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Guyana Times is pleased to publish the Education Ministry’s National Grade Six Assessment Past Papers and CXC questions. Below are the first part of Mathematics paper 2, 2016 and CXC Mathematics.
MINISTRY OF EDUCATION NATIONAL GRADE SIX ASSESSMENT MATHEMATICS PAPER 2
Read these instructions carefully before you attempt to answer the questions.
1. Write your candidate number clearly on each page. 2. This paper contains six questions. You are required to answer question 1 and three others. Each question is worth 5 marks
Note: You must answer only four questions.
Be sure to answer the four questions completely. 3. Write the answer for each question in the space provided in this booklet. 4. Answers must be written in complete sentences where possible. 5. Each step of your work must be clearly shown in this booklet. 6. If you have to erase, do so cleanly.
7. look over your work when you have finished. 8. Do not take away any part of this booklet.
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO.
1. (a) Solve, giving your answer in the lowest terms,
3 – x – + 1 –2 3 3 4 2 6 Answer_______________________________________________
(b) At a sale, books are sold at $90.75 each, which is 75% of the original price. (i) What is the original price of a book?
Answer_________________________________________ (1 mark)
(ii) Paul buys 10 books at the sale and pays VAT of 16% on the sale price. Calculate the total amount he paid for the 10 books.
Answer_________________________________________ (2 marks) 2. (a) Jai bought 4 different items from the list shown below. Two of the items cost the same amount. He paid with $200.00. If Jai received $23.60 change, what four items did he buy? Answer_______________________________________________ saved the rest of the money.
(i) What fraction of her pocket money did Mia spend on stationery?
Answer_________________________________________ (1 mark)
(ii) If Mia saved $28.00, how much pocket money did she receive?
Answer_________________________________________ (2 marks)
3. Figure ABCD shown below is made up of a semicircle and a rectangle. 0 is the centre of the line DC. (a) Calculate the area of triangle AOB. Answer_______________________________________________ (1 mark) (b) Calculate the area of the semicircle.
(use ∏ = –– ) 22 7 Answer________________________________________cm² (2 marks) (c) What is the area of the shaded region of the figure?
Answer________________________________________cm² (2 marks)
TO BE CONTINUED
CXC MATHEMATICS
1.ABC is a right triangle and r is the radius of the inscribed circle. a) Express r in terms of angle x and the length of the hypotenuse h. b) Assume that h is constant and x varies; find x for which
(b) Mia received some pocket money. She spent – of it on 3 5 food and – of the remaining amount on stationery. She 3 10
r is maximum.
Solution to Problem: a) Let M, N and P be the points of tangency of the circle and the sides of the triangle. OM, ON and OP are perpendicular to CB, CA and AB respectively.
Triangles COM and CON are right triangles and have two congruent sides: CO and OM and ON; the two triangles are therefore congruent. We denote the size of angle MCN by x and write
tan(x / 2) = r / CM
Triangles BOM and BOP are right triangles and have two congruent sides: BO and OM and OP; the two triangles are therefore congruent. We denote the size of angle MBP by y and write
tan(y / 2) = r / BM
Note that
y + x = 90 which gives y / 2 = 45 - x / 2
Substitute y / 2 by 45 - x / 2 in the equation tan(y / 2) = r / BM to obtain
tan(45 - x / 2) = r / BM
We now solve the equation tan(x / 2) = r / CM for CM and solve equation tan(45 - x / 2) = r / BM for BM to obtain
CM = r / tan(x/2) and BM = r / tan(45 - x/2)
We now use the fact that h = CM + BM to write the equation
h = r / tan(x/2) + r / tan(45 - x/2) = r [ 1 / tan (x/2) + 1 / tan(45 - x/2) ]
We now use trigonometric identities to simplify the above equation. The first identity we will use is
