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Test your basic knowledge |
GRE Math: Facts
Start Test
Study First
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 does it mean if y is inversely proportional to x?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Then the product xy is a constant.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
2. What are the properties of a rectangle?
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
3. Law of exponents 3
Shifted down 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(b^m)^n = b^mn
An equation that states that two ratios are equivalent. 4/6 = 10/15
4. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted up 2 units.
M = (y2 - y1)/(x2 - x1)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
5. What is the square root of a number?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
B^m/b^n = b^m-n
The two pairs of opposite angles formed are equal to each other.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
6. What is the ratio of similitude?
For any right triangle - a^2 + b^2 = c^2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The ratio of corresponding sides of similar triangles.
Shifted left 2 units.
7. How do you find the y-intercept of a graph?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Set x = 0 - and solve.
A^m*b^m = (ab)^m
8. How do you find a percent of a number?
Their sum is 90°.
(x + y)(x - y) = x^2 - y^2
An integer greater than one that is not prime.
Write the percent as a decimal - and multiply.
9. What is a ratio?
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10. Properties of zero 5
(b^m)^n = b^mn
For any number b: b = -b if and only if b = 0.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An integer greater than one that is not prime.
11. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
M = (y2 - y1)/(x2 - x1)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
12. How do you find the x-intercept of a graph?
[(x1 + x2)/2] -[(y1 + y2)/2]
Set y = 0 - and solve.
0 is a multiple of every integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
13. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
360°
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
14. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted up 2 units.
(x + y)(x - y) = x^2 - y^2
15. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
In the expression x^b - x is the base and b is the exponent.
A^m/b^m = (a/b)^m
The product of their slopes is -1 (negative reciprocal).
16. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
B^m*b^n = b^m+n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
An angle formed by extending the side of the polygon.
17. What is a negative exponent?
[(x1 + x2)/2] -[(y1 + y2)/2]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(n - 2)(180°)
For any number n: x^-n means 1/x^n.
18. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
[(x1 + x2)/2] -[(y1 + y2)/2]
Equal slopes.
0 is a multiple of every integer.
19. What is the formula for the volume of a cylinder?
A^m*b^m = (ab)^m
At least one of the factors is 0.
D = 2r
V = pr^2h
20. What important property do similar triangles have?
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.
Corresponding sides of similar triangles are in proportion.
Equal slopes.
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°.
21. What is the relationship between a radius of a circle and a line that is tangent to the circle?
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number a: a * 1 = a and a / 1 = a.
22. If the product of two or more numbers is 0 - what do you know about the numbers?
In the expression x^b - x is the base and b is the exponent.
(n - 2)(180°)
At least one of the factors is 0.
A = [(s^2*v3)/4]
23. What is the formula for the area of a triangle?
In the expression x^b - x is the base and b is the exponent.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = (1/2)bh.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
24. Properties of zero 1
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The ratio of corresponding sides of similar triangles.
0 is the only number that is neither positive nor negative.
25. What is a function?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Arc = (x°/360)(2pr) where x is the central angle.
360°
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
26. Properties of zero 2
For any number b: b = -b if and only if b = 0.
Divide - then multiply by 100.
If a is negative and b is positive - then a < 0 < b.
V = lwh
27. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Corresponding sides of similar triangles are in proportion.
They are both the same. A divisor or factor of an integer leaves no remainder.
Equal slopes.
360°
28. What is true about the slopes of parallel lines?
Area = (x°/360)(pr^2) where x is the central angle.
Even numbers are divisible by 2 and odd numbers are not.
Equal slopes.
For any integer n: 1^n = 1.
29. What is true about the measures of the two acute angles in a right triangle?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Their sum is 90°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
30. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = lw
Write the percent over 100 and reduce.
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°.
Shifted right 2 units.
31. What is p?
The two pairs of opposite angles formed are equal to each other.
A = pr^2
A = 2(lw + lh + hw)
(Circumference/diameter) of a circle - or approximately 3.14.
32. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
V = l^3
A fraction whose denominator is 100 i.e. 17% = 17/100
A = 2(lw + lh + hw)
33. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
Cannot is 0 - must is 1 - all others are in between.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any number n: x^-n means 1/x^n.
34. Properties of one 3
(b^m)^n = b^mn
1 is a divisor (or factor) of every integer.
In the expression x^b - x is the base and b is the exponent.
Set y = 0 - and solve.
35. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
An angle formed by extending the side of the polygon.
36. What are similar triangles?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
D = 2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
[(x1 + x2)/2] -[(y1 + y2)/2]
37. What formula is used for an average?
Then the quotient y/x is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
[(x1 + x2)/2] -[(y1 + y2)/2]
Avg = sum of n numbers/n
38. In a circle of radius r - what is the formula for the circumference?
C = p2r
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number n: x^-n means 1/x^n.
A = bh
39. What is a divisor and a factor of an integer?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m*b^m = (ab)^m
C = p2r
They are both the same. A divisor or factor of an integer leaves no remainder.
40. Law of exponents 5
V = pr^2h
A^m/b^m = (a/b)^m
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = s^2 or A =d^2/2 where d is the diagonal
41. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Write the percent over 100 and reduce.
All positive and negative whole numbers - and zero.
Cannot is 0 - must is 1 - all others are in between.
Shifted left 2 units.
42. How do you find the slope of a line?
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.
M = (y2 - y1)/(x2 - x1)
Their sum is 90°.
43. Properties of one 4
(n - 2)(180°)
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m
Even numbers are divisible by 2 and odd numbers are not.
44. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
If a is negative and b is positive - then a < 0 < b.
The product of their slopes is -1 (negative reciprocal).
A = lw
45. Properties of one 2
A = [(s^2*v3)/4]
For any integer n: 1^n = 1.
Their sum is 90°.
(b^m)^n = b^mn
46. What is the sum of the measures of the n angles of a polygon with n sides?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m*b^m = (ab)^m
(n - 2)(180°)
Divide - then multiply by 100.
47. What is an integer?
All positive and negative whole numbers - and zero.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
At least one of the factors is 0.
48. What is the sum of the measures of all angles around a point?
B^m*b^n = b^m+n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The two pairs of opposite angles formed are equal to each other.
No matter how many angles there are - the sum around the point is 360°.
49. What is the sum of the measures of the four angles in a quadrilateral?
(b^m)^n = b^mn
V = l^3
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°
50. Properties of zero 3
A = pr^2
(n - 2)(180°)
An integer greater than one that is not prime.
0 is a multiple of every integer.