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GRE Math: Facts

Subjects : gre, math

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. What is true about the measures of the three angles in 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.
(n - 2)(180°)
Their sum is 180°.
Shifted left 2 units.

2. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = pr^2h
The set of all ordered pairs (x -y) such that y = f(x).
A = pr^2

3. Law of exponents 2
Shifted right 2 units.
B^m/b^n = b^m-n
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

4. What are the median and the mode of a set of data?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
The two pairs of opposite angles formed are equal to each other.
0 is the only number that is neither positive nor negative.

5. What are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = 6(l^2)
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

6. What is the area of a square?
A = (1/2)bh.
Shifted right 2 units.
A = s^2 or A =d^2/2 where d is the diagonal
0 is a multiple of every integer.

7. What formula is used for an average?
Avg = sum of n numbers/n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
C = p2r
1 is the smallest positive odd integer.

8. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
An integer greater than one that is not prime.
Cannot is 0 - must is 1 - all others are in between.
(x + y)(x - y) = x^2 - y^2

9. How you convert a fraction or a decimal to a percent?
Then the quotient y/x is a constant.
Divide - then multiply by 100.
If a is negative and b is positive - then a < 0 < b.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

10. What does it mean if y is directly proportional to x?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Then the quotient y/x is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

11. Properties of zero 3
0 is a multiple of every integer.
A = bh
Shifted right 2 units.
Cannot is 0 - must is 1 - all others are in between.

12. What is the formula for the surface area of a cube?
Arc = (x°/360)(2pr) where x is the central angle.
In the expression x^b - x is the base and b is the exponent.
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.
A = 6(l^2)

13. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Their sum is 90°.
(Circumference/diameter) of a circle - or approximately 3.14.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

14. What is special formula for the area of an equilateral triangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = [(s^2*v3)/4]
Area = (x°/360)(pr^2) where x is the central angle.
Arc = (x°/360)(2pr) where x is the central angle.

15. What is the distance formula?
An integer greater than one that is not prime.
Cannot is 0 - must is 1 - all others are in between.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

16. What are the properties of a rectangle?
A = [(s^2*v3)/4]
For any number n: x^-n means 1/x^n.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Then the quotient y/x is a constant.

17. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
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.
Shifted left 2 units.
For any integer n: 1^n = 1.

18. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Their sum is 90°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted right 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

19. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
V = l^3
A = pr^2

20. What is a fractional exponent?
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.
Area = (x°/360)(pr^2) where x is the central angle.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

21. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
360°
The set of all ordered pairs (x -y) such that y = f(x).
Set x = 0 - and solve.

22. In a circle of radius r - what is the formula for the circumference?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
C = p2r
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

23. How do you find the probability that an event will occur?
0 is the only number that is neither positive nor negative.
(Circumference/diameter) of a circle - or approximately 3.14.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any integer n: 1^n = 1.

24. What is a ratio?

25. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
If a is negative and b is positive - then a < 0 < b.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = bh

26. What are the quotient and the remainder?

27. What is the formula for the area of a triangle?
A^m/b^m = (a/b)^m
Equal slopes.
Is a right triangle with a ratio of sides x:xv3:2x.
A = (1/2)bh.

28. Properties of zero 1
0 is the only number that is neither positive nor negative.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
0 is a multiple of every integer.
For any number n: x^-n means 1/x^n.

29. 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.
The set of all ordered pairs (x -y) such that y = f(x).
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted down 2 units.

30. What is the graph of a function?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The set of all ordered pairs (x -y) such that y = f(x).
D = 2r
A = 2(lw + lh + hw)

31. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
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.
Then the product xy is a constant.

32. What is a multiple of an integer?
B^m/b^n = b^m-n
[(x1 + x2)/2] -[(y1 + y2)/2]
(b^m)^n = b^mn
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.

33. What is an exterior angle of a polygon?
V = l^3
A = s^2 or A =d^2/2 where d is the diagonal
An angle formed by extending the side of the polygon.
The set of all ordered pairs (x -y) such that y = f(x).

34. What is the volume of a cube?
0 is a multiple of every integer.
V = pr^2h
V = l^3
The ratio of corresponding sides of similar triangles.

35. Properties of zero 2
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If a is negative and b is positive - then a < 0 < b.
1 is the smallest positive odd integer.

36. Properties of one 4
An equation that states that two ratios are equivalent. 4/6 = 10/15
Cannot is 0 - must is 1 - all others are in between.
1 is the smallest positive odd integer.
Avg = sum of n numbers/n

37. What is true about the slopes of parallel lines?
They are both the same. A divisor or factor of an integer leaves no remainder.
If a is negative and b is positive - then a < 0 < b.
Equal slopes.
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.

38. What is the sum of the measures of the four angles in a quadrilateral?
(b^m)^n = b^mn
A = bh
180°. If two or more angles form a straight angle - their sum is 180°.
360°

39. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any integer n: 1^n = 1.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

40. In a circle of radius r - what is the formula for the diameter?
All positive and negative whole numbers - and zero.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any number n: x^-n means 1/x^n.
D = 2r

41. Important binomial 3
No matter how many angles there are - the sum around the point is 360°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.

42. What is the formula for the surface area of a rectangular solid?
For any number n: x^-n means 1/x^n.
A = (1/2)bh.
A = 2(lw + lh + hw)
Write the percent as a decimal - and multiply.

43. What is true about the measures of the four angles formed by two intersecting lines?
Then the product xy is a constant.
An integer greater than one that is not prime.
The ratio of corresponding sides of similar triangles.
The two pairs of opposite angles formed are equal to each other.

44. Properties of one 2
180°. If two or more angles form a straight angle - their sum is 180°.
For any integer n: 1^n = 1.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = lwh

45. How do you find the y-intercept of a graph?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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.
Set x = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

46. What are the properties of a square?
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = pr^2

47. How do we write the equation of a line?
(Circumference/diameter) of a circle - or approximately 3.14.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = 6(l^2)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

48. Law of exponents 4
A^m*b^m = (ab)^m
A^m/b^m = (a/b)^m
(n - 2)(180°)
For any number n: x^-n means 1/x^n.

49. If you were given the graph of y = f(x) - what does f(a) represent?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A fraction whose denominator is 100 i.e. 17% = 17/100
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

50. Properties of zero 5
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any number b: b = -b if and only if b = 0.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.