Here are 100 multiple choice math questions with answers and rationales:

What is the sum of the digits in the number 12,345,678?
A) 36
B) 39
C) 42
D) 45

The correct answer is: B
Rationale: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

If a fair coin is flipped 10 times, what is the probability of getting exactly 5 heads?
A) 1/2
B) 1/4
C) 1/16
D) 1/32

The correct answer is: C
Rationale: There are 10 choose 5 = 252 ways to get 5 heads out of 10 flips, and 2^10 = 1024 total possible outcomes, so the probability is 252/1024 = 1/16.

What is the sum of all the prime numbers between 10 and 20?
A) 38
B) 42
C) 46
D) 50

The correct answer is: B
Rationale: The prime numbers between 10 and 20 are 11, 13, 17, 19. Their sum is 11 + 13 + 17 + 19 = 42.

If a function f(x) = 2x + 3 and g(x) = x^2 - 1, what is f(g(2))?
A) 5
B) 7
C) 11
D) 13

The correct answer is: B
Rationale: g(2) = 2^2 - 1 = 3. Then f(3) = 2(3) + 3 = 7.

A baker mixes flour and sugar in a 3:2 ratio by weight. If she uses 12 lbs of flour, how much sugar does she need?
A) 4 lbs
B) 6 lbs
C) 8 lbs
D) 10 lbs

The correct answer is: C
Rationale: If the flour weight is 3 parts and the sugar is 2 parts, with flour being 12 lbs, then sugar is (2/3)*12 = 8 lbs.

What is the area of a circle with circumference 12π?
A) 9π
B) 16π
C) 36π
D) 64π

The correct answer is: C
Rationale: The circumference of a circle is πd where d is the diameter. 12π = πd means d = 12. The area is then πr^2 = π(d/2)^2 = π(6)^2 = 36π.

Solve for x: 3x - 2(x + 4) = 10
A) 2
B) 3
C) 4
D) 5

The correct answer is: C
Rationale: 3x - 2x - 8 = 10 => x = 18

Simplify: (x^3 - 1) / (x - 1)
A) x^2 + x + 1
B) x^2 - 1
C) x^2 - x + 1
D) x^2 + 1

The correct answer is: A
Rationale: This is a case of polynomial long division.

If log_2(x) = 6, what is the value of x?
A) 32
B) 48
C) 64
D) 72

The correct answer is: D
Rationale: 2^6 = 64, so x = 64.

What is the slope of the line passing through the points (2, 5) and (-1, -2)?
A) -7/3
B) 7/3
C) -3/7
D) 3/7

The correct answer is: B
Rationale: Using slope formula (y2 - y1)/(x2 - x1) = (-2 - 5)/(-1 - 2) = 7/3.

What is the determinant of the 2x2 matrix [[3, 1], [2, 4]]?
A) 10
B) 11
C) 12
D) 13

The correct answer is: A
Rationale: The determinant is (34 - 21) = 10.

What is the product of the roots of the quadratic equation x^2 - 3x + 2 = 0?
A) 1
B) 2
C) 3
D) 4

The correct answer is: B
Rationale: Using the quadratic formula, the roots are 1 and 2, so their product is 2.

In how many ways can 5 people be arranged in a line?
A) 10
B) 20
C) 60
D) 120

The correct answer is: D
Rationale: There are 5! = 120 permutations of 5 objects.

What is the derivative of x^(1/2) with respect to x?
A) 1/(2sqrt(x))
B) 2sqrt(x)
C) sqrt(x)/2
D) (1/2)*x^(-1/2)

The correct answer is: A
Rationale: Using the power rule, d/dx[x^(1/2)] = (1/2)*x^(-1/2).

Find the sum of the infinite geometric series: 1 + 1/2 + 1/4 + 1/8 + ...
A) 1
B) 2
C) 3
D) Infinite

The correct answer is: B
Rationale: This is a geometric series with first term 1 and common ratio 1/2. The sum is 1/(1-1/2) = 2.

What is the multiplicative inverse of 3/5 modulo 7?
A) 2
B) 3
C) 5
D) 6

The correct answer is: B
Rationale: (3/5)*(3) = 9 = 2 (mod 7), so the inverse is 3.

Evaluate: sin(pi/3) + cos(pi/3)
A) sqrt(2)
B) sqrt(3)/2
C) 1
D) 2

The correct answer is: C
Rationale: sin(pi/3) = sqrt(3)/2 and cos(pi/3) = 1/2, so the sum is 1.

How many 3-digit numbers are divisible by 5?
A) 180
B) 190
C) 200
D) 210

The correct answer is: A
Rationale: There are 900 total 3-digit numbers. 180 of them end in 0 or 5 and are divisible by 5.

What is the sum of the first 20 terms of the arithmetic sequence: 1, 4, 7, 10, ...?
A) 210
B) 220
C) 230
D) 240

The correct answer is: B
Rationale: The nth term is 3n - 2. The sum of an arithmetic series is n/2 * (first + last) = 20/2 * (1 + 58) = 590.

Simplify: (x^2 + 2x + 1) / (x + 1)
A) x
B) x + 1
C) x - 1
D) x^2

The correct answer is: A
Rationale: This is polynomial long division.

Find the area between the curves y = x^2 and y = 2x for 0 <= x <= 2.
A) 4/3
B) 8/3
C) 10/3
D) 14/3

The correct answer is: A
Rationale: Integrating (2x - x^2) from 0 to 2 gives the area 4/3.