(a)(i) Write down the expansion of \((1 + x)^{7}\) in ascending powers of x.

(ii) If the coefficients of the fifth, sixth and seventh terms in the expansion in (a)(i) above form a linear sequence(A.P), find the common difference of the A.P.

(b) Using the trapezium rule with ordinates at 1, 2, 3, 4 and 5, calculate, correct to two decimal places,

\(\int_{1}^{5} \sqrt{(2x + 8x^{2})} \mathrm {d} x\).

Vaccination results in

• A. aiding red blood cells to carry more oxygen
• B. production of antibodies which destroy toxins of germs
• C. arresting excessive bleeding
• D. production of white blood cells which engulf and digest bacteria.

From the words or group of words lettered A to D below each of the following sentences, choose the one that is nearest in meaning to the underlined word or group of words as it is used in the sentence.

The decision I have taken is irrevocable

• A. inapplicable
• B. unacceptable
• C. irreversible
• D. irregular

In the adult frog gaseous exchange takes the

• A. buccal cavity, skin and lungs
• B. buccal cavity, skin and spiracles
• C. gills, skin and buccal cavity
• D. tympanic membrane, lungs and gills

The fundamental assumption on which the idea of the rule of law is based is

• A. supremacy of the constitution
• B. rationality of human beings
• C. equality of human beings
• D. love for social justice

Choose the optionnearest in meaning to the underlined world(s).

Adamu woke up with a start a took to his heels, claiming that something wason his trail?

• A. in his food
• B. giving him the chase
• C. hiding near the bed
• D. staring at him

Kreb’s cycle occurs in the

• A. mitochondria
• B. cytoplasm
• C. nucleus
• D. ribosomes

A vote taken by the citizenry on an important political issue is a

• A. recall
• B. general election
• C. bye-election
• D. referendum

Alloys are best prepared by

• A) Electroplating
• B) Arc-welding
• C) Reducing and mixture of their metallic oxide
• D) Cooling a molten mixture of the metals

Resolve \(\frac{3}{x^2 + x - 2}\) into partial fractions

• A. \(\frac{1}{x - 1} - \frac{1}{x + 2}\)
• B. \(\frac{1}{x + 1} + \frac{1}{x - 2}\)
• C. \(\frac{1}{x + 1} - \frac{1}{x - 2}\)
• D. \(\frac{1}{x - 2} + \frac{1}{x + 2}\)