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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. In a circle of radius r - what is the formula for the area?
Shifted down 2 units.
A = pr^2
V = lwh
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

2. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
A = 2(lw + lh + hw)
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Area = (x°/360)(pr^2) where x is the central angle.

3. What is the relationship between the graph of f(x) the graph of y = f(x + 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.
Shifted left 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

4. What is the distance formula?
Even numbers are divisible by 2 and odd numbers are not.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = [(s^2*v3)/4]
Their sum is 90°.

5. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Set y = 0 - and solve.
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted up 2 units.

6. What are the median and the mode of a set of data?
Corresponding sides of similar triangles are in proportion.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.
B^m/b^n = b^m-n

7. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Shifted right 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.
In the expression x^b - x is the base and b is the exponent.

8. What is an integer?
A = 2(lw + lh + hw)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
All positive and negative whole numbers - and zero.
A = (1/2)bh.

9. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Their sum is 180°.
B^m*b^n = b^m+n
(Circumference/diameter) of a circle - or approximately 3.14.

10. How do you find the y-intercept of a graph?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.
Set x = 0 - and solve.

11. What is a composite number?
In the expression x^b - x is the base and b is the exponent.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
An integer greater than one that is not prime.
Divide - then multiply by 100.

12. What is the sum of the measures of the n angles of a polygon with n sides?
The product of their slopes is -1 (negative reciprocal).
How steep the line is. Horizontal line = 0 - vertical has no slope.
If a is negative and b is positive - then a < 0 < b.
(n - 2)(180°)

13. Properties of zero 5
For any number b: b = -b if and only if b = 0.
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.
A = lw

14. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
V = l^3
B^m/b^n = b^m-n
Shifted right 2 units.

15. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(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°.
D = 2r

16. Properties of one 1
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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°.
For any number a: a * 1 = a and a / 1 = a.

17. What is the formula for the area of a triangle?
Area = (x°/360)(pr^2) where x is the central angle.
A = (1/2)bh.
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.

18. How do you calculate percent increases and decreases?
For any number a: a * 1 = a and a / 1 = a.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

19. What are the important properties of a 45-45 - 90 triangle?
For any number a: a * 1 = a and a / 1 = a.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
No matter how many angles there are - the sum around the point is 360°.
(Circumference/diameter) of a circle - or approximately 3.14.

20. What is true about the measures of the three angles in a triangle?
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°.
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

21. 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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(Circumference/diameter) of a circle - or approximately 3.14.
360°

22. What is true about the measures of the four angles formed by two intersecting lines?
For any right triangle - a^2 + b^2 = c^2.
In the expression x^b - x is the base and b is the exponent.
The two pairs of opposite angles formed are equal to each other.
A = lw

23. What are the important properties of 30-60-90 triangle?
(n - 2)(180°)
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]
Is a right triangle with a ratio of sides x:xv3:2x.

24. What is special formula for the area of an equilateral triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Write the percent over 100 and reduce.
A = [(s^2*v3)/4]
The product of their slopes is -1 (negative reciprocal).

25. What is the formula for the area of a parallelogram?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
0 is the only number that is neither positive nor negative.
The set of all ordered pairs (x -y) such that y = f(x).
A = bh

26. What formula is used for an average?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Avg = sum of n numbers/n
An angle formed by extending the side of the polygon.
D = 2r

27. Important binomial 3
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number n: x^-n means 1/x^n.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

28. What are the quotient and the remainder?

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29. What is the sum of the measures of the four angles in a quadrilateral?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
360°
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.

30. Properties of one 4
Corresponding sides of similar triangles are in proportion.
An equation that states that two ratios are equivalent. 4/6 = 10/15
1 is the smallest positive odd integer.
They are both the same. A divisor or factor of an integer leaves no remainder.

31. How do you convert a percent to a fraction or a decimal?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Write the percent over 100 and reduce.
Their sum is 90°.
(n - 2)(180°)

32. In a circle of radius r - what is the formula for the circumference?
Divide - then multiply by 100.
C = p2r
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

33. How do you find the probability that an event will occur?
1 is a divisor (or factor) of every integer.
C = p2r
A^m*b^m = (ab)^m
P(e) = (# of favorable outcomes)/(# of possible outcomes)

34. What is an exponent?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted right 2 units.
In the expression x^b - x is the base and b is the exponent.
An equation that states that two ratios are equivalent. 4/6 = 10/15

35. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = 6(l^2)
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

36. Important binomial 1
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
They are both the same. A divisor or factor of an integer leaves no remainder.
(x + y)(x - y) = x^2 - y^2
Shifted right 2 units.

37. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Set x = 0 - and solve.
Shifted down 2 units.

38. What is an even and an odd number?
Divide - then multiply by 100.
B^m/b^n = b^m-n
Even numbers are divisible by 2 and odd numbers are not.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

39. What is the formula for the area of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = lw
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
1 is a divisor (or factor) of every integer.

40. What is the formula for the volume of a cylinder?
V = pr^2h
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted left 2 units.
No matter how many angles there are - the sum around the point is 360°.

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

42. Properties of zero 3
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.
Their sum is 180°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

43. Properties of one 2
For any integer n: 1^n = 1.
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
C = p2r

44. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
The ratio of corresponding sides of similar triangles.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
All positive and negative whole numbers - and zero.

45. How do you find the area of a sector of a circle?
If a is negative and b is positive - then a < 0 < b.
Area = (x°/360)(pr^2) where x is the central angle.
Then the product xy is a constant.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

46. Law of exponents 1
B^m*b^n = b^m+n
Area = (x°/360)(pr^2) where x is the central angle.
A^m*b^m = (ab)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.

47. What is the area of a square?
Equal slopes.
At least one of the factors is 0.
A = pr^2
A = s^2 or A =d^2/2 where d is the diagonal

48. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

49. Properties of zero 4
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

50. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Then the product xy is a constant.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.