°)
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
M = (y2 - y1)/(x2 - x1)
Shifted right 2 units.

26. What is the formula for the volume of a rectangular solid?
Area = (x°/360)(pr^2) where x is the central angle.
V = lwh
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

27. What is an exterior angle of a triangle?
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.
360°
B^m/b^n = b^m-n
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

28. How do we write the equation of a line?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
At least one of the factors is 0.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

29. What is a negative exponent?
A = (1/2)bh.
Shifted up 2 units.
For any number n: x^-n means 1/x^n.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

30. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.

31. Properties of one 1
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
V = pr^2h
For any number a: a * 1 = a and a / 1 = a.
A = pr^2

32. Properties of zero 2
The product of their slopes is -1 (negative reciprocal).
If a is negative and b is positive - then a < 0 < b.
(n - 2)(180°)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

33. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
For any right triangle - a^2 + b^2 = c^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
0 is a multiple of every integer.

34. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
Cannot is 0 - must is 1 - all others are in between.
0 is a multiple of every integer.
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.

35. What is the formula for the area of a parallelogram?
A = bh
The product of their slopes is -1 (negative reciprocal).
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = l^3

36. What is a prime number?
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
B^m/b^n = b^m-n
Write the percent as a decimal - and multiply.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

37. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Is a right triangle with a ratio of sides x:xv3:2x.
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted left 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.

38. What is the sum of the measures of all angles around a point?
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
No matter how many angles there are - the sum around the point is 360°.

39. What is the distributive law?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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°.

40. Properties of one 3
A^m*b^m = (ab)^m
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
1 is a divisor (or factor) of every integer.

41. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
1 is a divisor (or factor) of every integer.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

42. What is a divisor and a factor of an integer?
C = p2r
They are both the same. A divisor or factor of an integer leaves no remainder.
Their sum is 90°.
For any number a: a * 1 = a and a / 1 = a.

43. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An integer greater than one that is not prime.
Arc = (x°/360)(2pr) where x is the central angle.

44. Important binomial 1
(x + y)(x - y) = x^2 - y^2
C = p2r
The set of all ordered pairs (x -y) such that y = f(x).
The two pairs of opposite angles formed are equal to each other.

45. What is a composite number?
An angle formed by extending the side of the polygon.
Area = (x°/360)(pr^2) where x is the central angle.
An integer greater than one that is not prime.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

46. What is the formula for the area of a rectangle?
V = lwh
Arc = (x°/360)(2pr) where x is the central angle.
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.
A = lw

47. What is a ratio?

48. Properties of zero 4
A = 6(l^2)
M = (y2 - y1)/(x2 - x1)
1 is a divisor (or factor) of every integer.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

49. What is a percent?
For any right triangle - a^2 + b^2 = c^2.
Even numbers are divisible by 2 and odd numbers are not.
The ratio of corresponding sides of similar triangles.
A fraction whose denominator is 100 i.e. 17% = 17/100

50. What formula is used for an average?
If a is negative and b is positive - then a < 0 < b.
Avg = sum of n numbers/n
All positive and negative whole numbers - and zero.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.