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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. How do you calculate a weighted average?
A = s^2 or A =d^2/2 where d is the diagonal
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
360°
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°.

2. How you convert a fraction or a decimal to a percent?
(n - 2)(180°)
[(x1 + x2)/2] -[(y1 + y2)/2]
Divide - then multiply by 100.
Their sum is 90°.

3. If you were given the graph of y = f(x) - what does f(a) represent?
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.
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°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

4. What is the formula for the volume of a rectangular solid?
V = lwh
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.
The ratio of corresponding sides of similar triangles.
The product of their slopes is -1 (negative reciprocal).

5. What is a proportion?
360°
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
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

6. What formula is used for an average?
Cannot is 0 - must is 1 - all others are in between.
The two pairs of opposite angles formed are equal to each other.
Avg = sum of n numbers/n
A fraction whose denominator is 100 i.e. 17% = 17/100

7. What is an exterior angle of a triangle?
Write the percent as a decimal - and multiply.
Shifted down 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

8. Properties of zero 5
A = s^2 or A =d^2/2 where d is the diagonal
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Write the percent over 100 and reduce.
For any number b: b = -b if and only if b = 0.

9. 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°.
They are both the same. A divisor or factor of an integer leaves no remainder.
The product of their slopes is -1 (negative reciprocal).

10. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
A = 2(lw + lh + hw)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

11. What is an exponent?
(x + y)(x - y) = x^2 - y^2
A^m*b^m = (ab)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.
In the expression x^b - x is the base and b is the exponent.

12. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted up 2 units.
The ratio of corresponding sides of similar triangles.

13. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
Cannot is 0 - must is 1 - all others are in between.
Shifted left 2 units.
Shifted up 2 units.

14. How do you find the area of a sector of a circle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Area = (x°/360)(pr^2) where x is the central angle.

15. What is the formula for the surface area of a cube?
For any number n: x^-n means 1/x^n.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = 6(l^2)
The ratio of corresponding sides of similar triangles.

16. What is the distance formula?
Set x = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
0 is the only number that is neither positive nor negative.

17. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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 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.
An integer greater than one that is not prime.
Arc = (x°/360)(2pr) where x is the central angle.

18. Law of exponents 3
[(x1 + x2)/2] -[(y1 + y2)/2]
(b^m)^n = b^mn
A = bh
A = 2(lw + lh + hw)

19. What is a fractional exponent?
D = 2r
Then the quotient y/x is a constant.
Set y = 0 - and solve.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

20. What is an exterior angle of a polygon?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
V = lwh
Equal slopes.
An angle formed by extending the side of the polygon.

21. Important binomial 3
B^m/b^n = b^m-n
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Set x = 0 - and solve.
Their sum is 180°.

22. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Set y = 0 - and solve.

23. What is an integer?
For any number n: x^-n means 1/x^n.
Arc = (x°/360)(2pr) where x is the central angle.
M = (y2 - y1)/(x2 - x1)
All positive and negative whole numbers - and zero.

24. What is the sum of the measures of the four angles in a quadrilateral?
Area = (x°/360)(pr^2) where x is the central angle.
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.
Shifted right 2 units.
360°

25. What important property do similar triangles have?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Then the quotient y/x is a constant.
Corresponding sides of similar triangles are in proportion.

26. What is true about the measures of the three angles in a triangle?
[(x1 + x2)/2] -[(y1 + y2)/2]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Their sum is 180°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

27. How do you find the y-intercept of a graph?
(n - 2)(180°)
No matter how many angles there are - the sum around the point is 360°.
For any right triangle - a^2 + b^2 = c^2.
Set x = 0 - and solve.

28. In a circle of radius r - what is the formula for the diameter?
Is a right triangle with a ratio of sides x:xv3:2x.
D = 2r
[(x1 + x2)/2] -[(y1 + y2)/2]
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

29. Properties of zero 1
For any integer n: 1^n = 1.
0 is the only number that is neither positive nor negative.
No matter how many angles there are - the sum around the point is 360°.
Set y = 0 - and solve.

30. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
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.
For any number n: x^-n means 1/x^n.
C = p2r
Shifted right 2 units.

31. What is a composite number?
Avg = sum of n numbers/n
An integer greater than one that is not prime.
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°.
360°

32. What is the relationship between a radius of a circle and a line that is tangent to the circle?
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = lw

33. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
In the expression x^b - x is the base and b is the exponent.
A = bh
The ratio of corresponding sides of similar triangles.

34. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Shifted left 2 units.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

35. How do you find the slope of a line?
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
M = (y2 - y1)/(x2 - x1)
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.

36. What is the triangle inequality?
Shifted up 2 units.
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.
Set y = 0 - and solve.
M = (y2 - y1)/(x2 - x1)

37. What is special formula for the area of an equilateral triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = [(s^2*v3)/4]
A = 2(lw + lh + hw)

38. In a circle of radius r - what is the formula for the circumference?
Then the product xy is a constant.
C = p2r
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.
360°

39. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
All positive and negative whole numbers - and zero.
For any number b: b = -b if and only if b = 0.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

40. What is the formula for the area of a parallelogram?
A = (1/2)bh.
A = bh
180°. If two or more angles form a straight angle - their sum is 180°.
Equal slopes.

41. Properties of one 2
For any integer n: 1^n = 1.
180°. If two or more angles form a straight angle - their sum is 180°.
A^m*b^m = (ab)^m
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

42. If the product of two or more numbers is 0 - what do you know about the numbers?
360°
360°
(Circumference/diameter) of a circle - or approximately 3.14.
At least one of the factors is 0.

43. What is the volume of a cube?
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.
Divide - then multiply by 100.
V = l^3
Their sum is 180°.

44. 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.
They are both the same. A divisor or factor of an integer leaves no remainder.
(b^m)^n = b^mn
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

45. What are the properties of a parallelogram?
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
V = l^3
The ratio of corresponding sides of similar triangles.

46. What is the midpoint formula?
The product of their slopes is -1 (negative reciprocal).
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
[(x1 + x2)/2] -[(y1 + y2)/2]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

47. Law of exponents 5
In the expression x^b - x is the base and b is the exponent.
A = [(s^2*v3)/4]
V = pr^2h
A^m/b^m = (a/b)^m

48. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
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.
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted down 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.

49. What is the Pythagorean theorem?
A^m*b^m = (ab)^m
For any right triangle - a^2 + b^2 = c^2.
An integer greater than one that is not prime.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

50. What are the properties of a square?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^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.
A fraction whose denominator is 100 i.e. 17% = 17/100
V = lwh

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