EmSAT Mathematics 5

Question 1

What is the 10th term of the arithmetic sequence 3, 7, 11, 15, …?

Accepted Answer

39

Answer

aₙ = a + (n−1)d = 3 + 9×4 = 3 + 36 = 39.

Question 2

Which expression is the derivative of f(x) = x⁴ − 5x² + 3x?

Accepted Answer

4x³ − 10x + 3

Answer

f'(x) = 4x³ − 10x + 3 by applying the power rule to each term.

Question 3

A bag contains 5 red and 3 blue balls. If two balls are drawn without replacement, what is the probability both are red?

Accepted Answer

5/14

Answer

P = (5/8) × (4/7) = 20/56 = 5/14.

Question 4

Which of the following is the inverse function of f(x) = 2x − 4?

Accepted Answer

f⁻¹(x) = (x+4)/2

Answer

Swap x and y then solve: x = 2y−4 → y = (x+4)/2.

Question 5

Express 0.000045 in standard form (scientific notation).

Accepted Answer

4.5 × 10⁻⁵

Answer

Moving the decimal 5 places right gives 4.5 × 10⁻⁵.

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