Explanation

\(a \Delta b = a^{3} - b^{3}\)

\((\sqrt{3} + \sqrt{2}) \Delta (\sqrt{3} - \sqrt{2}) = (\sqrt{3} + \sqrt{2})^{3} - (\sqrt{3} - \sqrt{2})^{3}\)

\((\sqrt{3} + \sqrt{2})^{3} = (\sqrt{3})^{3} + 3(\sqrt{3})^{2}(\sqrt{2}) + 3(\sqrt{3})(\sqrt{2})^{2} + (\sqrt{2})^{3}\)

= \(3\sqrt{3} + 9\sqrt{2} + 6\sqrt{3} + 2\sqrt{2}\)

= \(9\sqrt{3} + 11\sqrt{2}\)

\((\sqrt{3} - \sqrt{2})^{3} = (\sqrt{3})^{3} + 3(\sqrt{3})^{2}(-\sqrt{2}) + 3(\sqrt{3})(-\sqrt{2})^{2} + (-\sqrt{2})^{3}\)

= \(3\sqrt{3} - 9\sqrt{2} + 6\sqrt{3} - 2\sqrt{2}\)

= \(9\sqrt{3} - 11\sqrt{2}\)

\((\sqrt{3} + \sqrt{2}) \Delta (\sqrt{3} - \sqrt{2}) = 9\sqrt{3} + 11\sqrt{2} - 9\sqrt{3} + 11\sqrt{3}\)

= \(22\sqrt{2}\)

Correct Answer: B. Presidential

Explanation

A presidential system is a democratic and republican government in which a head of government leads an executive branch that is separate from the legislative branch. This head of government is in most cases also the head of state, which is called president.

Correct Answer: B. prevent algae from growing in the solution

Correct Answer: C. 4

Explanation

A. (i) THE ACTIVITIES OF THE TWO ROBBERS (MATT. 27: 38 & 44, LUKE. 23:39-43)

i. Two robbers were crucified with Jesus, one on the right and the other on the left.

ii. Matthew records that they joined the Chief Priests and those who passed by to revile/mock Jesus.

iii. In Mark's account, one of the robbers mocked Jesus, asking, "Are you not the Christ? save yourself and save us".

iv. The other robber rebuked him pointing out that Jesus was innocent yet was being crucified.

v. And unlike Jesus, they deserved the punishment they were receiving.

vi. He pleaded with Jesus to remember him in His kingdom/paradise.

vii. Jesus assured him a place in paradise.

A. (ii) THE ACTIVITIES OF JOSEPH OF ARIMATHEA (MATT. 27:57-66, MARK 15:42- 47, LUKE 23:50-56)

i. Joseph of Arimathea was a rich and respected member of the Council/Sanhedrin.

ii. A good and righteous man/secret disciple of Christ who was after the Kingdom of God.

iii. He was aware that it was against Jewish custom to have a dead body on the cross over night.

iv. He approached Pilate and requested for the body of Christ for burial.

v. Pilate, been assured of Jesus' death, released the body.

vi. He wanted to bury Jesus because the next day was Sabbath.

vii. Joseph took the body of Christ and wrapped it in a clean linen shroud/cloth.

viii. Afterwards, he laid the body of Christ in his own new tomb, where nobody had ever been laid.

ix. He closed the entrance of the tomb with a great rock, and departed.

B. WAYS THE BEHAVIOR OF THE ROBBERS ARE SIGNIFICANT TO CHRISTIANS

i. It shows that been punished for a crime one had committed is different from persecution.

ii. Irrespective of our sins, Jesus Christ is ready to forgive us if we sincerely repent/There is need for humility.

iii. We should not judge others because we ourselves are sinners before God.

iv. We should always stand up for the truth irrespective of the challenges we face.

v. We should not mock the weaknesses of others/ Christians should avoid blasphemy.

vi. It shows that grace and salvation are needed before one can enter paradise/Need to trust and have faith in Christ who is merciful.

vii. One should learn to serve one's punishment without feeling castigated.

viii. We should learn to take responsibility for our actions without shifting blame to others.

ix. Salvation is available even at the last hour

x. Dependence on God in times of troubles and challenges.

Correct Answer: A. sets out the rights and obligations of member states

Correct Answer: C. undertaking the registration of campaigns on drug trafficking

Correct Answer: A. hyperbole

Correct Answer: C. 0< x< 1/2

Correct Answer: B. raising of the son of the widow of Nain