THE UNITED REPUBLIC OF TANZANIA NATIONAL EXAMINATIONS COUNCIL OF TANZANIA FORM TWO NATIONAL ASSESSMENT 041 BASIC MATHEMATICS Time: 2:30 Hours Tuesday, 12 th November 2019 a.m. Instructions 1. This paper consists of ten (10) compulsory questions. 2. Show clearly all the working and answers in the space provided. 3. All writing must be in blue or black ink except drawings which must be in pencil. 4. Four figure mathematical tables, geometric instruments and graph papers may be used where necessary. 5. All communication devices, calculators and any unauthorized materials are not allowed in the examination room. 6. Write your Examination Number at the top right hand corner of every page. FOR EXAMINERS’ USE ONLY QUESTION NUMBER SCORE EXAMINER’ INITIALS 1 2 3 4 5 6 7 8 9 10 TOTAL CHECKER’S INITIALS This paper consists of 8 printed pages.

Candidate's Examination No ………………… 1. (a) Find the Greatest Common Factor (GCF) of 18, 24 and 60. (b) The population of three towns are 65,600, 13,400 and 29,700. Approximate the total population of the three towns to the nearest thousands. 2. (a) Rehema spent 1/8 of her salary on transport and 1/4 on food. If she remained with sh. 80,000, what was her salary? (b) Change 5/8 into: (i) percentage. (ii) decimal.

Candidate's Examination No ………………… 3. (a) A machine that costs sh. 180,000 was sold at a profit of 40%. Find the selling price. (b) A father divided sh. 150,000 among Rose and Japheth in the ratio 2:3 respectively. How much money did each get? 4. (a) Use the following figure to find the value of a + b + c. (b) The perimeter of triangle ABC is 16 cm. If AB = (5 + x) cm, AC = (2 + x) cm and BC = 5 cm, find the value of x and hence the actual lengths of AB and AC .

Candidate's Examination No ………………… 5. (a) Solve { x + y = 4 2x − y = 5 by using the substitution method. (b) Find two consecutive positive numbers such that the sum of their squares is equal to 145. 6. (a) If the gradient of the straight line ky = kx + x + 7 is 2, find: (i) the value of k, (ii) the y-intercept. (b) By using a sketch, find the image of point A(2,3) after a reflection in the line y = x followed by another reflection in the line y = -x.

Candidate's Examination No ………………… 2 7. (a) Solve for n in the equation 16 (3−n) × 2 (1+n) = 1 . (b) Find the value of x in the equation log (2x + 1) + log 4 = log (7x + 8). ︿ ︿ 8. (a) In the following figure, AB = DC and ABC = DCB . Prove that ΔABC = ΔDCB . (b) If ΔABC ~ ΔPQR and AC = 20 cm , PR = 10 cm , QR = 12 cm and PQ = 9 cm , find the lengths of AB and BC .

Candidate's Examination No ………………… 9. (a) Use the following figure to find the values of x and y. (b) Find the value of each of the following expressions and simplify the answer. (i) sin 60°(cos 45° + sin 30°), (ii) tan 45°(4cos 60° − √3 tan 30°).

Candidate's Examination No ………………… 10. (a) In a class of 35 students, 21 study commercial subjects, 15 study both commercial and science subjects and 4 students study science subjects only. Use a Venn diagram to find the number of students who study: (i) either science or commercial subjects. (ii) neither science nor commercial subjects. (iii) commercial subjects only. (iv) science subjects. (b) The following pie chart represents the distribution of form two students who were selected to participate in sports activities. If there are 200 students who were selected, how many students participate in each activity?