EmSAT Mathematics 2 — Questions and Answers
Question 1: What is the probability of drawing a red card from a standard deck of 52 playing cards?
- 1/4
- 1/2 (Correct answer)
- 1/13
- 3/4
Correct answer: 1/2
A standard deck has 26 red cards (13 hearts + 13 diamonds) out of 52 total cards. Probability = 26/52 = 1/2.
Question 2: What is the value of log₁₀(1000)?
- 2
- 3 (Correct answer)
- 4
- 10
Correct answer: 3
log₁₀(1000) = 3 because 10³ = 1000.
Question 3: If the mean of five numbers is 12, what is their sum?
- 12
- 24
- 48
- 60 (Correct answer)
Correct answer: 60
Mean = Sum / Count, so Sum = Mean × Count = 12 × 5 = 60.
Question 4: What is the length of the hypotenuse of a right triangle with legs of 5 cm and 12 cm?
- 13 cm (Correct answer)
- 17 cm
- 10 cm
- 15 cm
Correct answer: 13 cm
Using the Pythagorean theorem: c² = a² + b² = 25 + 144 = 169, so c = √169 = 13 cm.
Question 5: What is the equation of a circle with center (3, -2) and radius 5?
- (x - 3)² + (y + 2)² = 25 (Correct answer)
- (x + 3)² + (y - 2)² = 25
- (x - 3)² + (y - 2)² = 5
- (x + 3)² + (y + 2)² = 5
Correct answer: (x - 3)² + (y + 2)² = 25
The standard form of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center and r is the radius: (x - 3)² + (y - (-2))² = 5² = (x - 3)² + (y + 2)² = 25.
Question 6: What is the domain of the function f(x) = √(x - 4)?
- x ≥ 0
- x ≥ 4 (Correct answer)
- x > 4
- All real numbers
Correct answer: x ≥ 4
The expression under the square root must be non-negative: x - 4 ≥ 0, so x ≥ 4.
EmSAT Mathematics 2
What is the probability of drawing a red card from a standard deck of 52 playing cards?