Solve the inequality: \(\frac{2x - 5}{2} < (2 - x)\)
პასუხი
(D)
x < 2\(\frac{1}{4}\)
11
If x = 64 and y = 27, evaluate: \(\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}\)
პასუხი
(C)
\(\frac{5}{11}\)
12
If \(\frac{1}{2}\)x + 2y = 3 and \(\frac{3}{2}\)x - 2y = 1, find (x + y)
პასუხი
(A)
3
13
Given that \(p^{\frac{1}{3}}\) = \(\frac{\sqrt[3]{q}}{r}\), make q the subject of the equation
პასუხი
(C)
q = pr3
14
A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord
პასუხი
(A)
2\(\sqrt{21}\)cm
15
A cube and cuboid have the same base area. The volume of the cube is 64cm\(^3\) while that of the cuboid is 80cm\(^3\). Find the height of the cuboid
პასუხი
(C)
5cm
16
If sin x = \(\frac{5}{13}\) and 0o \(\leq\) x \(\leq\) 90o, find the value of (cos x - tan x)
პასუხი
(C)
\(\frac{79}{156}\)
17
An object is 6m away from the base of a mast. The angle of depression of the object from the top pf the mast is 50o, Find, correct to 2 decimal places, the height of the mast
პასუხი
(C)
7.15m
18
The bearing of Y from X is 060º and the bearing of Z from Y = 060º. Find the bearing of X from Z
პასუხი
(B)
240o
19
Which of the following is not a probability of Mary scoring 85% in a mathematics test?
პასუხი
(D)
1.01
20
If 2 log x (3\(\frac{3}{8}\)) = 6, find the value of x
პასუხი
(A)
\(\frac{3}{2}\)
21
If p = (y : 2y \(\geq\) 6) and Q = (y : y -3 \(\leq\) 4), where y is an integer, find p\(\cap\)Q
პასუხი
(C)
{3, 4, 5, 6, 7}
22
Find the values of k in the equation 6k2 = 5k + 6
პასუხი
(B)
{\(\frac{-2}{3}, \frac{3}{2}\)}
23
If y varies directly as the square root of (x + 1) and y = 6 when x = 3, find x when y = 9
პასუხი
(A)
8
24
The graph of the relation y = x2 + 2x + k passes through the point (2, 0). Find the values of k
პასუხი
(D)
-8
25
What is the locus of the point X which moves relative to two fixed points P and M on a plane such that < PXM = 30o
პასუხი
(B)
an arc of a circle with PM as a chord
26
When a number is subtracted from 2, the result equals 4 less than one-fifth of the number. Find the number
პასუხი
(C)
5
27
Express \(\frac{2}{x + 3} - \frac{1}{x - 2}\) as a simple fraction
პასუხი
(A)
\(\frac{x - 7}{x^2 + x - 6}\)
28
An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?
პასუხი
(B)
12
29
Given that P = x2 + 4x - 2, Q = 2x - 1 and Q - p = 2, find x
პასუხი
(B)
-1
30
A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume
პასუხი
(B)
448m3
31
The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole number, the volume of the cone. ( Take \(\pi = \frac{22}{7}\))
პასუხი
(C)
38cm3
32
The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used
პასუხი
(A)
1: 1,000,000
33
Given that (x + 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M
პასუხი
(D)
x2 - x
34
An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. calculate the arc of the sector (Take \(\pi = \frac{22}{7}\))
პასუხი
(A)
8800cm2
35
In the diagram, PRST is a square. If |PQ| = 24cm. |QR| = 10cm and < PQR = 90o, find the perimeter of the polygon PQRST.
პასუხი
(A)
112cm
36
in the diagram, the height of a flagpole |TF| and the length of its shadow |FL| re in the ratio 6:8. Using k as a constant of proportionality, find the shortest distance between T and L
პასუხი
(B)
10K units
37
In the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?
პასუხი
(D)
\(\bigtriangleup\) XYZ= \(\bigtriangleup\) NOM
38
In the diagram, PQRS is a rhombus and < PSQ = 35º. Calculate the size of < PRQ
პასუხი
(B)
55o
39
Find the value of m in the diagram
პასუხი
(D)
17o
40
In the diagram, O is the centre of the circle. OM||XZ and < ZOM = 25º. Calculate ∠XYZ
პასუხი
(D)
65o
41
Using the histogram, estimate the mode of distribution
პასუხი
(C)
53.5
42
Using the histogram, what is the median class?
პასუხი
(C)
40.5 - 50.5
43
The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. How many textbooks are for the technical class?
პასუხი
(D)
250
44
The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. What percentage of the total number of textbooks belongs to science?
პასუხი
(A)
12\(\frac{1}{2}\)%
45
In the diagram, PQRST is a regular polygon with sides QR and TS produced to meet at V. Find the size of < RVS
