EJU EJU Mathematics Course 1 Practice 2

Question 1

Solve the inequality x² - 3x - 10 < 0. Which interval represents all solutions?

Accepted Answer

-2 < x < 5

Answer

Factor: (x - 5)(x + 2) < 0. The parabola opens upward, so the expression is negative between the roots: -2 < x < 5.

Question 2

If sin θ = 3/5 and 0 < θ < π/2, what is tan θ?

Accepted Answer

3/4

Answer

In a right triangle, if sin θ = 3/5, then the opposite side is 3 and hypotenuse is 5. By the Pythagorean theorem, adjacent = 4. So tan θ = opposite/adjacent = 3/4.

Question 3

A geometric sequence has first term a = 2 and common ratio r = 3. What is the sum of the first 4 terms?

Accepted Answer

80

Answer

S₄ = a(r⁴ - 1)/(r - 1) = 2(81 - 1)/(3 - 1) = 2(80)/2 = 80.

Question 4

A data set has values: 2, 4, 4, 4, 6, 8, 8, 8, 10. What is the standard deviation?

Accepted Answer

√(64/9)

Answer

Mean = (2+4+4+4+6+8+8+8+10)/9 = 54/9 = 6. Variance = [(16+4+4+4+0+4+4+4+16)/9] = 56/9. Wait — let me recalculate: deviations: -4,-2,-2,-2,0,2,2,2,4; squares: 16,4,4,4,0,4,4,4,16; sum=56; variance=56/9. SD = √(56/9) = 2√(14/9). Closest: the answer is √(56/9).

Question 5

Two vectors are given: a⃗ = (3, 4) and b⃗ = (1, -2). What is the dot product a⃗ · b⃗?

Accepted Answer

-5

Answer

a⃗ · b⃗ = (3)(1) + (4)(-2) = 3 - 8 = -5.

EJU - Examination for Japanese University Practice Test

EJU - Examination for Japanese University Practice Test

EJU EJU Mathematics Course 1 Practice 2