WAEC SSCE - General Mathematics - 1994 (Objective)
Question 1 Report
Evaluate \( \frac{27^{\frac{1}{3}}}{16^{-\frac{1}{4}}} \)
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Question 2 Report
Factorise: 6x\(^2\) + 7xy - 5y\(^2\)
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Question 4 Report
The length of an exercise book is given as 20cm correct to the nearest centimeter. In which of the following ranges of possible measurement does the actual length lie?
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Question 5 Report
Question 6 Report
What is the number whose logarithm to base 10 is \(\bar{3}.4771\)?
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Question 7 Report
The angle subtended at the centre by a chord of a circle radius 6cm is 120°. Find the length of the chord.
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In a circle, the angle subtended by a chord at the centre of the circle is twice the angle subtended by the chord at any point on the circumference. Therefore, if the angle subtended by a chord at the centre is 120°, then the angle subtended by the chord at any point on the circumference is 60°.
Consider the triangle formed by joining the endpoints of the chord to the centre of the circle. We know that the angle at the centre of the circle is 120°, and we know that the radius of the circle is 6 cm.
Now we can use trigonometry to find the length of the chord. Let the length of the chord be 2x. Then, in the triangle we have:
\[\sin 60^\circ = \frac{x}{6}\]
\[\Rightarrow x = 6\sin 60^\circ = 6\cdot\frac{\sqrt{3}}{2} = 3\sqrt{3}\]
Therefore, the length of the chord is 2x, which is equal to:
\[2\cdot3\sqrt{3} = 6\sqrt{3}\]
Hence, the answer is (E) \(6\sqrt{3}\) cm.
Question 9 Report
Which of the following equations can be solved by the points of intersection P and Q of the curve and the line PQ?
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Question 10 Report
Which of the following is a point on the curve y = x\(^2\) - 4x + 7?
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Question 11 Report
A house bought for N100,000 was later auctioned for N80,000. Find the loss percent.
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Question 12 Report
If sin\( \theta \) = K find tan\(\theta\), 0° \(\leq\) \(\theta\) \(\leq\) 90°.
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Question 13 Report
Simplify: 16\(^{\frac{5}{4}}\) x 2\(^{-3}\) x 3\(^0\)
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Question 14 Report
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Question 15 Report
Calculate, correct to 2 significant figures, the length of the arc of a circle of radius 3.5cm which subtends an angle of 75° at the centre of the circle. [Take π = 22/7].
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The formula for the length of an arc of a circle is given by:
L = (θ/360) x 2πr
where θ is the angle subtended at the centre of the circle in degrees, r is the radius of the circle, and π is pi.
Using the given values, we have:
θ = 75° r = 3.5cm π = 22/7
Substituting these values into the formula, we get:
L = (75/360) x (2 x 22/7 x 3.5) L = (5/24) x (44/7) L = 110/24 L ≈ 4.58cm (correct to 2 significant figures)
Therefore, the length of the arc of the circle is approximately 4.58cm. The correct option is (b) 4.6cm.
Question 16 Report
A string is 4.8m. A boy measured it to be 4.95m. Find the percentage error.
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Question 17 Report
For what value of x is the expression \(\frac{x^2 + 15x + 50}{x - 5}\) not defined ?
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Question 18 Report
If 8x- 4 = 6x- 10, find the value of 5x,
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Question 20 Report
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Question 22 Report
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Question 23 Report
simplify; 2log\(_{3}\) 6 + log\(_{3}\) 12 - log\(_{3}\) 16
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Question 24 Report
Find the quadratic equation whose roots are 3 and \(\frac{2}{3}\).
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Question 25 Report
In the diagram ST and QR are parallel. |PS| = 6cm, |SQ| = 8cm and |PR] = 18 2/3. Find |PT|
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Question 26 Report
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Question 28 Report
If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term
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Question 29 Report
A cuboid of base 12.5cm by 20cm holds exactly 1 litre of water. What is the height of the cuboid? (1 litre =1000cm3)
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Question 30 Report
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Question 31 Report
Which of the following is not a factors of 2p\(^2\) - 2?
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Question 32 Report
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Question 33 Report
Which of the following is a root of the equation x\(^2\) +6x = 0?
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Question 34 Report
E = (integers \(\leq\) 20), P = (multiples of 3), Q = (multiples of 4), what are the elements of P'∩Q?
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Question 35 Report
Express in \( \frac{8.75}{0.025} \)standard form
Question 36 Report
Which of the following is equal to \(\frac{72}{125}\)
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Question 37 Report
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Question 38 Report
In the diagram above, PQ is the tangent to the circle RST at T.|ST| = ST and ?RTQ = 68o. Find ?PTS
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Question 40 Report
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Question 42 Report
The diagram above shows a circle PQRS in which ∠PRQ = 54o and ∠SPQ = 97o. Find ∠PQS.
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Question 43 Report
In the diagram |PS| is a diameter of circle PQRS. |PQ| = |QR| and ∠RSP = 74o. Find ∠QPS
Question 44 Report
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Question 45 Report
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Question 46 Report
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We know that prime numbers are numbers that are divisible only by 1 and themselves. To solve this problem, we can simply list the prime numbers between 30 and 50, and count how many there are. The prime numbers between 30 and 50 are: 31, 37, 41, 43, and 47. There are 5 prime numbers in this range.
The total number of integers between 30 and 50 (inclusive) is 21 (50 - 30 + 1 = 21). Therefore, the probability of selecting a prime number from this range is:
5 prime numbers
--------------- = 5/21
21 numbers
So the answer is 5/21.
Question 47 Report
Given that 2p - m = 6 and 2p + 4m = 1, find the value of (4p + 3m).
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We can solve for the values of p and m by adding the two given equations:
2p - m = 6
2p + 4m = 1
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4p + 3m = 7
So the value of (4p + 3m) is 7. Therefore, the correct option is (7).
Question 49 Report
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Question 50 Report
The sum of the 1st and 2nd terms of an A.P. is 4 and the 10th term is 19. Find the sum of the 5th and 6th terms.
