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Test your basic knowledge |
GRE Math: All In One
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. Formula to calculate arc length?
1
1
Arc length = (n/360) x pi(2r) where n is the number of degrees.
C=2 x pi x r OR pi x D
2. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
75:11
= (actual decrease/Original amount) x 100%
2²
12sqrt2
3. a/Ø
28
5 - 12 - 13
Null
Every number
4. Formula for the area of a circle?
$11 -448
An angle which is supplementary to an interior angle.
C=2 x pi x r OR pi x D
A = pi(r^2)
5. Solve the quadratic equation ax^2 + bx + c= 0
Members or elements
1/a^6
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
12.5%
6. 5/6 in percent?
y = (x + 5)/2
130pi
83.333%
Undefined - because we can'T divide by 0.
7. Vertical lines
Do not have slopes!
The sum of digits is divisible by 9.
1/x
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
8. If the two sides of a triangle are unequal then the longer side.................
Lies opposite the greater angle
N! / (k!)(n-k)!
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
F(x-c)
9. Formula for the area of a sector of a circle?
1/x
1
Sector area = (n/360) X (pi)r^2
2.592 kg
10. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
Diameter(Pi)
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
7 / 1000
1
11. Reduce: 4.8 : 0.8 : 1.6
1
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3 - and 44 is a multiple of 4 - so 144 is a multiple of 12.)
The sum of the digits is a multiple of 3 (i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)
6 : 1 : 2
12. When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
4a^2(b)
Two (Ø×2=Ø)
13. Probability of Event all cases
55%
The sum of digits is divisible by 9.
180°
Ø=P(E)=1
14. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
4.25 - 6 - 22
Positive or Negative
2^9 / 2 = 256
F(x-c)
15. What is the sum of the angles of a triangle?
Negative
180 degrees
26
EVEN
16. How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
A= (1/2) b*h
360/n
5
17. 1/6 in percent?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The steeper the slope.
Ab=k (k is a constant)
16.6666%
18. What is an isoceles triangle?
Two equal sides and two equal angles.
3 - 4 - 5
(p + q)/5
(2x7)³
19. How to recognize a # as a multiple of 4
1.0843 X 10^11
The last 2 digits are a multiple of 4. (i.e 144 .... 44 is a multiple of 4 - so 144 must also be a multiple of 4.)
55%
441000 = 1 10 10 10 21 * 21
20. What is the 'Solution' for a system of linear equations?
5 - 12 - 13
The point of intersection of the systems.
X
C=2 x pi x r OR pi x D
21. the slope of a line in y=mx+b
NOT A PRIME
26
M
1:1:sqrt2
22. Evaluate 3& 2/7 / 1/3
9 & 6/7
The triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.
(a + b)^2
3
23. Which is greater? 200x^295 or 10x^294?
3
Relationship cannot be determined (what if x is negative?)
D=rt so r= d/t and t=d/r
70
24. 1 is an
1/2 times 7/3
ODD number
Positive or Negative
1:sqrt3:2
25. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
Straight Angle
The steeper the slope.
1:1:sqrt2
26. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
1
(pi)r²
2^9 / 2 = 256
Negative
27. If an inequality is multiplied or divided by a negative number....
The direction of the inequality is reversed.
An angle which is supplementary to an interior angle.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
x²-y²
28. How do you solve proportions? a/b=c/d
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
(x+y)(x+y)
(length)(width)(height)
29. Acute Angle
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
an angle that is less than 90°
11 - 13 - 17 - 19
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
30. 2 is the only
Even prime number
M
11 - 13 - 17 - 19
The triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.
31. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
A subset.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
48
Lies opposite the greater angle
32. (x-y)(x+y)
Be Zero!
V=side³
x²-y²
0
33. b¹
Ø=P(E)=1
The greatest value minus the smallest.
1
y/x is a constant
34. 25/2³
A chord is a line segment joining two points on a circle.
3 - -3
2²
A grouping of the members within a set based on a shared characteristic.
35. Simplify (a^2 + b)^2 - (a^2 - b)^2
7 / 1000
Add them. i.e. (5^7) * (5^3) = 5^10
(2x7)³
4a^2(b)
36. Circumference of a circle?
V=side³
The set of elements which can be found in either A or B.
9 : 25
Diameter(Pi)
37. X is the opposite of
28
180°
... the square of the ratios of the corresponding sides.
X
38. (x-y)²
Two equal sides and two equal angles.
NOT A PRIME
C = 2(pi)r
x²-2xy+y²
39. Ø is a multiple of
Every number
The direction of the inequality is reversed.
2^9 / 2 = 256
A reflection about the axis.
40. Ø divided by 7
Factors are few - multiples are many.
Ø
13pi / 2
Distance=rate×time or d=rt
41. -3³
The triangle is a right triangle. The hypotenuse is twice the length of the shorter leg. The ratio of the length of the three sides is x:xv3:2x
27
Ø Ø=Ø
5 - 12 - 13
42. What is the 'Range' of a function?
1 & 37/132
A chord is a line segment joining two points on a circle.
(amount of decrease/original price) x 100%
The set of output values for a function.
43. Define a 'Term' -
Diameter(Pi)
6
70
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
44. The reciprocal of any non-zero number is
1/x
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
1.7
Undefined
45. Find distance when given time and rate
M= (Y1-Y2)/(X1-X2)
x²+2xy+y²
D=rt so r= d/t and t=d/r
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3 - and 44 is a multiple of 4 - so 144 is a multiple of 12.)
46. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
1
3 - -3
10! / 3!(10-3)! = 120
12! / 5!7! = 792
47. What is the graph of f(x) shifted upward c units or spaces?
The triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.
The empty set - denoted by a circle with a diagonal through it.
F(x) + c
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)
48. 1/2 divided by 3/7 is the same as
1
Subtract them. i.e (5^7)/(5^3)= 5^4
Every number
1/2 times 7/3
49. Area of a triangle
9 : 25
A= (1/2) b*h
2 & 3/7
(a - b)(a + b)
50. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
y = 2x^2 - 3
A = pi(r^2)
360°