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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. Simplify (a^2 + b)^2 - (a^2 - b)^2
A= (1/2) b*h
The empty set - denoted by a circle with a diagonal through it.
4a^2(b)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
2. A number is divisible by 9 if...
1:sqrt3:2
.0004809 X 10^11
The sum of digits is divisible by 9.
Ø
3. The percent decrease of a quantity
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
90pi
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)
= (actual decrease/Original amount) x 100%
4. What are 'Supplementary angles?'
Two angles whose sum is 180.
Sum of digits is a multiple of 3 and the last digit is even.
67 - 71 - 73
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
5. (6sqrt3) x (2sqrt5) =
3 - 4 - 5
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
2 & 3/7
6. What are complementary angles?
Two angles whose sum is 90.
Two angles whose sum is 180.
360°
Every number
7. Legs 6 - 8. Hypotenuse?
130pi
10
The set of output values for a function.
V=side³
8. a^2 + 2ab + b^2
441000 = 1 10 10 10 21 * 21
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
23 - 29
(a + b)^2
9. Consecutive integers
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
x - x+1 - x+2
NOT A PRIME
1:sqrt3:2
10. The sum of all angles around a point
The interesection of A and B.
Even prime number
360°
C = (pi)d
11. If E is certain
P(E) = 1/1 = 1
P(E) = ø
75:11
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
12. Perimeter of a rectangle
P= 2L + 2w
2 & 3/7
Two (Ø×2=Ø)
F(x-c)
13. First 10 prime #s
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 sum of the digits is a multiple of 9.
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
90°
14. If a is negative and n is even then an is (positive or negative?)
90°
Ø=P(E)=1
Distance=rate×time or d=rt
An is positive
15. The product of any number x and its reciprocal
Null
(rate)(time) d=rt
1
(a - b)(a + b)
16. A quadrilateral where two diagonals bisect each other
Parallelogram
31 - 37
4096
Negative
17. 1 is an
53 - 59
C=2 x pi x r OR pi x D
No - only like radicals can be added.
ODD number
18. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
Null
441000 = 1 10 10 10 21 * 21
2(pi)r
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
19. What is a percent?
A percent is a fraction whose denominator is 100.
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
3/2 - 5/3
Yes - like radicals can be added/subtracted.
20. Obtuse Angle
All numbers multiples of 1.
Relationship cannot be determined (what if x is negative?)
A-b is positive
angle that is greater than 90° but less than 180°
21. Number of degrees in a triangle
1/2 times 7/3
180
(a + b)^2
1:sqrt3:2
22. The Perimeter of a rectangle
M
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The sum of digits is divisible by 9.
P=2(l+w)
23. Slope
Reciprocal
y2-y1/x2-x1
90
180 degrees
24. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
1/2 times 7/3
90
6
A = pi(r^2)
25. 1/6 in percent?
16.6666%
X
The direction of the inequality is reversed.
48
26. Circumference of a Circle
C=2 x pi x r OR pi x D
12sqrt2
zero
1
27. factored binomial product of (x+y)²
2
Can be negative - zero - or positive
x²-y²
x²+2xy+y²
28. Solve the quadratic equation ax^2 + bx + c= 0
90°
y = (x + 5)/2
Lies opposite the greater angle
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
29. formula for area of a triangle
A=½bh
$3 -500 in the 9% and $2 -500 in the 7%.
1 & 37/132
an angle that is less than 90°
30. Important properties of a 30-60-90 triangle?
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
A=(base)(height)
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Undefined
31. What is the ratio of the sides of a 30-60-90 triangle?
Even prime number
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
A=(base)(height)
1:sqrt3:2
32. 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?
y = 2x^2 - 3
27^(-4)
The set of input values for a function.
F(x-c)
33. Evaluate 3& 2/7 / 1/3
9 & 6/7
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
75:11
1:1:sqrt2
34. What are the irrational numbers?
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35. For any number x
An is positive
Add them. i.e. (5^7) * (5^3) = 5^10
A=pi*(r^2)
Can be negative - zero - or positive
36. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
1/2 times 7/3
1:1:sqrt2
0
The sum of digits is divisible by 9.
37. What is the surface area of a cylinder with radius 5 and height 8?
Smallest positive integer
M= (Y1-Y2)/(X1-X2)
130pi
Positive
38. Area of a circle
(pi)r²
Sector area = (n/360) X (pi)r^2
1:1:sqrt2
90pi
39. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
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)
26
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.)
500
40. Is 0 even or odd?
Two angles whose sum is 180.
Even
The interesection of A and B.
90°
41. If a pair of parallel lines is cut by a transversal that'S not perpendicular - the sum of any acute angle and any obtuse angle is
180
A=½bh
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.
x²+2xy+y²
42. What is a minor arc?
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43. Pythagorean theorem
Infinite.
A²+b²=c²
1 & 37/132
The greatest value minus the smallest.
44. What is a major arc?
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45. binomial product of (x-y)²
0
20.5
13pi / 2
(x+y)(x-y)
46. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
A reflection about the axis.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
27^(-4)
9 : 25
47. Formula for the area of a circle?
A = pi(r^2)
V=l×w×h
180
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
48. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
4:5
The set of elements which can be found in either A or B.
70
10! / (10-3)! = 720
49. 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?
(a - b)(a + b)
M
75:11
90°
50. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
1/x
Smallest positive integer
2.592 kg