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5. A small figure is made by placing half a cylinder on top of a rectangular cuboid as

shown in the diagram below, find the volume of the figure.

A 42.84 cm3

* B 31.57 cm3

C 4.284 cm3

D 3.157 cm3

6. Which of the following gives the asymptote for the function given below.

* A

B C

D 7. Which of the following correctly states the domain and range for the function given

below.

A B C * D

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8. In the figure below, the triangle has one of its sides as the diameter of the circle.

Find the radius of the circle.

A 2.88 cm

B 4.33 cm

* C 5 cm

D 10 cm

9. The value of . Find the value of.* A

B C D

10. State the characteristics of the system of equations below.

A Consistent and independent

B Consistent but dependant

C Inconsistant but solvable

* D Inconsistant

11. Evaluate the determinant of the matrix below.

* A 0

B 35

C 225D -450

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12. Which of the fractions below is equivalent to

A B C

* D

13. The roots of the equation above are

* A Real and unequal

B Real and equal

C Imaginary and unequal

D Imaginary and equal

14. For the quadratic function above, the vertex is

A A maximum at ( 0.17, 1.67 )

B A maximum at ( - 0.17, 3 )

* C A minimum at ( 0.17, 1.67 )

D A minimum at ( - 0.17, 3 )

15. Convert 2.5 rad into degrees.

A 0.043

* B 143.23

C 216.77

D 360

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16. Which of the following shows the formula to calculate the arc length (s) given an

angle in radians?

A B C

* D

17. What are the rectilinear components of a vector given its magnitude is 75 andhave an angle of 50 to the x-axis.

A (57.5, 48.2)* B (48.2 , 57.5)

C (50 , 75)

D (75 , 50)

18. In the triangle below, find the length of side AB

* A 21.16 m

B 24.03 m

C 37.15 m

D 49 m

19. How does the characteristics of the two graphs below compare?

A has a larger amplitude and has a longer period compared to B has a larger amplitude and has a smaller period compared to C has a smaller amplitude and has a longer period compared to

* D has a smaller amplitude and has a smaller period compared to

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20. What is the period of the function * A

B

C D

21. Which of the following is the answer after rationalizing the denominator of the

expression given above

A B

* C D

22. Evaluate the expression below

A B C

* D

23. What is the complex conjugate of

A B C

* D

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24. Multiply the complex numbers and .A B

* C

D

25. Convert the complex number into trigonometric form.A 8.06 (cos (60.25) + i sin (60.25))

* B 8.06 (cos (-60.25) + i sin (-60.25))

C 8.06 (sin (-60.25) + i cos (-60.25))

D 8.06 (sin (60.25) + i cos (60.25))

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Section B: Answer all questions [50 marks]

1. a. Simplify the function f(x) below. [2]

b. Complete the square for f(x). [3]

c. Sketch the function f(x) showing all intercepts and vertex. [4]

d. Hence or otherwise, find the roots of the equation [1]

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2. a. Solve using the algebraic method (not using cramers rule), the following set of

equations. [4]

b. Use cramers rule to solve the set of equations above again. [3]

c. Factorize and simplify

[3]

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3. a. Find the area of the shaded figure. [3]

b. In the figure below,

i. Use the cosine rule to calculate angle . [2]ii. Hence or otherwise, calculate the angle [2]

c. A plane approaching Changi Airport from a height of 10km sees the control

tower at an angle of depression of 10 as shown in the diagram below. Find the

distance PC from the plane to the airport. [3]

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4. a. The figure shows a hemispherical sphere attached to a cone. The volume of the

cone is 125 cm3. The length of the cone is 3 times the radius of the cone.

Calculate the volume of the hemisphere correct to 3 significant figures. [5]

b. In the graph below, two vectors are shown, and .

i. What is the vector s magnitude and direction? [2]ii. Find the resultant vector + . Sketch the resultant vector

and express it in rectangular form. [3]

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5. For the complex number and a. Express in rectangular form. [2]b. Verify your answer to (i) using an Argand Diagram to evaluate . [3]c. Express in exponential form. [3]d. Evaluate

given [2]

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