Assessment Mathematics A & AS Level

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Jenjang yang dikuasai:
1) (Bisa pilih lebih dari satu)

A) Matematika SD

B) Matematika SMP

C) Matematika SMA

D) Mathematics Primary

E) Mathematics Secondary

F) Mathematics A & AS Level

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2) Name

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3) E-mail

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4) Solve 2 sin² x + cos x - 1 = 0 for 0 ≤ π ≤ 180°.

A) x = {0°, 90°, 120°}

B) x = {90°, 120°}

C) x = {0°, 120°}

D) x = {0°, 90°, 120°, 180°}

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5) Evaluate

A) -44/3

B) -40/3

C) 4/3

D) 8/3

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6) The parametric equations of a curve are x = 2 sin θ, y = 1 - 3 cos 2θ. Find the equation of the tangent to the curve at the point where θ = π/3.

A) 6x + 2y = 5 + 2√3

B) 6x - 2y = 5 + 2√3

C) 2y - 6x = 5 + 2√3

D) 6x + 2y = 5 - 2√3

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Convert y = 2e^{7) 5x} into the form Y = mX + c

A) Y = 10x ln 2e, where Y = ln y

B) Y = 10x + ln 2, where Y = ln y

C) Y = 5x ln 2, where Y = ln y

D) Y = 5x + ln 2, where Y = ln y

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A line passes through the point with position vector 28) i + 3j - 4k and is parallel to the vector i + j - k. Find the parametric equations of the line!

A) x = -2 - t, y = 3 - t, z = -4 - t

B) x = 2 - t, y = 3 - t, z = 4 - t

C) x = 2 + t, y = 3 + t, z = -4 - t

D) x = 2 + t, y = 3 - t, z = -4 - t

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9) Find the exact value of

A) π

B) -π/2

C) π/2

D) 1

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10) A girl is sitting on a sledge. The girl and the sledge have a combined mass of 50 kg. When the girl and the sledge are moving at 2 m/s her sister standing in front of the sledge throws a snowball at the sledge. The snowball has mass 0.2 kg and is travelling at 10.55 m/s when it hits the sledge, head on. The snowball, the girl and the sledge continue together. Assuming that the total momentum is unchanged, find the new speed of the sledge.

A) 1.95 m/s

B) 2.15 m/s

C) 2.56 m/s

D) 3.85 m/s

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11) A woman of mass 50 kg is travelling in a lift of mass 450 kg. The tension in the cable pulling the lift upwards is 5250 N. Calculate the acceleration of the lift.

A) 0.5 m/s²

B) 0.25 m/s²

C) 0.15 m/s²

D) 0.75 m/s²

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12) Given that X ~ B(8, 0.7), find P(X > 5), correct to 3 significant figures.

A) 0.255

B) 0.296

C) 0.434

D) 0.552

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Two children are randomly selected from 9 boys (13) B) and 7 girls (G). What is the probability that the selection consists of two boys?

A) 1/2

B) 4/7

C) 3/10

D) 1/8

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The continuous random variable 14) X has the following probability density function. What is the variance of 14) X?

A) 2.25

B) 1.67

C) 0.88

D) 0.34

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15) The mass of a randomly chosen 11-year-old student at a large school may be modelled by a normal distribution with mean 35 kg and standard deviation 2.4 kg. Five students are chosen from this group. How large does n have to be for there to be at most a 5% chance that the mean mass of the sample differs from the mean mass of the population by more than 1kg?

A) 21

B) 22

C) 23

D) 24

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