PRESIDENT OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
HAI DISTRICT COUNCIL
FORM THREE JOINTS TERMINAL EXAMINATION BASIC MATHEMATICS.
TIME:3 Hours May 2025
Instructions:
This paper consists of two sections. Section A and B with 14 questions.
Answer all questions in section A and B.
Mathematical table/calculators may be used
iv. Write your Number on every page of your answer sheet (s)
SECTION A (60 MARKS)
a) Four bells are set to ring at intervals of 20 minutes, 25 minutes, 35 minutes and 40 minutes. If they started together at 8:00AM. Find at what time the bells ring together for the second time. b). If if x=0.2̇, y=0.3̇, and z=0.9̇, find
a). Without using mathematical table simplify
b) by substitution t = 3x solve the equation 32(1+x) – 3x =3(x +3) -3
a).i. How many subsets are there in A= {a, b, c, d, e, f} ii. List all subsets of A= {2, 3, 6}
b). In a certain street with 200 houses. 170 houses have electricity and 145 houses have glass doors. By using a Venn diagram how many houses have both electricity and glass doors?
a). The line joining (2,-3) and (x, 5) has gradient -2, find x
b). Express “y” in term of x; 3x+2y=6 and state the gradient, the y- intercept x- intercept in the equation
a). The width of the rectangle is 40cm. If the area of the rectangle is 1700cm
i. find the length of the rectangle.
a). If X varies directly as Y and inversely as Z and X=8, Y=12 and Z=6
express X in term of Y and z
If Y=16 and Z=4. Find the value of X
b). Water from a tap gets into a tank at a rate of 20 liters per minute. How long will it take to fill a tank that is 10,000 liters? Give your answer in hours and minutes.
a). John bought a calculator for 42,000 Tsh and sold it at loss of
%.How much did he sell the calculator?
b). Alex borrowed 100,000 Tsh. for 5 years at 10% simple interest. What amount of money did Alex pay back?.
a). How many grams are there in 0.0915 tones?
b). from the top of a tower, the angle of depression of a point on the ground 20m away from the base of the tower is 60°. How high is the tower?
a). Hamisi has to share fifty books with his daughters, Nandy and Rose . He divided that for every two books Nandy gets, Rose gets three books and he gets five books. Find the number of books each gets. b). solve by elimination
a). Solve for x if 5-2x≥7x-4
b). Find two consecutive even numbers whose product is 80.
SECTION B (40 MARKS)
The given frequency distribution table shows the score of 30 students in mathematics test
Class interval |
40-49 |
50-59 |
60-69 |
70-79 |
80-89 |
90-99 |
Frequency |
2 |
4 |
7 |
9 |
5 |
3 |
a). Calculate the median score, correct to two decimal places.
b). Find the mean score, correct to four significant figures.
c). Draw a histogram and use it to estimate mode.
a). Solve the equation x2+5x-14=0 by completing the square.
b). Solve the value of x and y by graphical method.
a). The function f is defined as
f(x)
=
i. Sketch the graph of f(x) ii. State domain and range
b).Given
that f(x) =
,
find f-1
(4)
a).Given that R={(x, y); y=x2+1 and y<5}
Draw the graph of R
State domain and range of R
b).Given that R={(x, y);y=4x2} find
iii. The inverse of R
iv. The domain and range of R-1