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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 is the ratio of similitude?
For any number a: a * 1 = a and a / 1 = a.
1 is a divisor (or factor) of every integer.
The ratio of corresponding sides of similar triangles.
An integer greater than one that is not prime.

2. What is p?
Set x = 0 - and solve.
(Circumference/diameter) of a circle - or approximately 3.14.
Is a right triangle with a ratio of sides x:xv3:2x.
The ratio of corresponding sides of similar triangles.

3. Law of exponents 5
A^m/b^m = (a/b)^m
The two pairs of opposite angles formed are equal to each other.
Their sum is 90°.
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.

4. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Area = (x°/360)(pr^2) where x is the central angle.
Cannot is 0 - must is 1 - all others are in between.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

5. In a circle of radius r - what is the formula for the area?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = pr^2

6. What is the sum of the measures of all angles around a point?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
No matter how many angles there are - the sum around the point is 360°.
Write the percent as a decimal - and multiply.
(b^m)^n = b^mn

7. In a circle of radius r - what is the formula for the diameter?
Shifted left 2 units.
D = 2r
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = lw

8. How do you find the area of a sector of a circle?
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°.
An integer greater than one that is not prime.
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.
Area = (x°/360)(pr^2) where x is the central angle.

9. What are the important properties of 30-60-90 triangle?
For any number a: a * 1 = a and a / 1 = a.
(n - 2)(180°)
At least one of the factors is 0.
Is a right triangle with a ratio of sides x:xv3:2x.

10. What is a fractional exponent?
(n - 2)(180°)
For any number n: x^-n means 1/x^n.
Equal slopes.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

11. What is a divisor and a factor of an integer?
Is a right triangle with a ratio of sides x:xv3:2x.
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
They are both the same. A divisor or factor of an integer leaves no remainder.

12. Law of exponents 2
B^m/b^n = b^m-n
Then the product xy is a constant.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Arc = (x°/360)(2pr) where x is the central angle.

13. What is an integer?
For any number b: b = -b if and only if b = 0.
All positive and negative whole numbers - and zero.
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.

14. Properties of zero 2
0 is a multiple of every integer.
Avg = sum of n numbers/n
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
If a is negative and b is positive - then a < 0 < b.

15. Law of exponents 3
B^m*b^n = b^m+n
(b^m)^n = b^mn
Shifted left 2 units.
For any number a: a * 1 = a and a / 1 = a.

16. What is true about the slopes of perpendicular lines?
Corresponding sides of similar triangles are in proportion.
The product of their slopes is -1 (negative reciprocal).
Their sum is 90°.
Shifted right 2 units.

17. What is true about the slopes of parallel lines?
M = (y2 - y1)/(x2 - x1)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Equal slopes.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

18. What is a multiple of an integer?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.

19. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(x + y)(x - y) = x^2 - y^2
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
They are both the same. A divisor or factor of an integer leaves no remainder.

20. What are the median and the mode of a set of data?
0 is the only number that is neither positive nor negative.
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.
If a is negative and b is positive - then a < 0 < b.
M = (y2 - y1)/(x2 - x1)

21. What does it mean if y is inversely proportional to x?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the product xy is a constant.
An angle formed by extending the side of the polygon.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

22. What is the distance formula?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Write the percent as a decimal - and multiply.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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.

23. What is the formula for the area of a parallelogram?
A = 6(l^2)
A = bh
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

24. What is the formula for the surface area of a rectangular solid?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
C = p2r
A = 2(lw + lh + hw)
Their sum is 90°.

25. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
B^m/b^n = b^m-n
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Set x = 0 - and solve.

26. What is the formula for the surface area of a cube?
A = 6(l^2)
For any number a: a * 1 = a and a / 1 = a.
Shifted left 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

27. What do we mean by the slope of the line?
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°.
All positive and negative whole numbers - and zero.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
How steep the line is. Horizontal line = 0 - vertical has no slope.

28. In a circle of radius r - what is the formula for the circumference?
A = [(s^2*v3)/4]
C = p2r
The two pairs of opposite angles formed are equal to each other.
For any number b: b = -b if and only if b = 0.

29. Important binomial 2
The set of all ordered pairs (x -y) such that y = f(x).
(b^m)^n = b^mn
Avg = sum of n numbers/n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

30. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
A = [(s^2*v3)/4]

31. Properties of square roots
0 is a multiple of every integer.
A = 6(l^2)
An integer greater than one that is not prime.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

32. Properties of zero 5
B^m/b^n = b^m-n
For any number b: b = -b if and only if b = 0.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
C = p2r

33. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
B^m/b^n = b^m-n
Cannot is 0 - must is 1 - all others are in between.
How steep the line is. Horizontal line = 0 - vertical has no slope.

34. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
Area = (x°/360)(pr^2) where x is the central angle.
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

35. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Set x = 0 - and solve.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = l^3

36. Properties of one 1
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any number a: a * 1 = a and a / 1 = a.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A^m*b^m = (ab)^m

37. What is an exterior angle of a polygon?
The product of their slopes is -1 (negative reciprocal).
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
How steep the line is. Horizontal line = 0 - vertical has no slope.
An angle formed by extending the side of the polygon.

38. Properties of zero 1
For any number n: x^-n means 1/x^n.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.
0 is the only number that is neither positive nor negative.

39. What is a ratio?

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40. What is a percent?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted up 2 units.
The product of their slopes is -1 (negative reciprocal).

41. How do you calculate a weighted average?
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
At least one of the factors is 0.

42. What is the probability of an event that cannot occur? That must occur?
Avg = sum of n numbers/n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Equal slopes.
Cannot is 0 - must is 1 - all others are in between.

43. Properties of zero 3
0 is a multiple of every integer.
Corresponding sides of similar triangles are in proportion.
An angle formed by extending the side of the polygon.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

44. 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.
Their sum is 180°.
A = lw

45. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
A = [(s^2*v3)/4]
Shifted right 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

46. Law of exponents 1
A fraction whose denominator is 100 i.e. 17% = 17/100
Even numbers are divisible by 2 and odd numbers are not.
B^m*b^n = b^m+n
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

47. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
360°

48. What are the sum - difference - products - and quotient of two numbers?
No matter how many angles there are - the sum around the point is 360°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Equal slopes.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

49. What is the formula for the area of a triangle?
A = (1/2)bh.
In the expression x^b - x is the base and b is the exponent.
Area = (x°/360)(pr^2) where x is the central angle.
360°

50. 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.
All positive and negative whole numbers - and zero.
A = lw
The set of all ordered pairs (x -y) such that y = f(x).