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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 are the properties of a rectangle?
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]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.

2. What are the sum - difference - products - and quotient of two numbers?
A = s^2 or A =d^2/2 where d is the diagonal
Avg = sum of n numbers/n
A = lw
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

3. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
A = lw
They are both the same. A divisor or factor of an integer leaves no remainder.
For any number b: b = -b if and only if b = 0.

4. What is p?
A = s^2 or A =d^2/2 where d is the diagonal
For any number n: x^-n means 1/x^n.
(Circumference/diameter) of a circle - or approximately 3.14.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

5. What are the important properties of 30-60-90 triangle?
Write the percent as a decimal - and multiply.
Is a right triangle with a ratio of sides x:xv3:2x.
Then the product xy is a constant.
No matter how many angles there are - the sum around the point is 360°.

6. 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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The ratio of corresponding sides of similar triangles.
(b^m)^n = b^mn

7. What formula is used for an average?
Avg = sum of n numbers/n
Write the percent as a decimal - and multiply.
Shifted down 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

8. What is the formula for the surface area of a rectangular solid?
V = lwh
A = 2(lw + lh + hw)
D = 2r
Divide - then multiply by 100.

9. 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.
At least one of the factors is 0.
A = 2(lw + lh + hw)
Shifted down 2 units.

10. 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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The product of their slopes is -1 (negative reciprocal).
(b^m)^n = b^mn

11. What is the formula for the volume of a rectangular solid?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = lw
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = lwh

12. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted left 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.

13. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
No matter how many angles there are - the sum around the point is 360°.
A = bh
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

14. Properties of one 2
For any number b: b = -b if and only if b = 0.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any integer n: 1^n = 1.
The two pairs of opposite angles formed are equal to each other.

15. Properties of zero 1
0 is the only number that is neither positive nor negative.
[(x1 + x2)/2] -[(y1 + y2)/2]
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Divide - then multiply by 100.

16. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Equal slopes.
How steep the line is. Horizontal line = 0 - vertical has no slope.
They are both the same. A divisor or factor of an integer leaves no remainder.

17. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
M = (y2 - y1)/(x2 - x1)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

18. What is the formula for the area of a triangle?
Set x = 0 - and solve.
An integer greater than one that is not prime.
A = (1/2)bh.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

19. Properties of one 3
1 is a divisor (or factor) of every integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A fraction whose denominator is 100 i.e. 17% = 17/100
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

20. What is an exterior angle of a polygon?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
V = lwh
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An angle formed by extending the side of the polygon.

21. What is a multiple of an integer?
Write the percent as a decimal - and multiply.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

22. What do we mean by the slope of the line?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
How steep the line is. Horizontal line = 0 - vertical has no slope.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Shifted down 2 units.

23. What is the probability of an event that cannot occur? That must occur?
No matter how many angles there are - the sum around the point is 360°.
Cannot is 0 - must is 1 - all others are in between.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Shifted down 2 units.

24. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At least one of the factors is 0.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A fraction whose denominator is 100 i.e. 17% = 17/100
Arc = (x°/360)(2pr) where x is the central angle.

25. How do we write the equation of a line?
A = s^2 or A =d^2/2 where d is the diagonal
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted up 2 units.
1 is the smallest positive odd integer.

26. What is a negative 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.
For any number n: x^-n means 1/x^n.
A^m/b^m = (a/b)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

27. Important binomial 3
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°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)

28. What is a proportion?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
An integer greater than one that is not prime.
Divide - then multiply by 100.
An equation that states that two ratios are equivalent. 4/6 = 10/15

29. How do you convert a percent to a fraction or a decimal?
A^m*b^m = (ab)^m
Divide - then multiply by 100.
Write the percent over 100 and reduce.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

30. What is the graph of a function?
An angle formed by extending the side of the polygon.
The set of all ordered pairs (x -y) such that y = f(x).
If a is negative and b is positive - then a < 0 < b.
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°.

31. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Is a right triangle with a ratio of sides x:xv3:2x.
A = [(s^2*v3)/4]

32. What is a ratio?

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33. If the product of two or more numbers is 0 - what do you know about the numbers?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
At least one of the factors is 0.
For any integer n: 1^n = 1.
Write the percent over 100 and reduce.

34. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
(x + y)(x - y) = x^2 - y^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = bh
Shifted left 2 units.

35. Properties of zero 3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Write the percent over 100 and reduce.
0 is a multiple of every integer.
(Circumference/diameter) of a circle - or approximately 3.14.

36. Important binomial 1
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)(x - y) = x^2 - y^2

37. 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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
A = (1/2)bh.

38. For what values of a function is the function undefined?
The ratio of corresponding sides of similar triangles.
C = p2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

39. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
They are both the same. A divisor or factor of an integer leaves no remainder.
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.

40. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
0 is the only number that is neither positive nor negative.
V = lwh
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.
Shifted down 2 units.

41. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
A = [(s^2*v3)/4]
Then the product xy is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

42. How do you find the x-intercept of a graph?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Set y = 0 - and solve.
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.
V = l^3

43. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
B^m/b^n = b^m-n
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

44. What is an exponent?
Corresponding sides of similar triangles are in proportion.
A fraction whose denominator is 100 i.e. 17% = 17/100
For any number n: x^-n means 1/x^n.
In the expression x^b - x is the base and b is the exponent.

45. Law of exponents 3
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A fraction whose denominator is 100 i.e. 17% = 17/100
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(b^m)^n = b^mn

46. How do you calculate percent increases and decreases?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The product of their slopes is -1 (negative reciprocal).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

47. What is an even and an odd number?
Shifted down 2 units.
Even numbers are divisible by 2 and odd numbers are not.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Area = (x°/360)(pr^2) where x is the central angle.

48. What is true about the measures of the two acute angles in a right triangle?
(x + y)(x - y) = x^2 - y^2
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted up 2 units.
Their sum is 90°.

49. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
At least one of the factors is 0.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

50. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Shifted right 2 units.
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.
Shifted down 2 units.
360°