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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. Properties of one 1
Write the percent over 100 and reduce.
A = s^2 or A =d^2/2 where d is the diagonal
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any number a: a * 1 = a and a / 1 = a.

2. What is an exterior angle of a triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.

3. How you convert a fraction or a decimal to a percent?
(b^m)^n = b^mn
Divide - then multiply by 100.
Area = (x°/360)(pr^2) where x is the central angle.
A = (1/2)bh.

4. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
The product of their slopes is -1 (negative reciprocal).
Then the quotient y/x is a constant.
Shifted down 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

5. Law of exponents 5
Shifted right 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
360°
A^m/b^m = (a/b)^m

6. If you were given the graph of y = f(x) - what does f(a) represent?
The product of their slopes is -1 (negative reciprocal).
A = s^2 or A =d^2/2 where d is the diagonal
B^m/b^n = b^m-n
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

7. What is the sum of the measures of the four angles in a quadrilateral?
(n - 2)(180°)
360°
A = lw
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.

8. What are the properties of a parallelogram?
No matter how many angles there are - the sum around the point is 360°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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 the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

9. Law of exponents 3
(b^m)^n = b^mn
Write the percent as a decimal - and multiply.
For any number a: a * 1 = a and a / 1 = a.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

10. What is true about the slopes of parallel lines?
A^m*b^m = (ab)^m
Equal slopes.
Shifted right 2 units.
A = bh

11. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
B^m/b^n = b^m-n
The product of their slopes is -1 (negative reciprocal).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

12. What is the volume of a cube?
A = pr^2
Then the product xy is a constant.
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.
V = l^3

13. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
At least one of the factors is 0.
A = (1/2)bh.

14. What is special formula for the area of an equilateral triangle?
Area = (x°/360)(pr^2) where x is the central angle.
A = [(s^2*v3)/4]
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Write the percent as a decimal - and multiply.

15. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the 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.
All positive and negative whole numbers - and zero.
For any right triangle - a^2 + b^2 = c^2.
180°. If two or more angles form a straight angle - their sum is 180°.

16. What is the formula for the surface area of a cube?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The two pairs of opposite angles formed are equal to each other.
Write the percent as a decimal - and multiply.
A = 6(l^2)

17. How do you find the x-intercept of a graph?
Cannot is 0 - must is 1 - all others are in between.
A = 2(lw + lh + hw)
Set y = 0 - and solve.
Area = (x°/360)(pr^2) where x is the central angle.

18. What is the formula for the volume of a rectangular solid?
V = lwh
Then the quotient y/x is a constant.
A = bh
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°.

19. What is the measure of a straight angle?
A = bh
Arc = (x°/360)(2pr) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.
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.

20. What is an integer?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
All positive and negative whole numbers - and zero.
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.
360°

21. What is the probability of an event that cannot occur? That must occur?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
B^m/b^n = b^m-n
Cannot is 0 - must is 1 - all others are in between.

22. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
1 is a divisor (or factor) of every integer.
0 is a multiple of every integer.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

23. What is the ratio of similitude?
In the expression x^b - x is the base and b is the exponent.
180°. If two or more angles form a straight angle - their sum is 180°.
(n - 2)(180°)
The ratio of corresponding sides of similar triangles.

24. What is a divisor and a factor of an integer?
Then the product xy is a constant.
They are both the same. A divisor or factor of an integer leaves no remainder.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any right triangle - a^2 + b^2 = c^2.

25. What is a fractional exponent?
Shifted down 2 units.
A = (1/2)bh.
D = 2r
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

26. What are the sum - difference - products - and quotient of two numbers?
D = 2r
Their sum is 90°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Arc = (x°/360)(2pr) where x is the central angle.

27. In a circle of radius r - what is the formula for the circumference?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
V = lwh
C = p2r
Equal slopes.

28. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
(b^m)^n = b^mn
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Divide - then multiply by 100.

29. How do you find the y-intercept of a graph?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Set x = 0 - and solve.
Shifted right 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

30. Important binomial 1
Equal slopes.
(x + y)(x - y) = x^2 - y^2
Shifted left 2 units.
The set of all ordered pairs (x -y) such that y = f(x).

31. What is the formula for the area of a triangle?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Their sum is 90°.
An angle formed by extending the side of the polygon.
A = (1/2)bh.

32. What formula is used for an average?
Avg = sum of n numbers/n
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
They are both the same. A divisor or factor of an integer leaves no remainder.
M = (y2 - y1)/(x2 - x1)

33. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
They are both the same. A divisor or factor of an integer leaves no remainder.
The two pairs of opposite angles formed are equal to each other.

34. What are the important properties of a 45-45 - 90 triangle?
B^m*b^n = b^m+n
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = bh
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

35. How do you find the length of an arc of a circle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Arc = (x°/360)(2pr) where x is the central angle.
A = 2(lw + lh + hw)

36. Properties of zero 3
A = lw
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 a multiple of every integer.
A = bh

37. How do you calculate a weighted average?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The product of their slopes is -1 (negative reciprocal).
Shifted right 2 units.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

38. What are the properties of a square?
M = (y2 - y1)/(x2 - x1)
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

39. What is an exterior angle of a polygon?
A = [(s^2*v3)/4]
An angle formed by extending the side of the polygon.
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

40. What is an exponent?
M = (y2 - y1)/(x2 - x1)
0 is the only number that is neither positive nor negative.
At least one of the factors is 0.
In the expression x^b - x is the base and b is the exponent.

41. What is a composite number?
In the expression x^b - x is the base and b is the exponent.
The set of all ordered pairs (x -y) such that y = f(x).
An integer greater than one that is not prime.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

42. What is the formula for the area of a rectangle?
They are both the same. A divisor or factor of an integer leaves no remainder.
A = lw
V = lwh
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.

43. What is a prime number?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
For any number b: b = -b if and only if b = 0.
An angle formed by extending the side of the polygon.

44. How do we write the equation of a line?
Their sum is 90°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

45. What does it mean if y is inversely proportional to x?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted up 2 units.
Then the product xy is a constant.
A = [(s^2*v3)/4]

46. If the product of two or more numbers is 0 - what do you know about the numbers?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any right triangle - a^2 + b^2 = c^2.
At least one of the factors is 0.
0 is the only number that is neither positive nor negative.

47. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
An integer greater than one that is not prime.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Is a right triangle with a ratio of sides x:xv3:2x.

48. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
In the expression x^b - x is the base and b is the exponent.
D = 2r
(x + y)(x - y) = x^2 - y^2

49. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
The two pairs of opposite angles formed are equal to each other.
360°
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°.

50. Law of exponents 4
Area = (x°/360)(pr^2) where x is the central angle.
A = 6(l^2)
Shifted down 2 units.
A^m*b^m = (ab)^m