Saint Maur International School

Final Examination – 9A1 Mathematics

4th June 2015 (A.M.)

Time Allowed: 120 minutes

Total Marks - / 120

Instructions: This paper is divided into 2 sections: Section A & Section B.

Answer all questions.

If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.

For π, use your calculator value.

Needed Materials: Pencil, Pen, Eraser, Straightedge, Compass, Protractor and Calculator

Section A: Q1-20 Marks - / 70

All working must be shown below the question.

Section B: Q21-24 Marks - / 50

Write your solution and all working on the sheets of loose leaf paper.

The loose leaf sheets of paper will be provided to you.

NAME

Section A

1.

2. Show all of your steps.

3.

4.

Construct the locus of the point D and label the ending location D’.

5.

6.

7.

Determine the solution(s).

𝑥 + 2𝑦 − 18 = 0 3𝑥 − 4𝑦 − 4 = 0 [3]

3 �12�𝑥

= 96 [2]

Simplify the following expressions.

𝑥2+7𝑥+10𝑥2−4

[2] 4𝑥32 ÷ 2𝑥

12 [2]

42𝑥+3

− 2𝑥−3

[2] (10𝑥𝑦−3)−2 [2]

8.

9.

The quantity p varies jointly as the inverse of the square of (𝑞 + 2) and directly as the square root of q. If p = 5 when q = 3, find p when q = 8. Provide an answer in simple radical form.

Solve the following problems.

a. The area of the rectangle shown exceeds the area of the square by 2 sq. cm. Find the perimeter of the rectangle. [3] 𝑥 − 1 𝑥 𝑥 + 2 𝑥

b. The angles in a triangle are in the ratio 1:3:5. Find the measure of the largest angle. [2]

10.

11.

12.

Solve and graph the solution to the inequalities.

2−5𝑥7

≤ 25 [2] 3|4 − 2𝑥| + 5 < 8 [3]

13.

14.

Write down the equation of the line in GENERAL FORM through B which is parallel to 𝑦 = 2𝑥 + 3

Use your calculator to work out √7 + 6 ∗ 2430.2 + 2 − tan(30°) ∗ tan (60°)

15.

16. [2]

17. [1]

(𝐴 ∪ 𝐵′)′

Find the perimeter and area of the following shape. The arcs are circular and every grid length is 1 cm long. Leave your simplified answers in terms of pi.

Perimeter [2]

Area [2]

18.

19.

20.

[1]

Answer all questions in Section B on SEPARATE sheets of paper. Be sure to write your name on every sheet, write a page number on every sheet, and indicate clearly the question number. Any working written on the exam paper will not be marked.

21.

Section B

[2]

(d) Directly on the diagram, construct (i) the bisector of angle ACB [2] (ii) the perpendicular bisector of segment CB. [2] (iii) Label the intersection of these two loci with the letter L and describe the special property L has in relation to the vertices and sides [2] of the triangle.

22.

23.

(iv) the total surface area of the solid wooden prism [4]

End of Section B

24.

End of Examination