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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 the relationship between a radius of a circle and a line that is tangent to the circle?
B^m*b^n = b^m+n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = bh
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

2. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Then the quotient y/x is a constant.
A^m/b^m = (a/b)^m
The product of their slopes is -1 (negative reciprocal).

3. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any integer n: 1^n = 1.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted right 2 units.

4. What is a ratio?

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5. What is the graph of a function?
Set x = 0 - and solve.
An angle formed by extending the side of the polygon.
The set of all ordered pairs (x -y) such that y = f(x).
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

6. For what values of a function is the function undefined?
Shifted down 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The product of their slopes is -1 (negative reciprocal).

7. What is the measure of a straight angle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
180°. If two or more angles form a straight angle - their sum is 180°.
In the expression x^b - x is the base and b is the exponent.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

8. Properties of one 1
No matter how many angles there are - the sum around the point is 360°.
Divide - then multiply by 100.
For any number a: a * 1 = a and a / 1 = a.
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°.

9. What is an exterior angle of a polygon?
[(x1 + x2)/2] -[(y1 + y2)/2]
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Area = (x°/360)(pr^2) where x is the central angle.
An angle formed by extending the side of the polygon.

10. Law of exponents 4
360°
A^m*b^m = (ab)^m
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.
Arc = (x°/360)(2pr) where x is the central angle.

11. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any right triangle - a^2 + b^2 = c^2.
A = bh
Shifted right 2 units.

12. If the product of two or more numbers is 0 - what do you know about the numbers?
Avg = sum of n numbers/n
B^m/b^n = b^m-n
At least one of the factors is 0.
0 is the only number that is neither positive nor negative.

13. Properties of zero 2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
If a is negative and b is positive - then a < 0 < b.
Shifted right 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

14. How do we write the equation of a line?
Shifted left 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent over 100 and reduce.
(x + y)(x - y) = x^2 - y^2

15. What is an integer?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
All positive and negative whole numbers - and zero.
0 is a multiple of every integer.
Set y = 0 - and solve.

16. Properties of zero 3
0 is a multiple of every integer.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Is a right triangle with a ratio of sides x:xv3:2x.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

17. What is the volume of a cube?
(Circumference/diameter) of a circle - or approximately 3.14.
V = l^3
Then the quotient y/x is a constant.
For any number n: x^-n means 1/x^n.

18. How do you find the x-intercept of a graph?
Cannot is 0 - must is 1 - all others are in between.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Set y = 0 - and solve.

19. Properties of zero 1
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.
360°
(b^m)^n = b^mn

20. Important binomial 1
How steep the line is. Horizontal line = 0 - vertical has no slope.
A^m/b^m = (a/b)^m
For any right triangle - a^2 + b^2 = c^2.
(x + y)(x - y) = x^2 - y^2

21. In a circle of radius r - what is the formula for the diameter?
No matter how many angles there are - the sum around the point is 360°.
D = 2r
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
B^m*b^n = b^m+n

22. What is an even and an odd number?
Is a right triangle with a ratio of sides x:xv3:2x.
Even numbers are divisible by 2 and odd numbers are not.
Write the percent over 100 and reduce.
For any number a: a * 1 = a and a / 1 = a.

23. What is an exponent?
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°.
In the expression x^b - x is the base and b is the exponent.
Arc = (x°/360)(2pr) where x is the central angle.

24. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
An angle formed by extending the side of the polygon.
The set of all ordered pairs (x -y) such that y = f(x).
In the expression x^b - x is the base and b is the exponent.

25. Properties of zero 5
For any number b: b = -b if and only if b = 0.
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.
If a is negative and b is positive - then a < 0 < b.
A = 6(l^2)

26. What do we mean by the slope of the line?
Divide - then multiply by 100.
How steep the line is. Horizontal line = 0 - vertical has no slope.
0 is the only number that is neither positive nor negative.
Area = (x°/360)(pr^2) where x is the central angle.

27. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
V = l^3
Set y = 0 - and solve.
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.

28. What is the probability of an event that cannot occur? That must occur?
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.
Their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.
A = 2(lw + lh + hw)

29. What is the sum of the measures of the four angles in a quadrilateral?
Avg = sum of n numbers/n
For any right triangle - a^2 + b^2 = c^2.
360°
Write the percent over 100 and reduce.

30. How do you calculate percent increases and decreases?
How steep the line is. Horizontal line = 0 - vertical has no slope.
(Circumference/diameter) of a circle - or approximately 3.14.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = lwh

31. 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.
Their sum is 180°.
Equal slopes.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

32. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
For any integer n: 1^n = 1.
(b^m)^n = b^mn

33. Properties of one 4
1 is the smallest positive odd integer.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

34. What is the ratio of similitude?
Divide - then multiply by 100.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The ratio of corresponding sides of similar triangles.
Set x = 0 - and solve.

35. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A^m*b^m = (ab)^m
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

36. Properties of zero 4
D = 2r
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted left 2 units.
1 is the smallest positive odd integer.

37. Law of exponents 3
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A^m/b^m = (a/b)^m
(b^m)^n = b^mn
1 is the smallest positive odd integer.

38. How do you find the length of an arc of a circle?
C = p2r
1 is a divisor (or factor) of every integer.
A = lw
Arc = (x°/360)(2pr) where x is the central angle.

39. What is a divisor and a factor of an integer?
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.
The product of their slopes is -1 (negative reciprocal).
Is a right triangle with a ratio of sides x:xv3:2x.

40. What is a prime number?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Write the percent over 100 and reduce.
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.
The set of all ordered pairs (x -y) such that y = f(x).

41. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted right 2 units.
Shifted left 2 units.
In the expression x^b - x is the base and b is the exponent.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

42. What is true about the slopes of perpendicular lines?
For any number n: x^-n means 1/x^n.
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.
0 is the only number that is neither positive nor negative.
The product of their slopes is -1 (negative reciprocal).

43. What is a function?
The ratio of corresponding sides of similar triangles.
Equal slopes.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any right triangle - a^2 + b^2 = c^2.

44. What formula is used for an average?
Then the product xy is a constant.
A = lw
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Avg = sum of n numbers/n

45. What is the formula for the area of a parallelogram?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = bh
Corresponding sides of similar triangles are in proportion.

46. What is the area of a square?
Then the product xy is a constant.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = s^2 or A =d^2/2 where d is the diagonal

47. What is a proportion?
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.
Cannot is 0 - must is 1 - all others are in between.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An equation that states that two ratios are equivalent. 4/6 = 10/15

48. Law of exponents 1
0 is the only number that is neither positive nor negative.
A = 2(lw + lh + hw)
B^m*b^n = b^m+n
Shifted up 2 units.

49. What are the median and the mode of a set of data?
For any integer n: 1^n = 1.
The set of all ordered pairs (x -y) such that y = f(x).
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.
A fraction whose denominator is 100 i.e. 17% = 17/100

50. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Their sum is 180°.
C = p2r
(b^m)^n = b^mn