EmSAT Mathematics 3

Question 1

If f(x) = 3x² − 2x + 1, what is f(−2)?

Accepted Answer

17

Answer

f(−2) = 3(4) − 2(−2) + 1 = 12 + 4 + 1 = 17.

Question 2

The equation of a circle with centre (3, −1) and radius 5 is:

Accepted Answer

(x−3)² + (y+1)² = 25

Answer

Standard form is (x−h)² + (y−k)² = r², giving (x−3)² + (y+1)² = 25.

Question 3

What is the sum of the infinite geometric series 8 + 4 + 2 + 1 + …?

Accepted Answer

16

Answer

S = a/(1−r) = 8/(1−0.5) = 8/0.5 = 16.

Question 4

If log₂(x) = 5, what is x?

Accepted Answer

32

Answer

log₂(x) = 5 means x = 2⁵ = 32.

Question 5

A triangle has vertices A(0,0), B(6,0), and C(3,4). What is its area?

Accepted Answer

12

Answer

Area = ½ × base × height = ½ × 6 × 4 = 12 square units.

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