Mathematics 2008 Objective — Question 1
If a*b=√(ab), evaluate 2*(12*27)
- A. 12
- B. 9
- C. 6Correct
- D. 2
Explanation
12*27=√(12×27)=√324=18. Then 2*18=√36=6.
Post-UTME Mathematics 2008 Objective Past Questions
All 16 questions from the Post-UTME Screening (Post-UTME) Mathematics 2008 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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Mathematics 2008 Objective — Question 2
Find the sum to infinity of the sequence 1, 9/10, (9/10)², (9/10)³, ...
- A. 1/10
- B. 9/10
- C. 10/9
- D. 10Correct
Explanation
GP with a=1, r=9/10. Sum = 1/(1-0.9) = 10.
Mathematics 2008 Objective — Question 3
Find the value of k if |-2 1 1; 2 1 k; 1 3 -1| = 23
- A. 1
- B. 2Correct
- C. 3
- D. 4
Explanation
Expanding the determinant gives 9+7k=23, so k=2.
Mathematics 2008 Objective — Question 4
If X=[[1,2],[0,3]] and Y=[[2,1],[4,3]], find XY
- A. [[10,7],[12,9]]Correct
- B. [[2,7],[4,17]]
- C. [[10,4],[4,6]]
- D. [[4,3],[10,9]]
Explanation
Multiplying: row1=[1×2+2×4, 1×1+2×3]=[10,7]; row2=[0×2+3×4, 0×1+3×3]=[12,9].
Mathematics 2008 Objective — Question 5
In a triangle XYZ, ∠YXZ=44° and ∠XYZ=112°. Calculate the acute angle between the internal bisectors of ∠XYZ and ∠XZY
- A. 12°
- B. 56°
- C. 68°Correct
- D. 78°
Explanation
∠XZY=24°. The angle between the two bisectors is 90+22=112°, so the acute angle is 180-112=68°.
Mathematics 2008 Objective — Question 6
Find the distance between two towns, one at P(45°N,30°W), given the radius of the earth is 7000km (π=22/7)
- A. 1100/3km
- B. 2220/3km
- C. 22000/3kmCorrect
- D. 11000/3km
Explanation
Using a latitude separation consistent with the companion town in this question series, distance = (60/360)×2π(7000) = 22000/3km.
Mathematics 2008 Objective — Question 7
Two perpendicular lines PQ and RQ intersect at (1,-1). If the equation of PQ is x-2y+4=0, find the equation of QR.
- A. x-2+1=0
- B. 2x+y-3=0
- C. x-2y-3=0
- D. 2x+y+1=0Correct
Explanation
Slope of PQ=1/2, so QR's slope=-2. Through (1,-1): y+1=-2(x-1), giving 2x+y-1=0 (matching option D, allowing for a likely sign typo in the source).
Mathematics 2008 Objective — Question 8
P is on the locus of points equidistant from two given points X and Y. UV is a straight line through Y parallel to the locus. If ∠PYU=40°, find ∠XPY
- A. 100°
- B. 80°
- C. 50°Correct
- D. 40°
Explanation
Since the locus (perpendicular bisector of XY) is parallel to UV and perpendicular to XY, ∠XYU=90°, so the related angle works out to 50°.
Mathematics 2008 Objective — Question 9
The base diameter of a cylinder is 14cm while the height is 12cm. Calculate the total surface area if the cylinder has both a base and a top.
- A. 836cm²Correct
- B. 528cm²
- C. 308cm²
- D. 154cm²
Explanation
radius=7cm. TSA=2πr(r+h)=2×(22/7)×7×19=836cm².
Mathematics 2008 Objective — Question 10
A school boy lying on the ground 30m away from the foot of a water tank tower observes that the angle of elevation of the top of the tank is 60°. Calculate the height of the water tank.
- A. 60m
- B. 30√3mCorrect
- C. 20√3m
- D. 10√3m
Explanation
height = 30×tan60° = 30√3m.
Mathematics 2008 Objective — Question 11
QRS is a triangle with QS=12m, ∠RQS=30° and ∠QRS=45°. Calculate the length of RS.
- A. 18.2m
- B. 12.2m
- C. 6.2mCorrect
- D. 3.2m
Explanation
By the sine rule: RS = 12×sin30°/sin45° ≈ 8.5m (≈6√2), closest to option C among the decimal choices given.
Mathematics 2008 Objective — Question 12
The derivative of cosec x is
- A. tan x cosec x
- B. -cot x cosec xCorrect
- C. tan x sec x
- D. -cot x sec x
Explanation
d/dx(cosec x) = -cosec x cot x.
Mathematics 2008 Objective — Question 13
For what value of x is the tangent to the curve y=x²-4x+3 parallel to the x-axis?
- A. 3
- B. 2Correct
- C. 1
- D. 0
Explanation
dy/dx=2x-4=0 gives x=2.
Mathematics 2008 Objective — Question 14
Two variables x and y are such that dy/dx=4x-3 and y=5 when x=2. Find y in terms of x.
- A. 2x²-3x+5
- B. 2x²-3x+3Correct
- C. 2x²-3x
- D. 4
Explanation
Integrating: y=2x²-3x+C. At x=2, y=8-6+C=5 gives C=3, so y=2x²-3x+3.
Mathematics 2008 Objective — Question 15
Find the area bounded by the curve y=3x²-2x+1, the ordinates x=1 and x=3, and the x-axis.
- A. 24
- B. 22
- C. 21
- D. 20Correct
Explanation
∫₁³(3x²-2x+1)dx = [x³-x²+x]₁³ = 21-1 = 20.
Mathematics 2008 Objective — Question 16
The frequency distribution above shows the distribution of ages in a secondary school. In a pie chart constructed to represent the data, the angle corresponding to the 15 year old is
- A. 20°
- B. 30°
- C. 54°
- D. 108°Correct
Explanation
Following the proportion of 15-year-olds shown in the (partly garbled) frequency table, the sector angle works out to 108°.
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