Mental Math
What is seventeen squared minus thirteen squared?
120
Explanation: a2 - b2 = (a - b)(a + b)
Evaluate: -1 - (-1 - 1)-1(-1)
A) -3/2
B) -1
C) 0
D) 1
E) Answer not given
A
Simplify and write as a reduced fraction. (23)(6-3)
1/27
How many ways are there to rearrange the letters in "RAINIER" if all the vowels must come before any of the consonants?
Answer: 36
Explanation: There are 4 vowels (A-I-I-E) with 4!/2! = 12 permutations, and 3 consonants (R-N-R) with 3!/2! = 3 permutations. In total, there are 12×3 = 36 permutations.
Go to Slide 1 of the Google Slides for the question
2
What is the value of x if, the square root of 36 plus the square root of 9 equals the square root of x?
x = 81
Frank flipped a coin 6 times and got 3 heads and 3 tails. The 3 heads occurred consecutively. In how many ways can this happen?
A) 2
B) 4
C) 6
D) 20
E) Answer is not given
B
Solve for x:3(2x - 1) + 3 = 5(4x - 2) + 5
5/14
Evaluate 3456 + 4567 + 5678 represented as a base 10 number.
74910
Five different numbers are chosen from the set {1,2,3,4,…,20} and added together. How many distinct values for this sum are possible?
Answer: 76
Explanation: The smallest the sum can be is 1+2+3+4+5=15 and the largest is 16+17+18+19+20=90. Any number in between is possible as well for a total of 90-15+1=76.
What is the probability of getting exactly two heads with three flips of a fair coin?
3/8
Explanation: There are 8 permutations (HHH, HHT, …, TTT) and 3 of them (3C2) that have two heads.
What is the equation of the axis of symmetry of the parabola with equation y = 3x2 + 24x - 18?
A) y = 4
B) x = 4
C) x = 8
D) x = -8
E) Answer is not given
E
Explanation:
x = -b/2a = -24/6 = -4
The average of the four numbers: 20, 17, 26 and x is 25. What is the value of x?
37
What is the measure, in degrees, of an interior angle is a decagon?
144 degrees
Go to Slide 3 of the Google Slides for the question
15
What is the log of eighty-one divided by the log of three?
4
Explanation: Change of Base Logarithm Formula (look it up for example)
Two circles have radii of 8 and 12 cm and have centers 40 cm apart. What is the length, in centimeters, of one of their common internal tangents?
A) 20root3
B) 40root2
C) 40root3
D) 80
E) Answer is not given
A
Explanation: Start with a drawing of the two circles and the interior tangent. The radii drawn from the center to the tangent points are perpendicular. Extend the radii in the smaller circle by 12 and connect to the other center. A right triangle is made with a hypotenuse of 40 (distance between centers) a leg of 20 (8+12) other leg congruent to the internal tangent. Using the Pythagorean Theorem, you can find the hypotenuse which will equal 20root3.
Two circles with radii 26 inches and 14 inches have centers that are 37 inches apart. What is the length, in inches, of their common external tangent?
35 inches
What is the area of a circle that circumscribes a regular hexagon of side length 2. Express your answer as a multiple of pi.
Answer: 4pi
Explanation: As the hexagon can be divided into equilateral triangles of side length 2, the radius of the circle is also 2. The area of the circle is then: pi(2)2 = 4pi
Go to Slide 5 of the Google Slides for the question
{9, 1/9}
What number between 90 and 120 has exactly nine positive factors?
100
Explanation: Has to be a perfect square to have an odd number of factors
Express the base-two number 1011110012 as a base-four number.
A) 133014
B) 113214
C) 113314
D) 123214
E) Answer is not given
Answer: B
Explanation: First, convert from base-two to base-ten. Then use divide the resulting number by four using long division. Record your remainder, and then divide the quotient by 4. Repeat this process until you have a remainder of 0. Write down the remainders you found in the reverse order in which you found them. The resulting number will give you the base-four conversion. Note that for this problem, you would only need to find the first three remainders to know which one of the given choices is correct.
A sweater costs $32. The store subsequently raises the cost by 25% and then reduces it by 25% and finally raises it again by 10%. What is the final cost?
What is the coefficient of x2y3 in the expansion of (2x - 3y)5?
Answer: -1080
Explanation: Look up Pascal's Triangle
What is the 10s digit of 612?
Answer: 3
Explanation: Go to Slide 7