Opener Math Exams: MATH CAT 1

FORM II MATHEMATICS
CAT 2 – 2019

Intsructions:

• Answer all the questions: 50 marks
• show all your working
• non programmable electronic calculators may be used

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1. The exterior angles of a hexagon are:

Find the value of the smallest angle.(2 marks)

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2.

Simplify:$$\frac{p^4 + 2p^2q^2 + q^4}{p^3 – p^2q + pq^2 – q^3}$$

(2 marks)

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3.

Simplify the expression:$$\frac{4x – 9x^2}{3x^2 – 4x – 4}$$

(3 marks)

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4. Evaluate using logarithms:

$$\sqrt[3]{\frac{14.3 \times 0.0090}{76.54}}$$

(4 marks)

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5.

Three business partners, Atieno, Wambui and Mueni contributed shs. 50,000, 40,000 and 25,000 respectively to start a business. After sometime, they made a profit which they decided to share in the ratio of their contributions. If Mueni’s share was shs. 10,000, by how much was Atieno’s share more than Wambui’s? (3 marks)

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5.

In the figure below, angles ABC and ADC are equal. Angle ACD is a right angle. The ratio of the sides: AC:BC = 4:3

f the area of triangle ABC is 2$\mathrm{4cm2}$ .Find the area of triangle ACD.3 mks

6.

The angle of elevation of the top of a cliff from point P is $45^\circ$. From a point Q, which is 10 m from P towards the foot of the cliff, the angle of elevation is $48^\circ$.Calculate the height of the cliff.(4 mks)

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7.

8. A solid S is made up of a cylindrical part and a conical part. The height of the solid is 4.5 m. The common radius of the cylindrical part and the conical part is 0.9 m. The height of the conical part is 1.5 m.

a) Calculate the volume of solid S, correct to 1 decimal place.4 mks

8.

In the figure below, $\overrightarrow{CA}=k,\ \overrightarrow{AX}=\overrightarrow{AY}=\frac{1}{7}\overrightarrow{AB},\ \overrightarrow{CB}=a$

Express $\overrightarrow{CX}$CX in terms of $a$a and $k$k. $(3 \text{ mks})$(3 mks)

9.

A bus left a petrol station at 9:20 a.m and travelled at an average speed of $75 \text{ km/h}$ to a town $N$N. At 9:40 a.m, a taxi travelling at an average speed of $95 \text{ km/h}$ left the same petrol station and followed the route of the bus. Determine the distance from the petrol station covered by the taxi at the time it caught up with the bus. $(3 \text{ mks})$

10. Solve the simultaneous equations:

11.

The hire purchase (H.P) price of a public address system was Ksh 276,000. A deposit of Ksh 60,000 was paid followed by 18 equal monthly instalments. The cash price of the public address system was 10% less than the H.P price.

Calculate:

(i) the monthly instalment. $(6 \text{mks})$

(ii) the cash price. $(2 \text{mks})$

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11 (b)

The cost of a car outside Kenya is US $5,000. You intend to buy one such car through an agent who deals in Japanese Yen. The agent will charge you 20% commission on the price of the car and a further 80,325 Japanese Yen for shipment of the car.

How many Kenya shillings will you need to send to an agent to obtain the car given that:

• 1 US $ = 65.00 Yen
• 1 US $ = 100.00 shillings $(3 \text{mks})$

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11 (c)

A salesman earns a basic salary of Ksh 9,000 per month. In addition, he is also paid a commission of 5% for sales above Ksh 15,000. In a certain month, he sold goods worth Ksh 120,000 at a discount of $2\frac{1}{2}\%$.Calculate his total earnings that month.(3marks)

12.

The frequency distribution table below represents the number of kilograms of meat sold in a butchery.

Mass in kg	1–5	6–10	11–15	16–20	21–25	26–30	31–35
Frequency	2	3	6	8	3	2	1

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(a) State the modal frequency. $(1 \text{mk})$

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(b) Calculate the mean mass. $(5 \text{mks})$

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(c) Calculate the median mass. $(4 \text{mks})$

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