THE PRESIDENT’S OFFICE
REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
MOSHI MUNICIPAL COUNCIL
SECONDARY EDUCATION EXAMINATIONS SYNDICATE
041 BASIC MATHEMATICS
FORM TWO MOCK EXAMINATION
Wednesday 29^{th}June 2022 Am Time: 2:30 Hour
INSTRUCTIONS
1. (a) Equal squares as large as possible are drawn on a rectangular board measuring 54cm by 78cm. Find the largest size of the squares.
(b) (i) Express 2.7̇9̇ as a fraction in the form a/b where a and b are integers and b≠0
(ii)Arrange 2/5, 5/8 ,48% and 0.6 in ascending order
(iii) Show on the number line the solution set of the inequality
│2x+1│>3
2. (a) write 624.3278 correct to :
(i) Five significant figures
(ii) Three decimal places
(b) i. A rope of 18m and 80cm is to divided into four equal parts . How long will each part be? (Give your answer in meters and centimeters).
ii. 50% of the contents in a box weigh 8kg 40gm. What does the whole content weigh?
3. (a) Rectangular table top is 2m long. If the area of the rectangular table top is
3.96m^{2}. find its width
(b) i. Solve the following simultaneous equations
2x+3y=5
4x+23=5y
ii. If Fatuma is 4 years less than Bakari and 3 times Fatuma's age is equal to 2 times Bakari's age. What are their ages ?
4. (a) i. If x^{2} +ax +4=0 is a perfect square . Find the value of a
ii. If x^{2} +bx +c =(x-3)(x+2) determine the values of b and c
iii. Solve the following quadratic equation by complete the square method x^{2} + 6x +7=0
(b) i. Solve 3 - of (6x+9) = 5-2x
ii. If U*V =UV+V, Find x given that (x*2)*5=60
5. (i) John, Ramadhani , Marry and Sam have 600 ,100, 500 and 300 shares in a cooperative shop respectively. Divide 150,000 shs among them in the ratio of their shares.
(ii) A real estate agent received a 6% discount on the selling price of a house . If the discount was Tsh.888,000. What was the selling price of the house ?
6. (a) i. A straight line passes through two points A(-3,6) and B (-6,3).
Find the gradient of the straight line AB.
ii. Find the Y- intercept of the line joining points (5,3) and (3,2). (b) i. The transformation T maps the point (x,y)(x-y,x). Find the image of the point (6,-2).
ii. Find the image of a point P(3,2) after rotating it about the origin through 90^{0} in a clockwise direction.
iii.What is the centre of an enlargement given that the image of A(3,2) under the enlargement scale factor 2 is A^{'}(6,4).
7. (a) (i) Solve for X if
(ii) Given that
make x as the subject of the formula.
(iii) Express
in the form a + b√c
(b) (i) If log 2=0.30103 and log 3 = 0.47712 evaluate log 48.
(ii) Use mathematical tables to evaluate the following mathematical expression,
8. (a) In the figure below, EH = GH and both ΔEHF and ΔGHF are right – angled triangles. Prove that ΔEHF and ΔGHF are congruent
(b) If ΔPQR ∼ ΔLMN and lengths PR = 20cm, NL = 10cm, NM = 12cm and LM = 9cm, find the length of the other sides of ΔPQR
9. a) In a right – angled triangle, tan θ = . Find the value of
iSin θ
ii 2Cos θ
(b) A ladder 15m long, rests against a vertical wall such that the foot of the ladder is 6m from the wall of a horizontal floor. Find
(i) the angle that the ladder makes with the wall
(ii) the height above the floor at the point where the ladder touches the wall
10. (a) (i) Given that n(A) = X, n(B) = X + 4, n(An B) = 3 and n(Au B) = 17 where A and B are joint sets. Find the value of X
. (ii) In a class of 42 students 31 students study History and 26 students study Physics. Using Venn diagram, find the number of students who study Physics only.
(b) The scores of mathematics examination done by 50 form two students in a certain school are shown in the table below
Marks (%) | 45 | 50 | 55 | 60 | 65 | 70 | 75 | 80 |
Number of students | 6 | x+3 | 2x+3 | x-2 | 9 | 4 | 5 | 2 |
(i) Find the value of x
(ii) Calculate the number of students who passed the examination if the pass mark was 50%.
(iii) What was the score obtained by majority of the students?
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS REGIONAL SERIES-28 YEAR-2022
PRESIDENT'S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
TANZANIA HEADS OF ISLAMIC SCHOOLS COUNCIL
FORM TWO INTER ISLAMIC MOCK EXAMINATION
041 BASIC MATHEMATICS
TIME: 2:30 HOURS Thursday, 23^{rd} September 2021 a.m.
Instructions
1. This paper consists of ten (10) compulsory questions.
2. Answer ALL questions
3. Each question carries ten (10) marks.
4. Show clearly all the workings and answers in the spaces provided.
5. All writings must be in blue or black ink except for drawings which must be in pencil.
6. Four figures/mathematical tables, geometric instruments and graph papers may be used where necessary.
7. Calculators, cellular phones and any unauthorized materials are not allowed in the examination room.
8. Write Your Examination Number at the top right corner of every page.
FOR EXAMINER’S USE ONLY | ||
QUESTION NUMBER | SCORE | EXAMINER’S INITIALS |
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2 | | |
3 | | |
4 | | |
5 | | |
6 | | |
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TOTAL | | |
CHECKER’S INITIALS | |
1. (a) Three bells ring at intervals of 20 minutes, 30 minutes and 40 minutes. If they start ringing together at 7.30 am
(i) After how long will they ring together again?
(ii) At what time will this be?
(b) Round off 349.678 to the nearest.
(i) Tens
(ii) Hundredth
(iii) One significant figure
2. (a) Write in form of , where b ≠0.
(b) In a class of 40 students are boys. Two fifth of the girls wear spectacles.
How many girls do not wear spectacles?
3.(a) Perform
(b) Find the time in which sh 200,000/= will earn sh 48,000/= at the rate of 4% interest per annum.
4. (a) Calculate the angles marked with letters X, Y and Z.
(b) Find the area of rectangle whose perimeter is 30cm and its length and width are (3W-7) cm and (W+2) cm respectively.
5. (a) Factorize the expression 6x^{2} – 11x + 4 by splitting the middle term.
(b) The sum and difference of the two numbers are 9 and 3 respectively. Find the possible numbers.
6. (a) (i) Find the equation of the straight line passing through (3,5) and (7,9).
(ii) Calculate the gradient and coordinates of the y-intercept of 2x+3y=12.
(b) Find the image of a point (-4, 3) after a reflection on y-axis followed by another reflection on y=0.
7. (a) If
Find the value of X.
(b) Rationalize writing the answer in the form a where a, b, c and d are real.
(c) Given log2 = 0.3010, log3 = 0.4770 and log7 = 0.8451. Find the value of log294.
8. (a) Calculate the length of EC and CD in figure below:
(b) Use the figure below to prove that triangle ADB ≡ Triangle ADC
9. (a) A rectangle has sides of 12mm and 16mm. Calculate the length of one of its diagonals.
(b) Calculate the exact value of .
10. (a) In the Venn diagram below:
U = { Boys in form II at a certain secondary school}
F = { Members in the football team}
B={ Members in basketball}
(i) How many boys are in the football team?
(ii) How many boys are in both teams?
(iii) How many are in the football team but not in the basketball team?
(iv) How many are neither basketball nor football team?
(v) How many boys in form II at the school?
10. (b) The table below shows the distribution of the score of 60 students in Mathematics table at MJI MWEMA secondary school.
Marks % | 45 – 55 | 56 – 66 | 67 – 77 | 78 – 88 | 89 - 99 |
No. of students | 11 | 15 | X | 17 | 10 |
(i) Find the value of X.
(ii) Find the percentages of the student score ate most 77 marks.
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS REGIONAL SERIES-11 YEAR-2021