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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 do we mean by the slope of the line?
Equal slopes.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Their sum is 180°.
How steep the line is. Horizontal line = 0 - vertical has no slope.

2. What is true about the slopes of parallel lines?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
180°. If two or more angles form a straight angle - their sum is 180°.
Equal slopes.
Their sum is 180°.

3. Properties of zero 1
A^m*b^m = (ab)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.
0 is the only number that is neither positive nor negative.
Avg = sum of n numbers/n

4. What are the properties of a parallelogram?
Then the quotient y/x is a constant.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Write the percent as a decimal - and multiply.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

5. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
The two pairs of opposite angles formed are equal to each other.
A = (1/2)bh.
The product of their slopes is -1 (negative reciprocal).

6. What are the quotient and the remainder?

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7. What is the formula for the volume of a rectangular solid?
B^m*b^n = b^m+n
V = lwh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The ratio of corresponding sides of similar triangles.

8. Properties of zero 4
If a is negative and b is positive - then a < 0 < b.
B^m*b^n = b^m+n
V = l^3
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

9. What is the graph of a function?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The set of all ordered pairs (x -y) such that y = f(x).
D = 2r
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

10. How do you find the x-intercept of a graph?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Set y = 0 - and solve.
0 is a multiple of every integer.

11. Properties of one 3
C = p2r
M = (y2 - y1)/(x2 - x1)
360°
1 is a divisor (or factor) of every integer.

12. What is the volume of a cube?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
V = l^3
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

13. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
If a is negative and b is positive - then a < 0 < b.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
They are both the same. A divisor or factor of an integer leaves no remainder.

14. Law of exponents 5
V = l^3
They are both the same. A divisor or factor of an integer leaves no remainder.
A = (1/2)bh.
A^m/b^m = (a/b)^m

15. If you were given the graph of y = f(x) - what does f(a) represent?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The product of their slopes is -1 (negative reciprocal).
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An angle formed by extending the side of the polygon.

16. What is a composite number?
A = 6(l^2)
A = bh
For any number a: a * 1 = a and a / 1 = a.
An integer greater than one that is not prime.

17. 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 90°.
(n - 2)(180°)
A^m*b^m = (ab)^m

18. For what values of a function is the function undefined?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = pr^2h
360°
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

19. What is the square root of a number?
For any number b: b = -b if and only if b = 0.
Shifted right 2 units.
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

20. What is a multiple of an integer?
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.
V = pr^2h
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
B^m/b^n = b^m-n

21. What is the formula for the volume of a cylinder?
V = pr^2h
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The ratio of corresponding sides of similar triangles.

22. What is a ratio?

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23. What is the sum of the measures of all angles around a point?
If a is negative and b is positive - then a < 0 < b.
Then the quotient y/x is a constant.
No matter how many angles there are - the sum around the point is 360°.
Arc = (x°/360)(2pr) where x is the central angle.

24. What is a Venn diagram?
360°
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any right triangle - a^2 + b^2 = c^2.
For any number a: a * 1 = a and a / 1 = a.

25. What is true about the slopes of perpendicular lines?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = lwh
180°. If two or more angles form a straight angle - their sum is 180°.
The product of their slopes is -1 (negative reciprocal).

26. What is true about the measures of the four angles formed by two intersecting lines?
The set of all ordered pairs (x -y) such that y = f(x).
A^m/b^m = (a/b)^m
The two pairs of opposite angles formed are equal to each other.
Their sum is 90°.

27. In a circle of radius r - what is the formula for the diameter?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any right triangle - a^2 + b^2 = c^2.
D = 2r
The set of all ordered pairs (x -y) such that y = f(x).

28. How do you calculate a weighted average?
For any number n: x^-n means 1/x^n.
At least one of the factors is 0.
(b^m)^n = b^mn
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

29. What is the formula for the area of a triangle?
They are both the same. A divisor or factor of an integer leaves no remainder.
Is a right triangle with a ratio of sides x:xv3:2x.
In the expression x^b - x is the base and b is the exponent.
A = (1/2)bh.

30. Properties of zero 2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
360°
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
If a is negative and b is positive - then a < 0 < b.

31. What is a proportion?
Shifted right 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Their sum is 180°.
An equation that states that two ratios are equivalent. 4/6 = 10/15

32. Law of exponents 3
A^m*b^m = (ab)^m
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.
(b^m)^n = b^mn
Cannot is 0 - must is 1 - all others are in between.

33. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = (1/2)bh.
Shifted down 2 units.
1 is a divisor (or factor) of every integer.

34. What is a negative exponent?
For any number n: x^-n means 1/x^n.
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.
180°. If two or more angles form a straight angle - their sum is 180°.

35. What is the relationship between a radius of a circle and a line that is tangent to the circle?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = lw
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
360°

36. What is a divisor and a factor of an integer?
Area = (x°/360)(pr^2) where x is the central angle.
A = 6(l^2)
They are both the same. A divisor or factor of an integer leaves no remainder.
Their sum is 180°.

37. What is the formula for the surface area of a rectangular solid?
For any number n: x^-n means 1/x^n.
A = 2(lw + lh + hw)
A = pr^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

38. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 90°.
A = lw
D = 2r

39. What is true about the areas of similar triangles?
A = s^2 or A =d^2/2 where d is the diagonal
Arc = (x°/360)(2pr) where x is the central angle.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Cannot is 0 - must is 1 - all others are in between.

40. Law of exponents 4
An integer greater than one that is not prime.
A^m*b^m = (ab)^m
A = pr^2
The product of their slopes is -1 (negative reciprocal).

41. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
(n - 2)(180°)
Shifted up 2 units.
A = pr^2
Corresponding sides of similar triangles are in proportion.

42. Law of exponents 2
The ratio of corresponding sides of similar triangles.
Shifted left 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
B^m/b^n = b^m-n

43. What is a fractional exponent?
A fraction whose denominator is 100 i.e. 17% = 17/100
A = pr^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

44. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Is a right triangle with a ratio of sides x:xv3:2x.
A^m*b^m = (ab)^m
In the expression x^b - x is the base and b is the exponent.

45. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
An equation that states that two ratios are equivalent. 4/6 = 10/15
All positive and negative whole numbers - and zero.
[(x1 + x2)/2] -[(y1 + y2)/2]

46. How do you find the length of an arc of a circle?
V = pr^2h
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = lwh
Arc = (x°/360)(2pr) where x is the central angle.

47. In a circle of radius r - what is the formula for the area?
A = pr^2
A fraction whose denominator is 100 i.e. 17% = 17/100
An integer greater than one that is not prime.
D = 2r

48. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Then the product xy is a constant.
For any integer n: 1^n = 1.
Shifted right 2 units.
Arc = (x°/360)(2pr) where x is the central angle.

49. How do you find a percent of a number?
0 is the only number that is neither positive nor negative.
Write the percent as a decimal - and multiply.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Then the quotient y/x is a constant.

50. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The product of their slopes is -1 (negative reciprocal).