# Mathematics Holiday Assignment Form 3

MUSINGU HIGH SCHOOL

MATHEMATICS HOLIDAY ASSIGNMENT FORM 3

**A. SEQUENCE AND SERIES**

1.The first term of an arithmetic progression (AP) with six terms is p and its common difference is c.Another AP with 5 terms has also its first term as p and a common difference of d. The last term of the two arithmetic progression are equal

a.Express d in terms of c

b.Given that the 4TH term of the second AP exceeds the 4th term of the 1st by 1.5, find the values of c and d

c.Calculate the value of p if the sum of the terms of the 1st AP is 10 more than sum of the terms of the 2nd AP.

2. Each month for 40 months, Wabs deposited some money in a saving scheme. In the 1stmonth he deposited sh. 200. Thereafter he increased his deposit by sh. 50 every month. Calculate

a.Last amount deposited by Wabs

b.Total amount Wabs had saved in the 40 months

3. The 3rd and 5th term of an AP are 10 and -10 respectively

a.Determine the 1st term and the common dofference

b.The sum of the 1st 15 terms

4. Saisi saved sh. 2000 during the 1st year of employment. In each subsequent year he saved 15% more than the preceding year until he retired

a.How much did he save in the second year

b.How much did he save in the 3rd year

c.Find the common ratio between th savings in two consecutive years

d.How many years did he take to save a sum of sh.58000

e.How much had he saved after 20 years of service

5. The average odf the 1st and the 4th term of a GP is 140. Given that the 1st term is 64, find the common ratio

**B. BINOMIAL EXPANSION**

1. a.Using binomial expansion, expand and simplify (1-2x)5 up to the term x3

b.Use the simplified expansion in a above to calculate to 4 d.p the approximate value of (0.98). Hence find the approximate value of (1.99)6 giving your answer to 3 d.p

3 a. Expand and simplify the 1st 4 terms of the binomial expression (1-3x)8

b. Use the simplified expression in a above to estimate the value of (o.97)8 correct to 5 d.p

**C. FORMULA AND VARIATION**

1.Three quantities t, x and y are such that t varies directly as x and inversely as the squareroot of y. find the percentage decrease in t, if x decreases by 4% when y increase by 44%?

2. Three quantities are R,S and T are such that R varies directly as S and inversely as the square of T.

a.Given that R is 480 when S is 150 and T 5, write an equation connecting R,S and T?

b. Find the value of R, when S is 360 and T is 1.5?

Find the percentage change in R if S increase by 5% and T decrease by 20%?

3 The mass of wire m grams (g) is partly a constant and partly varies as the square of its thickness t mm. When t = 2 mm, m=40 grams and when t = 3mm, m=65grams.Determine the value of m, when t=4mm?

APPROXIMATION AND ERRORS

1. The length and breadth of a rectangular room are 15cm and 12 cm respectively. If each of these measurement is liable to 1.5% error. Calculate the absolute error in the perimeter of the room.

2. The length and width of a rectangle are stated as 18.5cm and 12.4cm respectively. Both measurement are given to the nearest 0.1cm.

a. Determine the upper and lower limit of each measurement?

b. Calculate the percentage error in area of the rectangle?

3. the top of a table is regular hexagon. Each side of the hexagon measures 50.0cm. Find the maximum percentage error in calculating the perimeter of the top of the table?

**D.SPEED, DISTANCE AND TIME**

1. A train whose length is 86m is travelling at 28km/hr in the same direction as a truck whose length is 10m. If the speed of the truck is 60km/hr and is moving parallel to the train, calculate the time it takes to overtake the train completely.

2.A stationary observer on a platform notice that a train completely passes him in 10.8sec. If the speed of the train is 25 km/hr, find the length of the train in meters?

3. Coast bus left Nairobi at 8 a.m. and travelled towards Mombasa at an average speed of 80km/hr. At 8.30 a.m.Lamu bus left Mombasa towards Nairobi at an average speed of 120km/hr. Given that the distance between Mombasa and Nairobi is 400km. Calculate

a. The time Lamu bus arrived in Nairobi?

b. The time the two vehicle met?

c. The distance from Nairobi to the meeting point?

d. The distance of the Coast bus from Mombasa when Lamu bus arrived in Nairobi?

E. SURDS

1. Rationalise the denominator leaving your answer in the form a+b√c, where a, b and c are real numbers

2. Simplify the expression (1+√3) (1-√3), hence evaluate correct to 3 s.f given that √3=1.7321

3. Given that sin Ɵ= where Ɵ is an acute angle, find without using mathematical table or calculator

a. Cos Ɵ in the form a√b where a and b are rational numbers

b. Tan (90-Ɵ)

**F.FURTHER LOGARITHMS**

1. Find without using mathematical tables the value of x which satisfy the equation

Log2(x2-9) =3log22+1

2. Given that log 4 =0.6021 and log 6 =0.7782, without using mathematical table or calculator evaluate log0.096

3. Find the value of x given that: log (15-5x)-1=log (3x-2)

4. Without using a mathematical table or calculator solve the equation

2log10x-3log102+log1032=2

G.INDICES

1. Solve the equation 9x+1+32x+1=36

2. Find the value of y in the equation:

3. Without using mathematical table or calculatorevaluate: 27 2/3-1/4

H.INCOME TAX

Monthly taxable pay K£ / Rate of tax Ksh. 1£1-435

436-970

971-1505

1506-2040

Excess over 2040 / 2

3

4

5

6

Danstone is a civil servant who earns a monthly basic salary of sh.40, 000. He is housed by the employer and pays a nominal rent of sh. 3500; he is also given the following allowances every month:

- Entertainment sh. 2800
- Medical sh.3000
- Travelling sh.2000

a. Calculate his taxable income in K per month

b. Calculate his total monthly tax in ksh.

c. If he is entitled to a personal tax relief of sh.800 per month. Determine the net tax

2. Mr. Wabuyabo is housed by his employer is entitled to a total monthly

Allowance of ksh.15000. His total monthly relief issh.200. If his monthly income tax is sh.8570, calculate his monthly salary using the income tax rates table below

Income P.A / Rate of taxation0-1980

1981- 3960

3961-5940

5941-7920

7921-9900

Over 9900 / 10

15

25

35

45

50

3. Rubia bought a new piece of furniture for sh.800000. After 5yrs he sold it through a second hand dealer who charged him a commission of 4% for the sale. If Rubbia received sh.480000. Calculate the annual rate of depression of the furniture as a percentage.

I.MATRIX

1. Use matrices to solve the simultaneous equation

2s-3t=7

3s-2t=8

2. Solve for the unknown:

3. a. Given the matrix A=Find A2

b. Find matrix B such that A2= B-2A

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