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Frage 1 Bericht
The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart?
Antwortdetails
The size of each sector in a pie chart represents the proportion of the data it represents compared to the whole. In this case, the total number of acres for all the crops is 2 + 5 + 3 + 11 + 9 = 30. To find the angle of the sector for cassava, we need to find the proportion of 3 acres to 30 acres, and then convert this proportion to degrees. The proportion of 3 acres to 30 acres is 3/30 = 1/10. In a full circle, there are 360 degrees, so the angle of the sector representing 1/10 of the data would be 360 x (1/10) = 36 degrees. Therefore, the angle of the sector for cassava in a pie chart is 36 degrees.
Frage 2 Bericht
Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13
Antwortdetails
x | x - x | (x - x)2 |
7 8 9 10 11 12 13
|
-3 -2 -1 0 1 2 3
|
9 4 1 1 0 4 9 -------------- 28
|
S.D = ∑√(x−x)2N=∑d2N=28√7
= 4–√
= 2
Frage 3 Bericht
The sum of the interior angle of pentagon is 6x + 6y. Find y in terms of x.
Antwortdetails
The sum of the interior angles of a pentagon is equal to (5-2) * 180 = 540 degrees. So, the equation 6x + 6y = 540 can be used to find the value of y in terms of x. Solving for y, we get y = 90 - x. This means that if we know the value of x, we can find the value of y by subtracting x from 90. So, the correct answer is y = 90 - x.
Frage 4 Bericht
A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room
Antwortdetails
ABCD is the floor. By pathagoras
AC2 = 144 + 81 = 225−−−√
AC = 15cm
Height of room 8m, diagonal of floor is 15m
Therefore, the cosine of the angle which a diagonal of the room makes with the floor is
EC2 = 152 + 82 cosine
adjHyp=1517
EC2 = 225+64−−−−−−−√
EC = 289−−−√
= 17
Frage 5 Bericht
Four boys and ten girls can cut a field first in 5 hours. If the boys work at 54 the rate at which the girls work, how many boys will be needed to cut the field in 3 hours?
Antwortdetails
Let x rep. numbers of boys that can work at 54 the rate at
which the 10 girls work
For 1 hrs, x boys will work for 15×104
x = 54 x 10
= 8 boys
8 boys will do the work of ten girls at the same rate
4 + 8 = 12 bous cut the field in 5 hrs for 3 hrs,
12×53 boys will be needed = 20 boys.
Frage 6 Bericht
Simplify 324−4x22x+18
Antwortdetails
234 - 4x2 = 182 - (2x)2 = (18 - 2x)(18 + 2x)
2x + 18 = 2x + 18 = (2x + 18)
18 - 2x = 2(a - x) or -2(x - a)
Frage 7 Bericht
A sector of circle of radius 7.2cm which substends an angle of 300o at the centre is used to form a cone. What s the radius of the base of the cone?
Antwortdetails
Frage 8 Bericht
Find the simple interest rate percent annum at which N1000 accumulates to N1240 in 3 years.
Antwortdetails
Simple interest is the interest calculated on the original amount of a loan or deposit, without taking into account any compound interest. To find the simple interest rate at which N1000 accumulates to N1240 in 3 years, we can use the formula for simple interest: I = Prt where I is the interest, P is the principal (original amount), r is the interest rate, and t is the time in years. We know that I = N1240 - N1000 = N240, and t = 3 years. So, we can plug in these values into the formula and solve for r: N240 = N1000 x r x 3 Dividing both sides by N1000 x 3, we get: r = N240 / (N1000 x 3) = 0.08 So, the interest rate is 8%. So, the answer is 8%.
Frage 9 Bericht
Find the equation of the line through the points (5, 7) parallel to the line 7x + 5y = 12.
Antwortdetails
The equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. To find the equation of a line parallel to another line, we need to use the same slope. The line 7x + 5y = 12 can be rewritten in the form y = -(7/5)x + 12/5. The slope of this line is -(7/5). To find a line through the point (5, 7) with the same slope, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values for (x1, y1) and m, we get: y - 7 = -(7/5)(x - 5) Expanding and simplifying, we get: y = -(7/5)x + 7 + (35/5) = -(7/5)x + 70/5 = 14x + 7. So the equation of the line through the point (5, 7) parallel to the line 7x + 5y = 12 is 7x + 5y = 70.
Frage 10 Bericht
Find all real number x which satisfy the inequality 13 (x + 1) - 1 > 15 (x + 4)
Antwortdetails
13 (x + 1) - 1 > 15 (x + 4) = x+13−1 > x+45
x+13−x+45−1 > 0
= 5x+5−3x−1215
2x - 7 > 15
2x > 22 = x > 11
Frage 11 Bericht
Antwortdetails
hn−2=n+3n
n2 = (n + 3) (n - 2)
n2 = n2 + n - 6
n2 + n - 6 - n2 = 0
n - 6 = 0
n = 6
Common ratio: nn−2=66−2=64 = 32
Frage 12 Bericht
Find all median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119
Antwortdetails
Arrange in ascending order
89, 100, 108, 119, 120,130, 131, 131, 141, 161
Median = 120+1302 = 125
Frage 13 Bericht
In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g of meat and 20g of bread crumbs. Find the angle of the sector which represent meat in a pie chart?
Antwortdetails
Rice = 75g, Margarine = 40g, Meat = 105g
Bread = 20g
Total = 240
Angle of sector represented by meat
= 105240×360o1
= 157.5
Frage 14 Bericht
Reach each number to two significant figures and then evaluate 0.02174×1.20470.023789
Antwortdetails
0.021741×1.20470.023789 = 0.0255×1.20.024(to 216)
= 0.02640.024= 1.1
Frage 15 Bericht
A crate of soft drinks contains 10 bottle of Coca-Cola 8 of Fanta and 6 of Sprite. If one bottle is selected at random, what is the probability that it is Not a Coca-Cola bottle?
Antwortdetails
Coca-Cola = 10 bottles, Fanta = 8 bottles, Spirite = 6 bottles
Total = 24
P(Coca-Cola) = 1024 ; P(not Coca-Cola)
1 - 1024
24−1024=1424=712
Frage 16 Bericht
What is the circumference of latitude 0o S if R is the radius of the earth?
Antwortdetails
Circumstances of latitude 0o s where R is the radius of the earth 2π r cos θ
Frage 17 Bericht
The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group.
Antwortdetails
Let's call the number of students in the group "n". The total of the ages of all students is 15n. When the teacher's age is added, the total becomes 15n + 45. The mean of the ages becomes 18, which means the total of the ages is divided by the number of people, which is "n + 1". We can set up an equation to represent the situation: (15n + 45) / (n + 1) = 18 Expanding the equation: 15n + 45 = 18 * (n + 1) 15n + 45 = 18n + 18 Subtracting 18n from both sides: -3n + 45 = 18 Subtracting 45 from both sides: -3n = -27 Dividing both sides by -3: n = 9 So, there are 9 students in the group.
Frage 18 Bericht
Antwortdetails
h = 30 tan 60
= 303–√
Frage 19 Bericht
A binary operation x is defined by a x b = ab . If a x 2 = 2 - a, find the possible values of a?
Antwortdetails
The equation a x 2 = 2 - a can be solved for the possible values of a. To do this, we can simplify the equation by adding a to both sides: a x 2 + a = 2 Combining like terms: a x 2 + a = 2 a(x + 1) = 2 Dividing both sides by x + 1: a = 2 / (x + 1) Since the binary operation x is defined as a x b = a, we can substitute this definition into the equation: a = 2 / (a x 1 + 1) a = 2 / (a + 1) Since a x b = a, we know that a x 1 = a, so we can substitute this into the equation: a = 2 / (a + 1) a = 2 / (a + 1) Solving for a, we get: a = 2 / (a + 1) = 2 / (2) = 1 So, the possible values of a are 1.
Frage 20 Bericht
Find the gradient of the line passing through the points (-2, 0) and (0, -4)
Antwortdetails
The gradient of a line describes how steep the line is, and it can be calculated as the change in the y-coordinate divided by the change in the x-coordinate between two points on the line. In this case, the two points are (-2, 0) and (0, -4), so the change in x is 0 - (-2) = 2, and the change in y is -4 - 0 = -4. Therefore, the gradient of the line passing through these two points is -4 ÷ 2 = -2. So, the answer is -2.
Frage 21 Bericht
Find the non-zero positive value of x which satisfies the equation
⎡⎣⎢x101x101x⎤⎦⎥ = 0
Frage 22 Bericht
Factorise (4a + 3) 2 - (3a - 2)2
Antwortdetails
[(4a + 3) 2 - (3a - 2)2 = a2 - b2 = (a + b) (a - b)
= [(4a + 3) + (3a - 2)] [(4a + 3) - (3a - 2)]
= [4a + 3 + 3a - 2] [4a + 3 - 3a + 2]
= (7a + 1)(a + 5)
(a + 5) (7a + 1)
Frage 23 Bericht
A number is selected at random between 20 and 30, both numbers inclusive. Find the probability that the number is a prime.
Antwortdetails
Probability is the measure of how likely an event is to occur. In this question, we want to find the probability of selecting a prime number between 20 and 30, both numbers inclusive. The prime numbers between 20 and 30 are 23 and 29. The total number of possible outcomes (or numbers between 20 and 30) is 11 (20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30). So, the probability of selecting a prime number is the number of favorable outcomes (prime numbers) divided by the total number of possible outcomes. The probability of selecting a prime number is 2/11. So, the answer is 2/11.
Frage 24 Bericht
The pie chart shows the income of a civil servant in month. If his monthly income is N6,000. Find his monthly basic salary.
Antwortdetails
360o - (60o + 60o + 67 + 50 = 237o )
360o - 237 = 130o
B. Salary = 123360XN60001
= N2,050
Frage 25 Bericht
A cylindrical tank has a capacity of 3080m3 . What is the depth of the tank if the diameter of its base is 14m?
Antwortdetails
V = 2080cm3 , h = ?
r = 7cm
V = Vπr2h
h = Vπr2=3080227×49
308054 = 20cm
Frage 26 Bericht
In a class of 40 students, 32 offer mathematics, 24 offer physics and 4 offer neither mathematics nor physics. How many offer both mathematics and physics?
Antwortdetails
40 = 32 - x + x + 24 + 4
40 = 60 - x
x = 60 - 40
x = 20
Frage 27 Bericht
The angle of a sector of a circle radius 10.5 cm is 48o . Calculate the perimeter of the sector.
Antwortdetails
The perimeter of a sector of a circle is equal to the circumference of the circle that is part of the sector plus the length of the arc of the sector. To calculate the perimeter of a sector, we need to find the length of the arc and the circumference of the circle first. The length of the arc is given by the formula: Arc length = (Angle of sector / 360) x Circumference of the circle The circumference of a circle is given by the formula: Circumference = 2 * pi * radius Plugging in the values we have, the circumference of the circle is 2 * pi * 10.5 = 65.97 cm. The length of the arc is (48 / 360) x 65.97 = 12.19 cm. Adding the length of the arc to the circumference of the circle, we get 65.97 + 12.19 = 78.16 cm, which is the perimeter of the sector. Therefore, the answer is 78.16 cm, which is closest to 29.8cm.
Frage 28 Bericht
If x is positive real number, find the range of values for which 13x + 12 x = 2+3x6x > 14x
Antwortdetails
13x + 12 x = 2+3x6x > 14x
= 4(2 + 3x) > 6x = 12x2 - 2x = 0
= 2x(6x - 1) > 0 = x(6x - 1) > 0
Case 1 (-, -) = x < 0, 6x - 1 > 0
= x < 0, x < 16 (solution)
Case 2 (+, +) = x > 0, 6x - 1 > 0 = x > 0
x > 16
Combining solutions in cases (1) and (2)
= x > 0, x < 16 = 0 < x < 16
Frage 29 Bericht
What is the product of 275 , (3)−3 and (15)−1 ?
Antwortdetails
275×3−3×(1)−15
= 275×133×115
275 x 127 x 51 = 1
Frage 30 Bericht
Find the value of x if 2√x+2√ = 1x−2√
Antwortdetails
2√x+2 = x - 12√
x2–√ (x - 2–√ ) = x + 2–√ (cross multiply)
x2–√ - 2 = x + 2–√
= x2–√ - x
= 2 + 2–√
x (2–√ - 1) = 2 + 2–√
= 2+2√2√−1×2√+12√+1
x = 22√+2+2+2√2−1
= 32–√ + 4
Frage 31 Bericht
In a class of 150 students, the sector in a pie chart representing the students offering physics has angle 12o . How many students are offering physics?
Antwortdetails
No of students offering physics are
12360x 150 = 5
Frage 32 Bericht
If log10 2 = 0.3010 and log10 3 = 0.4771, eventually without using the logarithm tables, log10 4.5
Antwortdetails
log10 2 = 0.3010 and log10 3 = 04771
log104.5=log10 (3×32 )
log10 3 + log10 3 - log10 2 = 0.4471 + 0.771 - 0.3010
= 0.6532
Frage 33 Bericht
The goals scored by 40 football teams from three league divisions are recorded below
No of goals | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
Frequency | 4 | 3 | 15 | 16 | 1 | 0 | 1 |
What is the total number of goals scored by all the teams?
Antwortdetails
The total number of goals scored by all the teams can be calculated by multiplying the number of goals by its frequency and then adding all of them up. For example, the number of goals scored by teams with 0 goals is 4 * 0 = 0. The number of goals scored by teams with 1 goal is 3 * 1 = 3. The number of goals scored by teams with 2 goals is 15 * 2 = 30. And so on. So, the total number of goals scored by all the teams is 0 + 3 + 30 + 48 + 4 + 0 + 6 = 91. Therefore, the answer is 91.
Frage 34 Bericht
In this fiqure, PQ = PR = PS and SRT = 68o
. Find QPS
Antwortdetails
Since PQRS is quadrilateral
2y + 2x + QPS = 360o
i.e. (y + x) + QPS = 360o
QPS = 360o - 2 (y + x)
But x + y + 68o = 180o
There; x + y = 180o - 68o = 112o
QPS = 360 - 2(112o )
= 360o - 224 = 136o
Frage 35 Bericht
If N225.00 yields N27.00 in x years simple interest at the rate of 4% per annum, find x.
Antwortdetails
Principal = N225.00, interest = N27.00
Year = x, Rate = 4%
1 = PRT100
27 = 225×4×x100 = 2700 = 900T
T = 2700900
= 3 years
Frage 36 Bericht
A surveyor walks 500m up a hill which slopes at an angle of 30o . Calculate the vertical height through which he rises
Antwortdetails
The vertical height through which the surveyor rises can be calculated using trigonometry. When a person walks up a hill, they are moving in two dimensions: horizontally and vertically. We can use a right triangle to represent this movement, where the horizontal distance is one side, the vertical distance is another side, and the slope of the hill is the angle between these sides. In this case, the horizontal distance is 500m and the angle is 30 degrees, so we can use the trigonometric function sine to find the vertical distance: sin(30) = vertical distance / 500 Multiplying both sides by 500, we get: 500 * sin(30) = vertical distance Using a calculator, we can find that sin(30) = 0.5, so: 500 * 0.5 = 250 Therefore, the vertical height through which the surveyor rises is 250m.
Frage 37 Bericht
The equation of the line in the graph is
Antwortdetails
Gradient of line = Change in yChange in x = y2−Yx2−x
y2 = 01
Y1 = 4
x2 = 3 and x1 = 0
y2−y1x2−x1=0−43−0=−43
Equation of straight line y = mx + c
Where m = gradient and c = y
intercept = 4
y = 4x + 43 multiply through y
3y = 4x + 23
Frage 38 Bericht
Evaluate (212)3 - (121)3 + (222)3
Antwortdetails
The answer is (1020)3, which is equal to (1 * (3^3)) + (0 * (3^2)) + (2 * (3^1)) + (0 * (3^0)). In this question, each number is given in base-3 format, which means that each digit in the number represents a power of 3. For example, the number (212)3 is equal to (2 * (3^2)) + (1 * (3^1)) + (2 * (3^0)). To evaluate the expression, we simply add and subtract the numbers as written, and convert the result back to base-3 format.
Frage 39 Bericht
The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST
Antwortdetails
r2r Sin θ = 12
θ = sin−1 (12 ) = 30o = 60o
Length of arc (minor)
ST = θ360 x 2πr
60360×2π×r=π3
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