19 questions. Try each one, then open the answer to check yourself and read the explanation.
An open wooden box is made up of material which is 4cm thick. The inner dimensions are 16cm by 12cm by 9cm. Calculate the volume of wood used in making the box
Answer: D (4512cm3)
With 4 cm walls on all sides and the base (open top), the outside is 24 × 20 × 13 = 6240 cm³; inside is 16 × 12 × 9 = 1728 cm³; wood = 4512 cm³.
A cuboid has a length 13cm, width 9cm and height 8cm. calculate its surface area
Answer: B (586cm2)
2(13 × 9 + 13 × 8 + 9 × 8) = 2(117 + 104 + 72) = 586 cm².
In the figure above, BK = KC = 5cm. AK = 3cm. find the area of the triangle.
Answer: C (15cm2)
AK is the height and the base BC = 10 cm, so area = ½ × 10 × 3 = 15 cm².
Find the third angle of a triangle when x = 60° and if the other two angles are (x + 30°) and (2x − 65°).
Answer: A (35°)
The two angles are 90° and 55°, so the third is 180° − 145° = 35°.
Simplify log16/log32
Answer: B (4/5)
log 2⁴/log 2⁵ = 4/5.
Find the distance between A(lat. 56°S, long 80°E) and B(lat. 65°N, long 80°E). Take π = 3.142 and R = 6400km
Answer: A (13518km)
They are on the same meridian, 56° + 65° = 121° apart: 121/360 × 2 × 3.142 × 6400 ≈ 13,518 km.
Find the radius of the parallel latitude of latitude 50°N, given that R = 6400km
Answer: B (4114km)
r = R cos 50° = 6400 × 0.6428 ≈ 4114 km.
A hemispherical bowl has a radius of 9cm. Calculate its total surface area and its volume
Answer: C (763.5cm2, 1527cm3)
Total surface area of a solid hemisphere = 3πr² = 3 × 3.142 × 81 ≈ 763.5 cm²; volume = ⅔πr³ = ⅔ × 3.142 × 729 ≈ 1527 cm³.
Calculate the circumference and area of a circle of radius 10.5cm
Answer: D (66cm, 346cm2)
C = 2πr = 2 × 22/7 × 10.5 = 66 cm; A = πr² ≈ 346.5 cm².
Find the positive square root of 7 − 2√10
Answer: A (√5 − √2)
(√5 − √2)² = 7 − 2√10, and √5 − √2 is positive.
Evaluate (1112)2 − (1012)2 leaving your answer in base two.
Answer: D (11000)
7² − 5² = 24 = 11000₂.
Given that log102 = 0.3, solve the equation 2x = 5
Answer: C (7/3)
x = log 5/log 2 = 0.7/0.3 = 7/3.
Simplify 8n × 22n ÷ 43n
Answer: A (2−n)
2³ⁿ × 2²ⁿ ÷ 2⁶ⁿ = 2⁻ⁿ.
Solve the simultaneous equation y = 3x; 3x−y = 1/81
Answer: B ((2, 6))
x − y = −4 and y = 3x give x = 2, y = 6.
Find the value of x such that log5(x + 2) + log5(x − 2) = 1
Answer: A (3)
x² − 4 = 5, so x = 3.
A lady invested a sum of money at 4% per annum simple interest. Find the sum invested if after 3years it amounts to N7,000.00
Answer: A (N6,250.00)
Amount = P(1 + 0.12) = 7000, so P = N6,250.
Convert the binary number 1111.101 to base ten.
Answer: C (15.625)
8 + 4 + 2 + 1 + 0.5 + 0.125 = 15.625.
Approximate 0.00629946 to 3 significant figures.
Answer: D (0.00630)
The first three significant figures are 6, 2, 9; rounding gives 0.00630.
Solve for x and y: (1 1; 3 y)(x; 1) = (4; 1) (matrix rows separated by semicolons)
Answer: C (x = 3, y = −8)
x + 1 = 4 gives x = 3; 3x + y = 1 gives y = 1 − 9 = −8.