Assignment – 1 :mathematics | Mathematics homework help
Assignment – 1 :MATHEMATICS
Answer all the questions.
Question1
(a) Simplify the following expressions:
(i)
(ii)
(iii)
(b) Express the following to a simplest fraction:
(i)
(ii)
(iii)
(c) Evaluate the value of
Question 2
(a) Express the following as a percentage:
(i)
(ii)
(iii) 46 marks out of a total of 80 marks
(iv) a discount of RM15 for a pair of shoes listed at RM120
(v) an increase of 5 cm to a height of 165 cm tall.
(b) The net selling prices of the following items are listed with the amount of
discount stated in brackets. Find the original price of each item.
(i) Smart phone RM1100 (20%)
(ii) Badminton racket RM175 (30%)
(iii) 1000cc Sedan RM44,200 (15%)
(c) (i) The Merdeka Stadium has a capacity of 23,500 seats. During a concert at
the stadium, 22,800 seats were taken. Find the percentage of vacant seat,
correct to the nearest 2 decimal places.
(ii) A receipt from a departmental store showed a tax of RM4.69 for the total
payment of RM53.63. Find the tax rate, correct to the nearest tenth percent.
Question 3
(a) Determine the domain of each of the functions below:
(i)
(ii)
(iii)
(iv)
(b) Let and
represent a cost function and a revenue function respectively,
where is the number of units of a certain product. At break-even point,
.
Find the values of , correct to the nearest whole number, for the following
products where the cost and revenue functions are as listed.
(i)
(ii)
(iii)
(iv)
(v)
Question 4
(a) Use completing the square method to find the values of at the minimum or
maximum point and state the minimum/maximum values of the following
functions.
(i)
(ii)
(iii)
(iv)
(v)
(b) The profit of a company is given by the function
where is the amount (in thousands) spent on advertising.
Find the amount spent on advertising that will bring in maximum profit.
Question 5
Solve the following inequalities and graph the solutions and also state the intervals in parenthesis.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Assignment – 2 :MATHEMATICS
Answer all the questions.
Question1
(a) Given the matrices
;
;
Compute the following:
(i) A + B (ii) C + F
(iii) BC (iv) AD
(v) DE (vi) EG
(b) The price of bus tickets varies from day to day and from time to time. On Sunday, Monday, Tuesday and Wednesday, the price at 9.00 am, 2.00pm and 7.00pm are RM12, RM14 and RM18 respectively. The price on Thursday to Saturday is an additional 10% on the prices stated. Construct a properly labeled matrix to represent the information stated.
(c) Find the values of and
in the following equations:
(i) (ii)
Question 2
(a) Solve the following system of 2 linear equations using substitution method:
(i) (ii)
(b) Solve the following system of 2 linear equations by elimination method:
(i) (ii)
(c) Find the inverse of the following 2 X 2 matrices:
(i) (ii)
(iii) (iv)
Question 3
(a) Rewrite the following system of linear equations as matrix equations and solve them using inverse matrix method:
(i) (ii)
(b) Write the following systems of linear equations as matrix equation and then as an augmented matrix:
(i) (ii)
(c) Use elimination method to solve the system of 3 linear equations in (b)(i).
(d) Use Cramer’s rule to solve the system of 2 linear equations in (a) above.
Question 4
(a) Use Gaussian elimination method to solve the equations in Q3 (b)(i) and (ii).
(b) Compute the following:
(i) An amount of RM50,000 was deposited in a bank paying simple interest of 3.8% per annum for a period of 3 years. What is the amount of interest gained?
(ii) What is the amount of interest gained after 3 years if a sum of RM50,000 is deposited in a bank that pays compound interest of 3.8% per annum.
(iii) Refer to part (b)(ii) above, find the interest gained if the interest is
compounded quarterly at the same rate of 3.8% per annum.
Question 5
(a)(i) Ragu took a loan of RM7,000 from a bank and the amount that he paid back to
the bank after 2 years amounted to RM7,700. Find the simple interest rate.
(ii) Ken paid a total of RM384 as interest for a sum of RM at a simple interest rate of 3.2% over a period of 3 years. Find the sum of money, RM
, that Ken borrowed from the bank.
(b)(i) A sum of RM6,000 was deposited in a bank at a rate of 4.2% compounded
semi-annually. Calculate the total amount after 3 years.
(ii) A sum of RM5000 yielded an interest of RM978.10 after 3 years compounded quarterly. Find the annual compounded interest rate, correct to one decimal place.
(c) An arithmetic sequence is given as 5, 11, 17, ………, 599.
(i) State the values of ‘a’, the first term of the sequence;
(ii) Find the value of ‘d’, the common difference of the sequence;
(iii) Find T15, the 15th term of the sequence;
(iv) Find the total number of terms, n, in the sequence, where 599 is the last term;
(v) Find the sum of all the terms of the sequence.
