2. Math Questions
1. What is the area of a circle with
radius √3?
A. π√3
B. 3π
C. 2π√3
D. 2π²
E. 3π²
The answer is B. The formula for area of
a circle is
A = πr²
A = π(√3)²
A = 3π
3. Math Questions
2. What is the area of this triangle?
A. 13
B. 21
C. 26
D. 39
E. 42
The answer is B. Formula for area of a
triangle is
A = (½)bh
A = (½)(7)(6)
A = 21
Don’t be fooled by the trick answer 42,
which you might pick if you forget to
divide by 2.
4. Math Questions
3. What is the area of the shaded
region?
A. 4π
B. 25π
C. 100 - 25π
D. 100π
E. 100 + 25π
The answer is C. You must first find the
area of the larger shape (the square)
then subtract from that the area of the
smaller shape (the circle). Area of a
square is
A = s2
= 102
= 100.
Radius of the circle is 5, so area is 25π.
SQUARE - CIRCLE = 100 - 25π
5. Math Questions
4. What is the distance between points
(2,3) and (-2,1)?
A. √5
B. √13
C. 4
D. 2√5
E. 8
The answer is D. Apply distance formula
to get √20.
d2
= (-2-2)2
+ (1-3)2
d2
= -42
+ -22
d2
= 16 + 4
d2
= 20
d = √20
The radical can be simplified to 2√5.
6. Math Questions
5. In the equation x⁄5 + 3 = ⅔ , the
value of x is equal to:
A. -35/3
B. -3
C. 2/3
D. 5
E. 15
The answer is A. Isolate x by subtracting
3 from both sides, simplify by creating a
common denominator, then multiplying
both sides by 5.
x/5 + 3 = ⅔
x/5 = ⅔ - 3
x/5 = ⅔ - 9/3
x/5 = -7/3
x = -35/3
7. Math Questions
6. The product of two positive,
consecutive numbers is 30. What is
the value of the smaller number?
A. 3
B. 4
C. 5
D. 6
E. 7
The answer is C. Two consecutive
numbers (number next to each other)
that multiply to 30: 5, 6.
To solve algebraically:
x(x + 1) = 30
x2
+ x = 30
x2
+ x - 30 = 0
(x + 6)(x - 5) = 0
x = -6, 5
The problem asks for a positive integer,
therefore, 5.
8. Math Questions
7. What is the sum of all the prime
factors of 20?
A. 2
B. 5
C. 9
D. 15
E. 20
The answer is C. The prime factors of 20
are 2, 2, and 5 (remembering that 1 is
not prime).
20 → 4 * 5
20 → 2 * 2 * 5
5 + 2 + 2 = 9
9. Math Questions
8. Which of the following numbers is a
multiple of 15?
A. 3
B. 14
C. 25
D. 30
E. 51
The answer is D. A multiple is a number
which results from multiplying the
original number by another integer.
15*2 = 30
10. 9. What is the greatest common factor
of x²yz and xy⁴z²?
A. xyz
B. x⁴y²
C. z
D. xy
E. x²yz
Math Questions
The answer is A. xyz is the largest factor
that both terms have in common,
meaning the greatest value that can fit
inside both terms.
The two terms share only one x, one y,
and one z.
11. Math Questions
10. The expression 4 + 8x² = ?
16x
A. 12x
B. 2 + 4x
C. 1 + 2x²
4x
D. x
4
E. 1 + 2x
4
The answer is C. Simplify the expression
by cancelling out a factor of 4 in both the
numerator and denominator. An x cannot
be cancelled out because it is not a
factor of the numerator.
12. Math Questions
11. If 5x = 11(x + 3) + 7, then x = ?
A. -8
B. -11/2
C. -20/3
D. -5
E. 5/3
The answer is C, -20/3. Solve for x. First
distribute the 11, then move all the x
terms to one side.
5x = 11(x + 3) + 7
5x = 11x + 33 + 7
5x = 11x + 40
-6x = 40
x = -(40/6)
x = -20/3
13. Math Questions
12. If 3y - 3x = 21, then what is the
value of x - y?
A. -21
B. -7
C. 7
D. 21
E. Cannot be determined from
the information given
The answer is B, -7. While this more
seem like a solving problem at first, you
actually want to manipulate the equation
to be in the form of x - y = ?
To do so, multiply both sides by -1 to get
the y term to be subtracted from the x
term, then factor out and divide by 3 to
find this form.
3y - 3x = 21
3x - 3y = -21
3(x - y) = -21
x - y = -7
14. Math Questions
13. What is the perimeter, in feet, of a
rectangle with length 21 ft and
width 16 ft?
A. 5
B. 37
C. 42
D. 74
E. 336
The answer is D, 74. Perimeter of a
rectangle is
2l + 2w = 2(21) + 2(16) = 74.
15. Math Questions
14. What is the least common multiple
of 10, 12, and 18?
A. 24
B. 40
C. 180
D. 216
E. 324
The answer is C, 180. To find LCM,
complete prime factorization, and then
take the most groupings of each factor.
10 = 2, 5
12 = 2, 2, 3
18 = 2, 3, 3
So we need two 2’s, two 3’s, and a 5 in
order for all three numbers to “fit” inside
the LCM.
2 * 2 * 3 * 3 * 5 = 180.
16. Math Questions
15. What is the area, in square feet, of
the right figure below?
A. 60
B. 108
C. 138
D. 180
E. 324
The answer is C, 138. In a right polygon,
angles are 90*, meaning opposite sides
are parallel and equal. Draw two
rectangles, determining side lengths by
the side lengths of opposite sides. Find
the area of each rectangle.
Rectangle 1: 10 x (6 + 3) = 10 x 9 = 90
Rectangle 2: 6 x (18 - 10) = 6 x 8 = 48
Add the two areas to find area of total
shape:
90 + 48 = 138
17. Math Questions
16. The right circular cylinder shown
below has a height of 7 meters and
a radius of 3 meters. What is the
volume, in cubic meters, of the
cylinder?
A. 21π
B. 49
C. 49π
D. 63
E. 63π
The answer is E, 63 . The formula for
volume of a right circular is
V = r²h
Pugging in the given values:
V = (3)²(7)
V = (9)(7)
V = 63
18. Math Questions
17. The midpoint of line segment AB in
the standard (x,y) coordinate plane is
(-5,9). If point A is (-8,12), where is point
B?
A. (-2,18)
B. (-2,6)
C. (-2,2)
D. (2,6)
E. (2,10)
The answer is B, (-2,6). The formula for
midpoint is:
(x,y) = ( (x1 + x2)/2, (y1 + y2)/2).
Since we were given the midpoint and
one of the endpoints, we can substitute
known values into our formula and solve
to find the other endpoint:
-5 = (-8 + x)/2
-10 = -8 + x
-2 = x value of midpoint
9 = (12 + y)/2
18 = 12 + y
6 = y value of midpoint
19. Math Questions
18. The area of a circle is 4x2
π. What is
the diameter of the circle?
A. 2x
B. πx
C. 4x
D. 4x2
E. 16
The answer is C. We are given the area of
the circle, so we can find the radius:
A = πr2
= 4x2
π
r2
= 4x2
r = 2x
Reading the question again, we see that
it is asking for diameter, not radius, so
we have to double the radius:
d = 2 * (2x) = 4x
20. Math Questions
19. What is three less than the product
of eleven and four?
A. 11
B. 21
C. 41
D. 44
E. 47
The answer is C. If we were to translate
this sentence into a mathematical
expression, we would get:
(11 * 4) – 3
44 -3
41
21. Math Questions
20. A negative number is decreased by 3
and then squared, resulting in 25.
What is the number?
A. -8
B. -5
C. -3
D. -2
E. -1
The answer is D. Translating this
statement results in the following
equation:
(x – 3)2
= 25
When we take the square root, we must
remember to consider both the negative
and the positive component:
(x-3) = 5 OR (x-3) = -5
x = 8 OR x = -2
22. Math Questions
21. The midpoint of points P and Q is
(0,1). Point P is located at (5, 4).
Where is point Q located?
A. (-5, -2)
B. (-2, 5)
C. (1, 0)
D. (4, 5)
E. (5, 2)
The answer is A. The formula for
midpoint is:
Plugging in the values we are given in the
question, we can create two questions,
one for the x value and one for the y
Using point P as x2
and y2
:
5 + x = (0)(2) and 4 + y = (1)(2)
x = - 5 and y = 2 - 4 = -2
Q is located at (-5, -2)
