NUSRAT SENIOR SECONDARY SSCHOOL – BUNDUNG

FIRST TERM EXAMINATION – DECEMBER, 2024

GRADE Twelve (12) SUBJECT Core Mathematics Paper 2 (Essay) TIME 1
22 hours

NAME: ________________________________________________ GR #: _____________ DATE: _________

SECTION A [40 marks]: Answer all questions in this section using the spaces provided with maximum clarity.
2𝑥
1. a) If 3𝑥 − 5𝑦 = 1 and = 4, find the value of (𝑥 + 𝑦)
𝑥−𝑦

b)
In the figure below, A, B and C are three points on
a circle with center O. The chord BA is extended
to a point T such that CT becomes a tangent to the
circle at point C. If < 𝐴𝑇𝐶 = 30° and
< 𝐴𝐶𝑇 = 50°, find the size of the angle <BOA.

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2. If the origin is the mid-point of the line segment joined by the points (2 , 3 ) and ( 𝑥 , 𝑦 ), find:
(a) the values of 𝑥 and 𝑦

(b) the equation of the line segment

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3.

The figure shows a circular sector OAB of radius

3𝑥𝑐𝑚, subtending an angle 𝑝 at O. The line AC is
perpendicular to OB and has length (2𝑥 − 1)𝑐𝑚.
The length of OC is (2𝑥 + 2)𝑐𝑚.
Find:

a) The value of 𝑥.

b) the area of the shaded region ACB.

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 Find the volume of frustum of a cone. The radius of the base and the top of the frustum are 6𝑚 and 4𝑚
4. a)
22
respectively and the slant height is 8𝑚. [Take 𝜋 = 7 ]

b). Factorize completely the expression 𝑝2 − 4𝑞2 + 6𝑞 − 3𝑝

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5. a) A market woman bought a basket of tomatoes containing 125 tomatoes for D250.00, she found that 20% of
the tomatoes are rotten. She sold the rest in equal portions of five tomatoes each. How much should she sell
each portion to make 15% profit.

3 sin 𝜃+2 cos 𝜃

b). If 3 tan 𝜃 = 4, find the value of 3 sin 𝜃−2 cos 𝜃

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 SECTION B [60 marks]: Answer any five (5) Questions in this section (All questions carry equal marks)

6. Man bought a house at $75,000.00. He paid 70% of the cost from his own resources and then the rest with a
loan he took from the bank at 3% per annum compound interest for 8 years. If the interest is compounded
quarterly, calculate
𝑎) total cost of the house to the man.
𝑏) percentage increase in the cost of the house as a result of the loan.
𝑐) percentage loss or profit correct to two decimal places if after paying the loan, he renovates the house at a
cost of $15,000.00 and sell the house for $135,000.00.

7. In a class of 200 students, 100 study Art, 70 study Biology and 46 study Chemistry. 30 study Art and
Biology, 28 study Art and Chemistry, 23 study Biology and Chemistry. If 18 students study all the three
subjects.
a) illustrate the information in a Venn diagram and find:
b) the number of students who do not study any of the three subjects.
c) how many students study only Art, only Biology and only Chemistry.

8.

In the diagram, O is center the circle PQRTU. |TS| is a tangent to the circle and |RS|= |RT|, < 𝑇𝑅𝑆 70°, <
𝑅𝑄𝑈 = 75° 𝑎𝑛𝑑 |𝑄𝑅|𝐼𝑆 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 |𝑃𝑇|. Find the value of:
𝑎) < 𝑈𝑇𝑃 𝑏) < 𝑄𝑈𝑅
9. a) In the triangle ABC, |𝐴𝐵| = 10 𝑐𝑚, |𝐶𝐷| = 6 𝑐𝑚, |𝐵𝐸| = 𝑛 + 2 𝑎𝑛𝑑 |𝐷𝐸| = 3𝑛. If the area of triangle
𝐴𝐵𝐸 = 40𝑐𝑚2, find the area of triangle 𝐴𝐵𝐶.

b) A manufacturing company requires an hour of direct labour to process every $18.25 worth of raw materials.
If the company uses $19162.50 worth of raw materials, what amount should it budget for a direct labour at
$87.00 per every 3 hours?

10. a) In the triangle ABC, |𝐴𝐵| = 10 𝑐𝑚, |𝐶𝐷| = 6 𝑐𝑚, |𝐵𝐸| = 𝑛 + 2 𝑎𝑛𝑑 |𝐷𝐸| = 3𝑛. If the area of triangle
𝐴𝐵𝐸 = 40𝑐𝑚2, find the area of triangle 𝐴𝐵𝐶.

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b). The radius of a wheel of a car is 60cm, how many revolutions to the nearest whole number will the wheel
make to cover a distance of 2.35km?

11.a) 𝐴𝐵𝐶𝐷 is a parallelogram in which 𝐴𝐵 = 12𝑐𝑚, 𝐵𝐶 = 8𝑐𝑚. If 𝐷𝐹 is perpendicular to 𝐵𝐶 at 𝐹 with

𝐷𝐹 = 9𝑐𝑚 and 𝐷𝐸 perpendicular to 𝐴𝐵 at 𝐸. Calculate the;
i. length of DE.
ii. length of EF

b). If 𝑃 = {𝑦: − 2 < 4𝑦 − 2 < 14 𝑎𝑛𝑑 𝑦 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 }, what is 𝑛(𝑃)

12. Given the lines 3𝑦 = 4𝑥 + 1 and 𝑎𝑦 = 𝑥 + 3 are parallel to each other. Find the:
a) value of a
b) equation of the line through the point (1, 3) and perpendicular to 𝑎𝑦 = 𝑥 + 3

13 a) A function 𝑓 is defined on the set, 𝑅, of real numbers by 𝑓: 𝑥 → 𝑚𝑥2 + 𝑛𝑥 + 2, where 𝑚 and 𝑛 are
constants. If 𝑓(−2) = 0 and 𝑓(1) = 3, find the values of 𝑚 and 𝑛.
b) Find a formula for the nth term of the sequence −9, −5, −1, 3 ….