A boy measured the length and breath of a rectangular lawn as 59.6m and 40.3m respectively instead of 60m and 40m. What is the percentage error in his calculation of the perimeter of the lawn?
პასუხი
(E)
0.1%
7
Find the 9th term of the arithmetic progression 18, 12, 6, 0, -6 .........
პასუხი
(B)
-30
8
Expand (2x - 5)(x - 3)
პასუხი
(B)
2x2 - 11x + 15
9
Simplify: \(\frac{5}{x - y} - \frac{4}{y - x}\)
პასუხი
(A)
9/x - y
10
If 3p - q = 6 and 2p + 3q = 4, find q
პასუხი
(A)
o
11
M varies directly as n and inversely as the square of p. If M = 3, when n = 2 and p = 1, find M in terms of n and p.
პასუხი
(D)
M = 3n/2p2
12
If x is a real number which of the following is more illustrated on the number line?
პასუხი
(E)
-2 ≤ x < 4
13
Solve the equation
4/a
+
1/5a
= 3
პასუხი
(B)
12/5
14
Make p the subject if formula y =
a + p/a - p
პასუხი
(C)
a(y -1)/y + 1
= p
15
Factorize 32x3 - 8xy2
პასუხი
(D)
8x(2x + y)(2x - y)
16
The roots of a quadratic equation are -1/4 and 3. The quadratic equation is
პასუხი
(B)
4x2 - 11x - 3 = 0
17
The graph of 2y = 5x2 - 3x2 - 2 cuts the y axis at the point
პასუხი
(C)
(0, -1)
18
In the diagram above, O is the center of the circle of radius 3.5cm, ∠POQ = 60o
Use the information to answer the question below [Take π = 22/7]
What is the length of the arc PXQ?
პასუხი
(C)
\(\frac{11}{3}\)cm
19
In the diagram above, O is the center of the circle of radius 3.5cm, ∠POQ = 60°. What is the area of the minor sector POQ?
[Take π = 22/7].
პასუხი
(D)
65/12cm2
20
If the hypotenuse of a right-angle isosceles triangle is 2, what is the length of each of the other side?
პასუხი
(D)
√2
21
Find, correct to 1 decimal place, the volume of cylinder of height 8cm and base radius 3cm. [Take π = 3.142]
პასუხი
(D)
226.2cm3
22
One side of a rectangle is 8cm and the diagonal is 10cm. What is the area of the rectangle?
პასუხი
(B)
48cm2
23
two towns X and Y both on latitude 60oS have longitude 27oE and 33oW respectively. Find to the nearest kilometers, the distance between X and Y measured along the parallel of latitude. [Take 2πR = 4 x 104km, where R is the Radius of the earth]
პასუხი
(E)
3333km
24
The angle of a sector of a circle of radius 35cm is 288o. Find the perimeter of the sector. [Take π = 22/7]
პასუხი
(A)
246cm
25
How many sides has a polygon if the sum of its interior angle is 1440o?
პასუხი
(E)
10
26
Each interior angle of a regular nonagon(nine sided polygon) is equal to
პასუხი
(C)
140o
27
In the diagram above, find x correct to the nearest degree
პასუხი
(C)
26o
28
In the diagram above, TRQ is a straight line. Find p, if p = \(\frac{1}{3}\)(a + b + c)
პასუხი
(A)
45o
29
Which of the following is not true? You may construct a
პასუხი
(D)
quatrilateral given all the four sides
30
In the diagram above, PQ is parallel to RST. /RS/ = /SQ/ = /TQ/ and ∠PQR = 35o.Calculate ∠SQT
პასუხი
(C)
40o
31
In the diagram above, /PQ/ = /PS/ and /QR/ = /SR/. Which of the following is/are true? i. the line PR bisects ∠QRS ii. The line PR is the perpendicular bisector of the line segment QS iii. Every point on PR is equidistant from SP and QP
პასუხი
(E)
I, II and III
32
In the diagram, ∠PMN = ∠PRQ and ∠PNM = ∠PQR. If /Pm/ = 3cm, /MQ/ = 7cm and /PN/ = 5cm, find /NR/
პასუხი
(A)
1cm
33
In the diagram above, PQ is a tangent to the circle MTN at T. What is the size of ∠MTN?
პასუხი
(C)
66o
34
In the diagram above, KLMN is a cyclic quadrilateral. /KL/ = /KN/, ∠NKM = 55o and ∠KML = 40o. Find ∠LKM
პასუხი
(C)
45o
35
In the diagram above, ∠SPQ = 79o. Find ∠SRQ
პასუხი
(E)
101o
36
Two angles (a + 31) and (b - 49o) are adjacent angles on a straight line. Which of the following is true
პასუხი
(A)
a + b = 198o
37
The trapezium PQRS parallel to SR,∠PQS = 34o and ∠SPQ = 2 ∠SRQ. Find the size of, SQR
პასუხი
(D)
90o
38
In the diagram above, AB, CD and XY are straight lines intersecting at W. Find ∠CWX
პასუხი
(B)
80o
39
If sin\(\theta\) cos\(\theta\), for 0o \(\leq\) θ \(\leq\) 360o, find the value of \(\theta\)
პასუხი
(A)
45o, 225o
40
If tan x = \(2\frac{2}{5}\), find the value of sin x; 0 \(\leq\) x \(\leq\) 90o
პასუხი
(D)
12/13
41
A town P is 150km from a town Q in the direction 050o. What is the bearing of Q from P?
პასუხი
(C)
230o
42
The angle of elevation of the top X of a vertical pole from a point P on a level ground is 60o. The distance from P to the foot of the pole is 55m. Without using tables, find the height of the pole.
პასუხი
(C)
55√3m
43
The number of goals scored by a football team in 20 matches is shown in the table above
What is the mean goal scored?
პასუხი
(B)
1.75
44
The number of goals scored by a football team in 20 matches is shown in the table above
What is the modal goal scored?
პასუხი
(C)
2
45
The cumulative frequency curve may be used to find the
