NBT Mathematics Proficiency 3

Question 1

Solve the simultaneous equations: x + y = 7 and 2x - y = 5

Accepted Answer

x = 4, y = 3

Answer

Add the equations: 3x = 12, so x = 4. Substitute: 4 + y = 7, so y = 3.

Question 2

What is the sum of the first 10 terms of an arithmetic sequence with first term 3 and common difference 4?

Accepted Answer

210

Answer

Sₙ = n/2 × [2a + (n-1)d] = 10/2 × [2(3) + 9(4)] = 5 × [6 + 36] = 5 × 42 = 210.

Question 3

Solve for x: log₂(x) = 5

Accepted Answer

x = 32

Answer

log₂(x) = 5 means 2⁵ = x. 2⁵ = 32.

Question 4

Find the derivative of f(x) = 3x² - 4x + 1

Accepted Answer

f'(x) = 6x - 4

Answer

Using the power rule: d/dx(3x²) = 6x, d/dx(-4x) = -4, d/dx(1) = 0. f'(x) = 6x - 4.

Question 5

In a geometric sequence, the first term is 2 and the common ratio is 3. What is the 5th term?

Accepted Answer

162

Answer

Tₙ = a × rⁿ⁻¹. T₅ = 2 × 3⁴ = 2 × 81 = 162.

(NBT) National Benchmark Test Practice Test