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Question 1 Report
Simplify and express in standard form 0.00275×0.006400.025×0.08
Answer Details
The expression 0.00275 × 0.00640 ÷ 0.025 × 0.08 can be simplified to 8.8 × 10^-3, which is the same as 8.8 x 10^-3. This is the standard form for writing very small numbers, and it means 8.8 times 0.001 or 0.0088.
Question 2 Report
Solve the following equation: 2(2r−1) - 53 = 1(r+2)
Answer Details
2(2r−1) - 53 = 1(r+2)
2(2r−1) - 1(r+2) = 53
The L.C.M.: (2r - 1) (r + 2)
2(r+2)−1(2r−1)(2r−1)(r+2) = 53
2r+4−2r+1(2r−1)(r+2) = 53
cross multiply the solution
3 = (2r - 1) (r + 2) or 2r2 + 3r - 2 (when expanded)
collect like terms
2r2 + 3r - 2 - 3 = 0
2r2 + 3r - 5 = 0
Factorize to get x = 1 or - 52
Question 3 Report
Three brothers in a business deal share the profit at the end of a contract. The first received 13 of the profit and the second 23 of the remainder. If the third received the remaining N12000.00 how much profit did they share?
Answer Details
use "T" to represent the total profit. The first receives 13
T
remaining, 1 - 13
= 23
T
The seconds receives the remaining, which is 23
also
23
x 23
x 49
The third receives the left over, which is 23
T - 49
T = (6−49
)T
= 29
T
The third receives 29
T which is equivalent to N12000
If 29
T = N12, 000
T = 1200029
= N54, 000
Question 4 Report
Simplify 2log 25 - log72125 + log 9
Answer Details
To simplify the expression 2log 25 - log 72125 + log 9, we need to use the logarithmic properties of logarithms. One of the properties of logarithms is log a^b = b log a, which allows us to rewrite log 25 as 5 log 5, log 72125 as 5 log 72, and log 9 as 2 log 3. Using this property, the expression becomes 2 log 5 - 5 log 72 + 2 log 3. Another property of logarithms is log a / log b = log a / b, which allows us to simplify the logarithm of the ratio of two numbers as the logarithm of the first number divided by the logarithm of the second number. Using this property, the expression becomes 2 log 5 - (5 / 5) log 72 + 2 log 3, which simplifies to 2 log 5 - log 72 + 2 log 3. Finally, we can simplify the expression further by using the property log a^m = m log a, which allows us to rewrite log 72 as log 2^6, so that the expression becomes 2 log 5 - 6 log 2 + 2 log 3. So, the simplified expression is 2 log 5 - 6 log 2 + 2 log 3 = 2 log (5 * 3^2 / 2^6) = 2 log (3^2 / 2^4) = 2 log 3 - 4 log 2 = 2 * 1.0986 - 4 * 0.3010 = 2.1976 - 1.2040 = 1 - 2 log 2. So, the answer is (D) 1 - 2 log 2.
Question 5 Report
The locus of a point which moves so that it is equidistant from two intersecting straight lines is the?
Answer Details
The required locus is angle bisector of the two lines
Question 6 Report
Find the derivative of the function y = 2x2 (2x - 1) at the point x = -1?
Answer Details
y = 2x2
(2x - 1)
y = 4x3
- 2x2
dy/dx = 12x2
- 4x
at x = -1
dy/dx = 12(-1)2
- 4(-1)
= 12 + 4
= 16
Question 7 Report
Factorize completely 81a4 - 16b4
Answer Details
81a4
- 16b4
= (9a2
)2
- (4b2
)2
= (9a2
+ 4b2
)(9a2
- 4b2
)
N:B 9a2
- 4b2
= (3a - 2b)(3a + 2b)
Question 8 Report
A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin
Answer Details
Average speed = totalDistanceTotalTime
from Calabar to Enugu in time t1, hence
t1 = PU
Also from Enugu to Benin
t2 qw
Av. speed = p+qt1+t2
= p+qp/u+q/w
= p + q x uwpw+qu
= uw(p+q)pw+qu
Question 9 Report
X is due east point of y on a coast. Z is another point on the coast but 6.0km due south of Y. If the distance ZX is 12km, calculate the bearing of Z from X
Answer Details
Sinθ = 612
Sinθ = 12
θ = Sin0.5
θ = 30°
Bearing of Z from X, (270 - 30)° = 240°
Question 10 Report
Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe?
Answer Details
To calculate the simple interest that Musa owes, we can use the following formula: Simple Interest = Principal * Rate * Time Where Principal is the amount of the loan, Rate is the interest rate per month and Time is the number of months the loan is taken for. In this case, the Principal is N10.00, the Rate is 2% per month, and the Time is 4 months. So, the simple interest would be: N10.00 * 2% * 4 = N0.80 This means that after 4 months, Musa would owe N10.00 + N0.80 = N10.80 Now, if we subtract the amount that he repaid (N8.00) from the total amount he owes (N10.80), we get N10.80 - N8.00 = N2.80 So, Musa still owes N2.80. Answer: N2.80
Question 11 Report
factorize m3 - m2 + 2m - 2
Answer Details
Using trial expansion of each option
(m2 + 2) (m - 1)
Question 12 Report
If the binary operation ∗ is defined by m ∗ n = mn + m + n for any real number m and n, find the identity of the elements under this operation
Answer Details
The identity element of a binary operation is an element "e" in a set such that for any element "x" in the same set, the result of the binary operation "e * x" or "x * e" is equal to "x". In other words, it's an element that doesn't change the result when it's multiplied with any other element. In this case, if we set "m = e" and "n = 0", the equation becomes: "e * 0 + e + 0 = e". This means that the identity element for this binary operation is "e = 0". So, the answer is: "e = 0".
Question 13 Report
wo numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even?
Answer Details
The probability that the sum of two numbers removed is even can be found by counting the number of even sums and dividing it by the total number of possible sums. Out of the 4 numbers, 2 are even (2 and 4) and 2 are odd (1 and 3). If we take one even and one odd number, the sum will be odd. If we take two even numbers, the sum will be even. And if we take two odd numbers, the sum will be even. So, there are 3 ways to get an even sum (taking 2 and 4, taking 2 and 2, or taking 1 and 3) and 6 total ways to choose two numbers (since order doesn't matter). So, the probability of getting an even sum is 3/6 or 1/2. In simple terms, there's a 50-50 chance that the sum of two numbers removed will be even.
Question 14 Report
What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?
Answer Details
The formula for the volume of a hemisphere is given by (2/3)πr^3, where r is the radius. To find the rate of change of the volume with respect to the radius, we need to take the derivative of this formula with respect to r. So, dV/dr = (2/3) * π * 3r^2 * dr/dr = (2/3) * π * 3r^2 = 2πr^2. Now, when r = 2, the rate of change of the volume with respect to the radius is given by 2π * 2^2 = 8π. So, the answer is 8π.
Question 15 Report
If (x + 2) and (x - 1) are factors of the expression Lx+2kx2+24 , find the values of L and k.
Answer Details
Given (x + 2) and (x - 1), i.e. x = -2 or +1
when x = -2
L(-2) + 2k(-2)2 + 24 = 0
f(-2) = -2L + 8k = -24...(i)
And x = 1
L(1) + 2k(1) + 24 = 0
f(1):L + 2k = -24...(ii)
Subst, L = -24 - 2k in eqn (i)
-2(-24 - 2k) + 8k = -24
+48 + 4k + 8k = -24
12k = -24 - 48 = -72
k = frac−7212
k = -6
where L = -24 - 2k
L = -24 - 2(-6)
L = -24 + 12
L = -12
That is; K = -6 and L = -12
Question 16 Report
P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
Answer Details
The radius of a circle is the distance from the center of the circle to any point on the circumference of the circle. In this question, we are given the two ends of the diameter of a circle, so the radius is half of the diameter. The distance between two points (x1, y1) and (x2, y2) can be calculated using the Pythagorean theorem: √((x2 - x1)^2 + (y2 - y1)^2). Applying this formula to points P and Q, we have: √((6 - (-6))^2 + (6 - 1)^2) = √(12^2 + 5^2) = √(144 + 25) = √169 = 13.0 So, the diameter is 13.0 units, and the radius is half of that, which is 6.5 units. Therefore, the answer is 6.5 units.
Question 17 Report
Answer Details
Given that 4, 16, 30, 20, 10, 14 and 26
Adding up = 120
nos ≥
16 are 16 + 30 + 20 + 26 = 92
The requires sum of angles = 92120
x 360o1
= 276o
Question 18 Report
A cylinder pipe, made of metal is 3cm thick.If the internal radius of the pipe is 10cm.Find the volume of metal used in making 3m of the pipe.
Answer Details
Volume of a cylinder = πr2 h
First convert 3m to cm by multiplying by 100
Volume of External cylinder = π×132×300
Volume of Internal cylinder = π×102×300
Hence; Volume of External cylinder - Volume of Internal cylinder
Total volume (v) = π(169−100)×300
V = π×69×300
V = 20700πcm3
Question 19 Report
Find the length of a side of a rhombus whose diagonals are 6cm and 8cm
Answer Details
Let's call the length of one side of the rhombus "s". We know that the diagonals of a rhombus bisect each other at 90 degrees, which means that each diagonal cuts the rhombus into two congruent right triangles. If we take one of these triangles and drop a perpendicular from the corner to the midpoint of the opposite side, we can use the Pythagorean theorem to find the length of "s". The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is one of the diagonals, and the other two sides are half of "s" and half of the other diagonal. So, we have: (1/2)^2 * 6^2 + (1/2)^2 * 8^2 = s^2 Simplifying this expression, we find: 9 + 16 = s^2 25 = s^2 And finally, taking the square root of both sides: s = 5 So, the length of one side of the rhombus is 5cm.
Question 20 Report
Simplify 27−−√ + 33√
Answer Details
√ + 33√
= 9×3−−−−√ + 3×3√3√×3√
= 33–√ + 3–√
= 43–√
Question 21 Report
The angles of a quadrilateral are 5x-30, 4x+60, 60-x and 3x+61.find the smallest of these angles
Answer Details
Sum of all 4 angles of a quadrilateral = 360°
(5x-30) + (3x + 61) + (60-x) + (4x+ 60) = 360°
11x + 151 = 360°
11x = 360 - 151 = 209
x = 209/11 = 19°
Each angles is :
5x - 30 = 65°
4x+ 60 = 136°
60 - x =41°
3x + 61 = 118°
Smallest of these angles is 41°
Question 22 Report
Find x if log9 x = 1.5
Answer Details
If log9 x = 1.5,
91.5 = x
9^32 = x
(√9)3
= 3
∴ x = 27
Question 23 Report
Three children shared a basket of mangoes in such a way that the first child took 14
of the mangoes and the second 34
of the remainder. What fraction of the mangoes did the third child take?
Answer Details
You can use any whole numbers (eg. 1. 2. 3) to represent all the mangoes in the basket.
If the first child takes 14
it will remain 1 - 14
= 34
Next, the second child takes 34
of the remainder
which is 34
i.e. find 34
of 34
= 34
x