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Question 1 Report
Solve for x in 8x-2 = 2/25
Answer Details
8x-2 = 2/25
x-2 = 2/25 x 1/8
x-2 = 2/200
x-2 = 1/100
1/x2 = 1/100
x2 = 100
x = 10
Question 2 Report
Find y, if (5−62−7)(52)=(7−11)
Answer Details
(5−62−7)(52)=(7−11)
By matrices multiplication;
5x - 6y = 7 ........(1)
2x - 7y = -11 ......(2)
2 x (1): 10x - 12y = 14 .......(3)
5 x (2): 10x - 35y = -55 ......(4)
(3) - (4): 23y = 69
y = 69/23 = 3
Question 3 Report
Express the product of 0.00043 and 2000 in standard form.
Answer Details
0.00043 x 2000
= 43 x 10-5 x 2 x 103
= 43 x 2 x 10-5+3
= 86 x 10-2
= 8.6 x 101 x 10-2
= 8.6 x 10-1
Question 4 Report
A cylindrical tank has a capacity of 6160m3. What is the depth of the tank if the radius of its base is 28cm?
Answer Details
Using V=πr2h
6160 = 22/7 x 28 x 28 x h
h=616022×4×28
h=2.5m
Question 5 Report
Find the equation of the straight line through (-2, 3) and perpendicular to 4x + 3y - 5 = 0
Answer Details
4x + 3y - 5 = 0 (given)
The equation of the line perpendicular to the given line takes the form 3x - 4y = k
Thus, substitution x = -2 and y = 3 in 3x - 4y = k gives;
3(-2) - 4(3) = k
-6 - 12 = k
k = -18
Hence the required equation is 3x - 4y = -18
3x - 4y + 18 = 0
Question 6 Report
If P = {1,2,3,4,5} and P ∪ Q = {1,2,3,4,5,6,7}, list the elements in Q
Question 7 Report
What is the solution of x-5/x+3<-1?
Question 8 Report
A man donates 10% of his monthly net earnings to his church. If it amounts to ₦4,500, what is his net monthly income?
Answer Details
We can begin by setting up an equation to represent the given situation. Let x be the man's net monthly income. Then, we know that he donates 10% of his net monthly income to his church, which amounts to ₦4,500. Mathematically, we can express this as: 10% of x = ₦4,500 To solve for x, we need to isolate the variable on one side of the equation. We can do this by dividing both sides of the equation by 10%, which is equivalent to multiplying both sides by 10/100 or 0.1: 10% of x ÷ 10% = ₦4,500 ÷ 10% x = ₦4,500 ÷ 0.1 x = ₦45,000 Therefore, the man's net monthly income is ₦45,000. Answer: ₦45,000
Question 9 Report
The pie chart above shows the monthly distribution of a man's salary on food items. If he spent ₦8,000 on rice, how much did he spent on yam?
Answer Details
The man's salary was divided into four food items: Rice, Yam, Beans, and Others. The chart shows that rice takes up 20% of his salary, and yam takes up 40% of his salary. Since rice takes up 20% of his salary, and he spent ₦8,000 on it, we can calculate the total salary of the man by dividing his spend on rice by 20%. ₦8,000 / 20% = ₦40,000 Since the total salary is ₦40,000 and yam takes up 40% of the salary, we can calculate how much he spent on yam by multiplying the total salary by 40%. ₦40,000 * 40% = ₦16,000 Therefore, the man spent ₦16,000 on yam.
Question 10 Report
Find the median of 5,9,1,10,3,8,9,2,4,5,5,5,7,3 and 6
Answer Details
To find the median of a set of numbers, we need to arrange the numbers in order from smallest to largest and then find the middle number. Arranging the given numbers in order from smallest to largest, we get: 1, 2, 3, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 9, 10 There are 15 numbers in this set, so the median will be the average of the two middle numbers: the 7th and 8th numbers. The 7th number is 5, and the 8th number is also 5, so the median of this set of numbers is: (median) = (5 + 5) / 2 = 10 / 2 = 5 So the median of the given set of numbers is 5. Looking at the given answer options, we see that the answer is (B) 5.
Question 11 Report
If ∣∣∣−x12−14∣∣∣=−12, find x
Answer Details
Question 12 Report
Values01234Frequency12219
Find the mode of the distribution above
Answer Details
To find the mode of the distribution, we look for the value that appears most frequently in the dataset. From the given frequency table, we can see that the value "4" appears 9 times, which is more than any other value. Therefore, the mode of this distribution is "4". In other words, the mode is the value that occurs most frequently in the data set. It is a measure of central tendency that can be useful in describing a dataset.
Question 13 Report
Evaluate Log28 + Log216 - Log24
Question 14 Report
Find the standard deviation of 5, 4, 3, 2, 1
Answer Details
To find the standard deviation of the numbers 5, 4, 3, 2, and 1, we need to follow these simple steps: Step 1: Calculate the mean (average) of the given numbers. - Add the numbers together: 5 + 4 + 3 + 2 + 1 = 15. - Divide the sum by the total number of values: 15 ÷ 5 = 3. Therefore, the mean of the numbers is 3. Step 2: Calculate the variance of the given numbers. - Subtract the mean from each number: 5 - 3 = 2, 4 - 3 = 1, 3 - 3 = 0, 2 - 3 = -1, 1 - 3 = -2. - Square each of the differences: 2^2 = 4, 1^2 = 1, 0^2 = 0, (-1)^2 = 1, (-2)^2 = 4. - Add up the squared differences: 4 + 1 + 0 + 1 + 4 = 10. - Divide the sum by the total number of values: 10 ÷ 5 = 2. Therefore, the variance of the numbers is 2. Step 3: Calculate the standard deviation of the given numbers. - Take the square root of the variance: √2 = 1.41421356. Therefore, the standard deviation of the numbers 5, 4, 3, 2, and 1 is approximately 1.41421356.
Question 15 Report
The locus of a dog tethered to a pole with a rope of 4m is a
Answer Details
The locus of a dog tethered to a pole with a rope of 4m is a circle with radius 4m. When a dog is tethered to a pole with a rope, it can move around the pole within the radius of the rope. Therefore, the dog's possible positions form a circle centered at the pole, with the radius equal to the length of the rope, which in this case is 4 meters. Since the circle has a fixed radius of 4m, it is not a semi-circle, but a full circle. Therefore, the correct answer is "circle with radius 4m."
Question 16 Report
If cos(x + 40)o = 0.0872, what is the value of x?
Answer Details
We are given that cos(x + 40) = 0.0872. To find the value of x, we need to use the inverse cosine function, also known as arccosine or cos^-1. Taking the inverse cosine of both sides, we get: arccos(cos(x + 40)) = arccos(0.0872) The inverse cosine and cosine functions are inverses of each other, so they "cancel out" on the left-hand side, leaving us with: x + 40 = arccos(0.0872) Using a calculator or a table of trigonometric values, we can find that arccos(0.0872) is approximately 84.74 degrees. Subtracting 40 from both sides, we get: x = 84.74 - 40 x = 44.74 So the value of x is approximately 44.74 degrees. None of the given options is an exact match, but the closest one is 45 degrees.
Question 17 Report
In how many ways can a team of 3 girls be selected from 7 girls?
Answer Details
A team of 2 girls can be selected from 7 girls in 7C3
=7!(7?3)!3!
=7!4!3!ways
Question 18 Report
Factorize 2y2 - 15xy + 18x2
Answer Details
The expression 2y^2 - 15xy + 18x^2 can be factored as (2y - 3x)(y - 6x). To factor this expression, we look for two binomials that multiply to the given expression and have a common factor. In this case, (2y - 3x) and (y - 6x) are two binomials that multiply to 2y^2 - 15xy + 18x^2 and have a common factor of y - 6x. So, the factorization of 2y^2 - 15xy + 18x^2 is (2y - 3x)(y - 6x).
Question 19 Report
Find the mid point of S(-5, 4) and T(-3, -2)
Answer Details
To find the midpoint of the line segment between two points, we need to average the x-coordinates and the y-coordinates of the two points separately. So, to find the midpoint of S(-5, 4) and T(-3, -2), we take the average of their x-coordinates and the average of their y-coordinates: Midpoint x-coordinate = (S x-coordinate + T x-coordinate) / 2 = (-5 + (-3)) / 2 = -4 Midpoint y-coordinate = (S y-coordinate + T y-coordinate) / 2 = (4 + (-2)) / 2 = 1 Therefore, the midpoint of S(-5, 4) and T(-3, -2) is (-4, 1).
Question 20 Report
Find the value of ∣∣ ∣∣032178054∣∣ ∣∣
Answer Details
0∣∣∣7854∣∣∣−3∣∣∣1804∣∣∣+2∣∣∣1705∣∣∣
= 0(28 - 40) - 3(4 - 0) + 2(5 - 0)
= 0(-12) - 3(4) + 2(5)
= 0 - 12 + 10
= -2
Question 21 Report
Numbers123456Frequency182220161014
The table above represents the outcome of throwing a die 100 times. What is the probability of obtaining at least a 4?
Answer Details
Let E demote the event of obtaining at least a 4
Then n(E) = 16 + 10 + 14 = 40
Hence, prob (E) = n(E)n(S)
=40100
=25
Question 22 Report
If y = cos 3x, find δyδx
Answer Details
To find the derivative of y = cos 3x, we need to use the chain rule of differentiation. The chain rule states that if y = f(g(x)), then the derivative of y with respect to x is given by the product of the derivative of f with respect to g multiplied by the derivative of g with respect to x. In other words, δy/δx = δf/δg * δg/δx. Using the chain rule, we have: δy/δx = δ(cos 3x)/δ(3x) * δ(3x)/δx The derivative of cos 3x with respect to 3x can be found using the chain rule again: δ(cos 3x)/δ(3x) = -sin(3x) The derivative of 3x with respect to x is simply 3. Substituting these values in the original equation, we get: δy/δx = -sin(3x) * 3 Simplifying, we have: δy/δx = -3 sin(3x) Therefore, the correct option is -3 sin 3x. In summary, the derivative of y = cos 3x is -3 sin 3x, which is obtained using the chain rule of differentiation.
Question 23 Report
A number is chosen at random from 10 to 30 both inclusive. What is the probability that the number is divisible by 3?
Answer Details
Sample space S = {10, 11, 12, ... 30}
Let E denote the event of choosing a number divisible by 3
Then E = {12, 15, 18, 21, 24, 27, 30} and n(E) = 7
Prob (E) = n(E)n(E)
Prob (E) = 721
Prob (E) = 13
Question 25 Report
What is the common ratio of the G.P. (√10+√5)+(√10+2√5)+...
?
Answer Details
Common ratio r of the G.P is
r=Tn+1Tn=T2T1
r=√10+2√5√10+√5
r=√10+2√5√10+√5×√10−√5√10−√5
=(√10)(√10)+(√10)(−√5)+(2√5)(√10)+(2√5)(−√5)(√10)2−(√5)2
10−√50+2√50−1010−5
√505
√25×25
5√25
√2
Question 26 Report
The mean of 2 - 4, 4 + t, 3 - 2t and t - 1 is
Answer Details
Mean x = ∑xn
= [(2 - t) + (4 + t) + (3 - 2t) + (2 + t) + (t - 1) ÷
] 5
= [11 - 1 + 3t - 3t] ÷
5
= 10 ÷
5
= 2
Question 27 Report
Calculate the mid point of the line segment y - 4x + 3 = 0, which lies between the x-axis and y-axis.
Answer Details
y - 4x + 3 = 0
When y = 0, 0 - 4x + 3 = 0
Then -4x = -3
x = 3/4
So the line cuts the x-axis at point (3/4, 0).
When x = 0, y - 4(0) + 3 = 0
Then y + 3 = 0
y = -3
So the line cuts the y-axis at the point (0, 3)
Hence the midpoint of the line y - 4x + 3 = 0, which lies between the x-axis and the y-axis is;
[12(x1+x2),12(y1+y2)]
[12(34+0),12(0+−3)]
[12(34),12(−3)]
[38,−32]
Question 28 Report
Evaluate the inequality x2+34≤5x6−712
Answer Details
x2+34≤5x6−712
12x2+1234≤125x6−12712
6x + 9 ≤
10x - 7
6x - 10x ≤
- 7 - 9
-4x ≤
-16
-4x/-4 ≥
-16/-4
x ≥
4
Question 30 Report
P varies directly as Q and inversely as R. When Q = 36 and R = 16, P = 27. Find the relation between P, Q and R.
Answer Details
P∝QR
P=KQR
When Q = 36, R = 16, P = 27
Then substitute into the equation
27=K3616
K=27×1636
K=12
So the equation connecting P, Q and R is
P=12QR
Question 31 Report
A binary operation * is defined by x * y = xy. If x * 2 = 12 - x, find the possible values of x
Answer Details
x * y = xy
x * 2 = 12 - x
Thus by comparison,
x = x, y = 2
But x * y = x * 2
xy = 12 - x
x2 = 12 - x
x2 + x - 12 = 0
x2 + 4x - 3x - 12 = 0
x(x + 4) - 3(x + 4) = 0
(x - 3)(x + 4) = 0
x - 3 = 0 or x + 4 = 0
So x = 3 or x = -4
Question 32 Report
ind the value of k if y - 1 is a factor of y3 + 4y2 + ky - 6
Answer Details
if y - 1 is a factor of y3 + 4y2 + ky - 6, then
f(1) = (1)3 + 4(1)2 + k(1) - 6 = 0 (factor theorem)
1 + 4 + k - 6 = 0
5 - 6 + k = 0
-1 + k = 0
k = 1
Question 33 Report
In the figure above, KL//NM, LN bisects < KNM. If angles KLN is 54?
and angle MKN is 35?
, calculate the size of angle KMN.
Answer Details
In the diagram above, α = 54∘ (alternate angles; KL||MN) < KNM = 2