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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. Properties of square roots
Divide - then multiply by 100.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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 right triangle - a^2 + b^2 = c^2.

2. Properties of zero 1
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The two pairs of opposite angles formed are equal to each other.
0 is the only number that is neither positive nor negative.
The product of their slopes is -1 (negative reciprocal).

3. What is an even and an odd number?
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.
Even numbers are divisible by 2 and odd numbers are not.
A^m/b^m = (a/b)^m
Set x = 0 - and solve.

4. What is the ratio of similitude?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The ratio of corresponding sides of similar triangles.
D = 2r

5. Law of exponents 1
B^m*b^n = b^m+n
The two pairs of opposite angles formed are equal to each other.
The set of all ordered pairs (x -y) such that y = f(x).
A = s^2 or A =d^2/2 where d is the diagonal

6. What is the formula for the area of a rectangle?
A = lw
For any number n: x^-n means 1/x^n.
C = p2r
Divide - then multiply by 100.

7. What is a proportion?
360°
A = lw
An equation that states that two ratios are equivalent. 4/6 = 10/15
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

8. How do we write the equation of a line?
(Circumference/diameter) of a circle - or approximately 3.14.
V = lwh
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted up 2 units.

9. Properties of one 4
360°
1 is the smallest positive odd integer.
Arc = (x°/360)(2pr) where x is the central angle.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

10. What is true about the measures of the three angles in a triangle?
A fraction whose denominator is 100 i.e. 17% = 17/100
Their sum is 180°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Write the percent as a decimal - and multiply.

11. How do you find the slope of a line?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Divide - then multiply by 100.
M = (y2 - y1)/(x2 - x1)

12. What is the triangle inequality?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
1 is the smallest positive odd integer.
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 = lw

13. What is a multiple of an integer?
For any number a: a * 1 = a and a / 1 = a.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

14. What formula is used for an average?
Avg = sum of n numbers/n
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Shifted left 2 units.

15. Properties of zero 4
Even numbers are divisible by 2 and odd numbers are not.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number b: b = -b if and only if b = 0.
At least one of the factors is 0.

16. How do you find a percent of a number?
In the expression x^b - x is the base and b is the exponent.
Write the percent as a decimal - and multiply.
Set x = 0 - and solve.
For any number n: x^-n means 1/x^n.

17. What does it mean if y is inversely proportional to x?
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.
Then the product xy is a constant.
A = [(s^2*v3)/4]
Equal slopes.

18. What is p?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Is a right triangle with a ratio of sides x:xv3:2x.
(Circumference/diameter) of a circle - or approximately 3.14.
A = 2(lw + lh + hw)

19. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
1 is a divisor (or factor) of every integer.
A^m*b^m = (ab)^m
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

20. What is true about the measures of the two acute angles in a right triangle?
Cannot is 0 - must is 1 - all others are in between.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.

21. How do you calculate a weighted average?
C = p2r
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

22. Properties of zero 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.
If a is negative and b is positive - then a < 0 < b.
In the expression x^b - x is the base and b is the exponent.
For any number n: x^-n means 1/x^n.

23. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted left 2 units.
Then the product xy is a constant.
(b^m)^n = b^mn

24. What is the sum of the measures of all angles around a point?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
No matter how many angles there are - the sum around the point is 360°.
C = p2r
(b^m)^n = b^mn

25. Law of exponents 4
A = s^2 or A =d^2/2 where d is the diagonal
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A^m*b^m = (ab)^m

26. In a circle of radius r - what is the formula for the diameter?
D = 2r
Shifted right 2 units.
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.
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.

27. How do you find the y-intercept of a graph?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Set x = 0 - and solve.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

28. What is special formula for the area of an equilateral triangle?
1 is a divisor (or factor) of every integer.
(n - 2)(180°)
A = [(s^2*v3)/4]
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.

29. What is the graph of a function?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
360°
An integer greater than one that is not prime.
The set of all ordered pairs (x -y) such that y = f(x).

30. Important binomial 3
B^m*b^n = b^m+n
C = p2r
Corresponding sides of similar triangles are in proportion.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

31. What is a function?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The set of all ordered pairs (x -y) such that y = f(x).
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

32. How you convert a fraction or a decimal to a percent?
Even numbers are divisible by 2 and odd numbers are not.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Is a right triangle with a ratio of sides x:xv3:2x.
Divide - then multiply by 100.

33. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

34. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Their sum is 180°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
360°
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

35. What is an integer?
All positive and negative whole numbers - and zero.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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 = bh

36. What are the properties of a parallelogram?
Arc = (x°/360)(2pr) where x is the central angle.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Corresponding sides of similar triangles are in proportion.
An equation that states that two ratios are equivalent. 4/6 = 10/15

37. What do we mean by the slope of the line?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted up 2 units.
A^m*b^m = (ab)^m

38. What is a divisor and a factor of an integer?
Divide - then multiply by 100.
Shifted down 2 units.
A = 6(l^2)
They are both the same. A divisor or factor of an integer leaves no remainder.

39. What is a fractional exponent?
Avg = sum of n numbers/n
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = lw
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

40. What is true about the slopes of parallel lines?
A = lw
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Equal slopes.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

41. What is true about the areas of similar triangles?
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The two pairs of opposite angles formed are equal to each other.

42. What is a prime number?
D = 2r
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°
P(e) = (# of favorable outcomes)/(# of possible outcomes)

43. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Divide - then multiply by 100.
360°

44. How do you find the probability that an event will occur?
Cannot is 0 - must is 1 - all others are in between.
Then the product xy is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Equal slopes.

45. What is the formula for the surface area of a cube?
For any number b: b = -b if and only if b = 0.
A = 6(l^2)
360°
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

46. What is the measure of a straight angle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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°.
The ratio of corresponding sides of similar triangles.
180°. If two or more angles form a straight angle - their sum is 180°.

47. Properties of one 3
C = p2r
1 is a divisor (or factor) of every integer.
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.

48. Important binomial 1
(b^m)^n = b^mn
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any right triangle - a^2 + b^2 = c^2.
(x + y)(x - y) = x^2 - y^2

49. How do you find the length of an arc of a circle?
Corresponding sides of similar triangles are in proportion.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Arc = (x°/360)(2pr) where x is the central angle.
For any integer n: 1^n = 1.

50. If you were given the graph of y = f(x) - what does f(a) represent?
Their sum is 90°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
How steep the line is. Horizontal line = 0 - vertical has no slope.
V = lwh