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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 an exponent?
180°. If two or more angles form a straight angle - their sum is 180°.
Corresponding sides of similar triangles are in proportion.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
In the expression x^b - x is the base and b is the exponent.

2. What is the sum of the measures of the four angles in a quadrilateral?
Then the product xy is a constant.
Shifted up 2 units.
360°
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

3. Properties of zero 2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Even numbers are divisible by 2 and odd numbers are not.
The ratio of corresponding sides of similar triangles.
If a is negative and b is positive - then a < 0 < b.

4. Properties of zero 1
0 is the only number that is neither positive nor negative.
C = p2r
Corresponding sides of similar triangles are in proportion.
All positive and negative whole numbers - and zero.

5. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
If a is negative and b is positive - then a < 0 < b.
360°
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

6. What is the probability of an event that cannot occur? That must occur?
In the expression x^b - x is the base and b is the exponent.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any number b: b = -b if and only if b = 0.
Cannot is 0 - must is 1 - all others are in between.

7. Properties of one 1
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The two pairs of opposite angles formed are equal to each other.
Their sum is 180°.
For any number a: a * 1 = a and a / 1 = a.

8. Properties of zero 3
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Avg = sum of n numbers/n
1 is a divisor (or factor) of every integer.
0 is a multiple of every integer.

9. Important binomial 1
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Set x = 0 - and solve.
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.
(x + y)(x - y) = x^2 - y^2

10. 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.
Even numbers are divisible by 2 and odd numbers are not.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The product of their slopes is -1 (negative reciprocal).

11. What is the formula for the area of a triangle?
The two pairs of opposite angles formed are equal to each other.
Then the product xy is a constant.
Divide - then multiply by 100.
A = (1/2)bh.

12. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Then the quotient y/x is a constant.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted up 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

13. Properties of one 2
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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 integer n: 1^n = 1.
Then the quotient y/x is a constant.

14. What is the formula for the area of a rectangle?
A^m*b^m = (ab)^m
A = lw
The product of their slopes is -1 (negative reciprocal).
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

15. What is the distance formula?
They are both the same. A divisor or factor of an integer leaves no remainder.
0 is the only number that is neither positive nor negative.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
All positive and negative whole numbers - and zero.

16. What is the formula for the surface area of a cube?
B^m/b^n = b^m-n
Set y = 0 - and solve.
A = 6(l^2)
For any number a: a * 1 = a and a / 1 = a.

17. What is the formula for the area of a parallelogram?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = bh
Shifted left 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

18. 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
M = (y2 - y1)/(x2 - x1)
Shifted right 2 units.
Write the percent as a decimal - and multiply.

19. What is an even and an odd number?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The ratio of corresponding sides of similar triangles.
Even numbers are divisible by 2 and odd numbers are not.
All positive and negative whole numbers - and zero.

20. 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°.
Even numbers are divisible by 2 and odd numbers are not.
360°
(Circumference/diameter) of a circle - or approximately 3.14.

21. How do you find the y-intercept of a graph?
How steep the line is. Horizontal line = 0 - vertical has no slope.
A^m*b^m = (ab)^m
Set x = 0 - and solve.
At least one of the factors is 0.

22. What is the measure of a straight angle?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
At least one of the factors is 0.
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted down 2 units.

23. Properties of zero 4
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
360°
An equation that states that two ratios are equivalent. 4/6 = 10/15
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

24. What is the area of a square?
(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
A = 2(lw + lh + hw)
Avg = sum of n numbers/n

25. How do you find the length of an arc of a circle?
Their sum is 90°.
Arc = (x°/360)(2pr) where x is the central angle.
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.
D = 2r

26. What formula is used for an average?
Avg = sum of n numbers/n
Their sum is 90°.
Set y = 0 - and solve.
For any right triangle - a^2 + b^2 = c^2.

27. What is special formula for the area of an equilateral triangle?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = [(s^2*v3)/4]
The set of all ordered pairs (x -y) such that y = f(x).

28. What is the formula for the volume of a cylinder?
For any integer n: 1^n = 1.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
1 is a divisor (or factor) of every integer.
V = pr^2h

29. What are the quotient and the remainder?

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30. What is the square root of a number?
Cannot is 0 - must is 1 - all others are in between.
C = p2r
360°
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

31. What is a prime number?
For any number a: a * 1 = a and a / 1 = a.
B^m*b^n = b^m+n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.

32. What is a composite number?
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.
Set x = 0 - and solve.
An integer greater than one that is not prime.
Write the percent over 100 and reduce.

33. How do you find the area of a sector of a circle?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Area = (x°/360)(pr^2) where x is the central angle.
At least one of the factors is 0.
Then the product xy is a constant.

34. What is true about the measures of the four angles formed by two intersecting lines?
A = lw
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
[(x1 + x2)/2] -[(y1 + y2)/2]
The two pairs of opposite angles formed are equal to each other.

35. What is the volume of a cube?
At least one of the factors is 0.
V = l^3
They are both the same. A divisor or factor of an integer leaves no remainder.
A fraction whose denominator is 100 i.e. 17% = 17/100

36. What is true about the slopes of parallel lines?
For any number n: x^-n means 1/x^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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Equal slopes.

37. In a circle of radius r - what is the formula for the diameter?
Area = (x°/360)(pr^2) where x is the central angle.
Is a right triangle with a ratio of sides x:xv3:2x.
1 is a divisor (or factor) of every integer.
D = 2r

38. If the product of two or more numbers is 0 - what do you know about the numbers?
A = bh
Write the percent as a decimal - and multiply.
At least one of the factors is 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.

39. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.
Cannot is 0 - must is 1 - all others are in between.

40. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Equal slopes.
A^m*b^m = (ab)^m
Shifted left 2 units.
B^m*b^n = b^m+n

41. What is a proportion?
Write the percent over 100 and reduce.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
An equation that states that two ratios are equivalent. 4/6 = 10/15
V = l^3

42. What is the graph of a function?
A = 2(lw + lh + hw)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The set of all ordered pairs (x -y) such that y = f(x).
Shifted up 2 units.

43. What is the distributive law?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
C = p2r
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
M = (y2 - y1)/(x2 - x1)

44. Properties of square roots
Set x = 0 - and solve.
B^m/b^n = b^m-n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

45. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
A = (1/2)bh.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
360°
Set y = 0 - and solve.

46. What is the Pythagorean theorem?
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any right triangle - a^2 + b^2 = c^2.

47. Properties of one 3
1 is a divisor (or factor) of every integer.
Shifted down 2 units.
Divide - then multiply by 100.
Is a right triangle with a ratio of sides x:xv3:2x.

48. What important property do similar triangles have?
C = p2r
Corresponding sides of similar triangles are in proportion.
For any number n: x^-n means 1/x^n.
A = (1/2)bh.

49. 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.
At least one of the factors is 0.
Write the percent as a decimal - and multiply.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

50. What is a Venn diagram?
C = p2r
For any number b: b = -b if and only if b = 0.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The product of their slopes is -1 (negative reciprocal).