WAEC SSCE - General Mathematics - 1995
Question 1 Report
The angle of a sector of a circle is 108°. If the radius of the circle is 31/2cm, find the perimeter of the sector
Answer Details
A sector of a circle is a region bounded by two radii and an arc. The perimeter of a sector is the sum of the arc length and the lengths of the two radii. In this case, we are given that the angle of the sector is 108° and the radius of the circle is 31/2 cm. To find the arc length, we need to know the circumference of the entire circle, which is given by 2πr, where r is the radius of the circle. So, the circumference of the circle is 2π(31/2) cm = 31π cm. The angle of the sector is 108°, which is 108/360 or 3/10 of the entire circle. So, the arc length of the sector is (3/10) × 31π cm = 9.3π cm. The two radii of the sector have length 31/2 cm each. Therefore, the perimeter of the sector is the sum of the arc length and the two radii, which is 9.3π cm + 31/2 cm + 31/2 cm = (9.3π + 31) / 2 cm. This is approximately equal to 13.6 cm. Therefore, the answer is (E) 13 3/5 cm.
Question 2 Report
In the diagram above, the value of angles b + c is
Answer Details
Since angles b and c are alternate angles, they are equal. Therefore, b + c = 2b or 2c. But since a straight line forms a straight angle of 180 degrees, we have that angle a + angle b + angle c = 180 degrees. Solving for b + c, we get: b + c = 180 - a Therefore, the answer is (A) 180o.
Question 3 Report
Use the graph of y = 3x\(^2\) + x - 7 above to answer the question
What is the minimum value of y?
Answer Details
Question 4 Report
If R = [2, 4, 6, 7] and S = [1, 2, 4, 8], then R∪S equal
Answer Details
In set theory, the union of two sets is a set containing all distinct elements from both sets. Therefore, to find R∪S, we need to combine all the elements in R and S without duplication. R = [2, 4, 6, 7] and S = [1, 2, 4, 8], so combining them without duplication gives us: R∪S = [1, 2, 4, 6, 7, 8] Therefore, the correct answer is (a) [1, 2, 4, 6, 7, 8].
Question 5 Report
In the diagram above, ?PRQ = 90°, ?QPR = 30° and /PQ/ = 10 cm. Find y.
Answer Details
We can use trigonometry to solve for y. Since we know that ?QPR = 30°, then we can determine that: sin 30° = y/PQ Solving for y: y = PQ * sin 30° y = 10 * (1/2) y = 5 Therefore, y is 5 cm.
Question 6 Report
Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. [Take π = 22/7]
Answer Details
Question 7 Report
If three children shares N10.50 among themselves in ratio 6:7:8, how much is the largest share?
Answer Details
To solve this problem, we need to first add up the parts of the ratio, which gives us 6+7+8 = 21. Next, we divide the total amount shared (N10.50) by the sum of the ratio parts (21) to find the value of one part: N10.50 ÷ 21 = N0.50 Now that we know the value of one part, we can find the value of each part of the ratio by multiplying the value of one part by the corresponding number in the ratio: - 6 parts: 6 × N0.50 = N3.00 - 7 parts: 7 × N0.50 = N3.50 - 8 parts: 8 × N0.50 = N4.00 So the largest share is N4.00, which corresponds to the 8 parts of the ratio. Therefore, the correct answer is option (C) N4.00.
Question 8 Report
In the diagram above. |AB| = 12cm, |AE| = 8cm, |DCl = 9cm and AB||DC. Calculate |EC|
Answer Details
In the given diagram, we can see that the two lines AB and DC are parallel. Hence, we can apply the intercept theorem or Thales' theorem which states that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then it divides those sides proportionally. So, we can use this theorem to find the length of |EC| as follows: First, we can notice that the triangles ABE and DCE are similar since they are both right triangles and share the same angle at E. Therefore, we can set up a proportion between their corresponding sides: \begin{align*} \frac{|EC|}{|DC|} &= \frac{|AE|}{|AB|} \\ \frac{|EC|}{9\text{ cm}} &= \frac{8\text{ cm}}{12\text{ cm}} \\ |EC| &= \frac{8\text{ cm}}{12\text{ cm}} \times 9\text{ cm} \\ |EC| &= 6\text{ cm} \end{align*} Therefore, the length of |EC| is 6cm. Thus, the correct option is (E) 6cm.
Question 9 Report
Given that log2a = log84, find a
Question 10 Report
The locus of a point which is equidistant from two given fixed points is the
Answer Details
The locus of a point which is equidistant from two given fixed points is the perpendicular bisector of the straight line joining them. This means that the locus of the point is the line that is perpendicular to the straight line joining the two given points and passes through the midpoint of that line.
Question 11 Report
What is the smaller value of x for which x\(^2\) - 3x + 2= 0?
Answer Details
The given equation is a quadratic equation in standard form, which is \(ax^2 + bx + c = 0\), where \(a = 1\), \(b = -3\), and \(c = 2\). We can solve for the roots of the quadratic equation by using the quadratic formula: \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\] Substituting the values of \(a\), \(b\), and \(c\) into the formula, we get: \[x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(2)}}{2(1)}\] \[x = \frac{3 \pm \sqrt{1}}{2}\] Thus, the solutions are: \[x_1 = \frac{3 - 1}{2} = 1 \text{ and } x_2 = \frac{3 + 1}{2} = 2\] Therefore, the smaller value of \(x\) is \(1\). Hence, the answer is 1.
Question 12 Report
The bearing of two points Q and R from a point P are 030° and 120° respectively, lf /PQ/ = 12 m and /PR/ = 5 m, find the distance QR.
Answer Details
Question 13 Report
In the diagram above; O is the centre of the circle and |BD| = |DC|. If ?DCB = 35°, find ?BAO.
Answer Details
We can start by using the fact that the angle at the center of the circle is twice the angle at the circumference that subtends the same arc. Therefore, since |BD| = |DC|, then angle CBD = angle BDC. Also, angle COB is equal to 2*angle BDC because it subtends the same arc as angle BDC. Therefore, angle COB = 2*angle CBD. Since triangle AOB is isosceles (|OA| = |OB|), then angle BAO = angle BOA. Using the fact that the angles in a triangle sum to 180 degrees, we can write: angle BAO + angle BOA + angle COB = 180 Substituting in the expressions we derived earlier, we get: angle BAO + angle BAO + 2*angle CBD = 180 Simplifying, we get: 2*angle BAO + 2*angle CBD = 180 angle BAO + angle CBD = 90 Now we can use the fact that angle DCB = 35 degrees and |BD| = |DC| to find angle CBD: angle DCB + angle BDC + angle CBD = 180 35 + 35 + angle CBD = 180 angle CBD = 110 Substituting this value back into the earlier equation, we get: angle BAO + 110 = 90 angle BAO = 90 - 110 = -20 Since angle BAO cannot be negative, we made an error along the way. Double-checking our work, we realize that we made a mistake when substituting in the value for angle COB. It should be equal to 2*angle DCB, not 2*angle BDC. Therefore: angle COB = 2*angle DCB = 2*35 = 70 Substituting this value back into the earlier equation, we get: angle BAO + 70 = 90 angle BAO = 20 Therefore, the answer is 20 degrees.
Question 14 Report
A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]
Find the total surface area of the container
Answer Details
The total surface area of a closed cylinder consists of the area of its curved surface and the area of its two circular ends. The area of the curved surface of a cylinder is given by 2πrh, where r is the radius of the base and h is the height. The area of each circular end is given by πr^2. In this case, the radius of the cylinder is 7cm and the height is 5cm. So, Area of curved surface = 2πrh = 2 × (22/7) × 7 × 5 = 220cm^2 Area of each circular end = πr^2 = (22/7) × 7^2 = 154cm^2 Total surface area = 2 × area of circular end + area of curved surface = 2 × 154 + 220 = 308 + 220 = 528cm^2 Therefore, the total surface area of the cylinder is 528cm^2. So, the correct option is (D) 528cm^2.
Question 15 Report
Find the median of the following numbers 2.64, 2.50, 2.72, 2.91 and 2.35.
Answer Details
To find the median, we first need to arrange the numbers in order from smallest to largest: 2.35, 2.50, 2.64, 2.72, 2.91 Now, we can see that the middle number is 2.64, which is the median. Therefore, the answer is: 2.64.
Question 16 Report
Without using tables, find the value of \(\frac{\sin 20°}{\cos 70°} + \frac{\cos 25°}{\sin 65°}\)
Answer Details
Question 17 Report
In the diagram above, AB//CD, the bisector of ?BAC and ?ACD meet at E. Find the value of ?AEC
Answer Details
Since AB is parallel to CD, then we have: \begin{align*} \angle AEC &= \angle AED + \angle DEC \\ &= \frac{1}{2} \angle BAC + \frac{1}{2} \angle ACD \\ &= \frac{1}{2}(\angle BAC + \angle ACD) \\ &= \frac{1}{2}(180^\circ) \qquad \text{(because } \angle BAC + \angle ACD = 180^\circ)\\ &= 90^\circ \end{align*} Therefore, the value of $\angle AEC$ is $\boxed{90^\circ}$.
Question 18 Report
Use the graph of y = 3x\(^2\) + x - 7 above to answer the question
Find the roots of the equation y=3x\(^2\) + x - 7
Answer Details
Question 19 Report
lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y.
Answer Details
Question 20 Report
The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.
Question 21 Report
Find the value(s) of x for which the expression is undefined: \(\frac{6x - 1}{x^2 + 4x - 5}\)
Answer Details
The given expression is undefined when the denominator is equal to zero because division by zero is undefined. Therefore, we need to find the values of x that make the denominator zero. The denominator of the expression is \(x^2 + 4x - 5\). We can factor this quadratic expression as \((x + 5)(x - 1)\). So the expression is undefined when either \(x + 5\) or \(x - 1\) equals zero, since division by zero is undefined. Therefore, the values of x that make the expression undefined are \(x = -5\) or \(x = 1\). So the answer is: - -5 or 1
Question 22 Report
Express 0.000834 in standard form
Answer Details
To express a number in standard form, we write it in the form \(a \times 10^b\), where \(1 \leq a < 10\) and \(b\) is an integer. To express 0.000834 in standard form, we need to move the decimal point to the right until we obtain a number between 1 and 10. We have: $$0.000834 = 8.34 \times 10^{-4}$$ Therefore, the answer is (a) 8.34 x 10-4.
Question 23 Report
Solve the inequality: \(\frac{1}{3}(2x - 1) < 5\)
Answer Details
To solve this inequality, we need to isolate x on one side of the inequality sign. We can start by multiplying both sides by 3, which gives: 2x - 1 < 15 Next, we can add 1 to both sides: 2x < 16 Finally, we can divide both sides by 2 to get: x < 8 Therefore, the solution to the inequality is x < 8. Option (d) is the correct answer.
Question 24 Report
Two fair dice are tossed together once. Find the probability that the sum of the outcome is at least 10.
Answer Details
When two dice are tossed together, there are 6 x 6 = 36 possible outcomes. We need to find the probability that the sum of the outcome is at least 10. The only possible pairs of outcomes that sum to at least 10 are: (4, 6), (5, 5), (6, 4). Each of these pairs can occur in two different ways: (4, 6) and (6, 4), (5, 5), and (6, 4). So, there are a total of 6 possible outcomes that sum to at least 10. Therefore, the probability of getting a sum of at least 10 is 6/36, which simplifies to 1/6. Thus, the correct option is (c) 1/6.
Question 25 Report
Find the nth term Un of the A.P., 11, 4, -3,....... .
Answer Details
The given sequence is an arithmetic progression (AP) since each term is obtained by subtracting 7 from the previous term. Let the first term be a = 11, and the common difference be d = -7. The nth term of an arithmetic progression can be found using the formula: Un = a + (n - 1)d Substituting the values of a and d, we get: Un = 11 + (n - 1)(-7) Simplifying, we get: Un = 11 - 7n + 7 Un = 18 - 7n Therefore, the nth term Un of the given AP is 18 - 7n. The answer is (d) Un= 18-7n.
Question 26 Report
If \(y \propto \frac{1}{x^2}\) and x = 3 when y = 4, find y when x = 2.
Answer Details
If we have that y is proportional to \(\frac{1}{x^2}\), then we can write: y = k\(\frac{1}{x^2}\) where k is a constant of proportionality. To find k, we can use the fact that when x = 3, y = 4: 4 = k\(\frac{1}{3^2}\) Simplifying: k = 36 Now we can use k to find y when x = 2: y = k\(\frac{1}{2^2}\) y = 9 Therefore, the answer is y = 9.
Question 27 Report
A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere.
Answer Details
Question 28 Report
Solve the equation (x +2)(x - 7) = 0
Answer Details
The given equation is a quadratic equation which can be solved by factoring the left-hand side of the equation: (x + 2)(x - 7) = 0 The product of two factors is equal to zero if and only if at least one of the factors is zero. So we can set each factor to zero and solve for x: x + 2 = 0 or x - 7 = 0 Solving for x in each case gives: x = -2 or x = 7 Therefore, the solutions to the equation (x + 2)(x - 7) = 0 are x = -2 and x = 7.
Question 29 Report
A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]
What is the volume of the container?
Answer Details
The volume of a cylinder can be calculated using the formula: V = πr2h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we have: V = (22/7) x 72 x 5 V = 770 cm3 Therefore, the volume of the container is 770cm3. The answer is option (E).
Question 30 Report
Which of the following angles is an exterior angle of a regular polygon?
Answer Details
An exterior angle of a polygon is an angle formed by extending one of the sides of the polygon. For a regular polygon, all the exterior angles have the same measure, which can be found by dividing the total sum of the exterior angles (which is always 360 degrees) by the number of sides. In this case, we have a list of angles and we need to determine which one is an exterior angle of a regular polygon. We can start by dividing 360 degrees by each of the answer choices and see if any of the results match the definition of an exterior angle. - 360/95 = 3.789, which is not a whole number and therefore cannot be an exterior angle of a regular polygon. - 360/85 = 4.235, which is not a whole number and therefore cannot be an exterior angle of a regular polygon. - 360/78 = 4.615, which is not a whole number and therefore cannot be an exterior angle of a regular polygon. - 360/75 = 4.8, which is a whole number and therefore could be an exterior angle of a regular polygon. We can confirm this by checking if the sum of this angle and any of the interior angles of a regular polygon add up to 180 degrees. For example, a regular pentagon has interior angles of 108 degrees, and 75 + 108 = 183, which is not 180 degrees. Therefore, 75 degrees is not an exterior angle of a regular pentagon. - 360/72 = 5, which is a whole number and therefore could be an exterior angle of a regular polygon. Again, we can confirm this by checking if the sum of this angle and any of the interior angles of a regular polygon add up to 180 degrees. For example, a regular pentagon has interior angles of 108 degrees, and 72 + 108 = 180 degrees. Therefore, 72 degrees is an exterior angle of a regular pentagon. Therefore, the answer is: 72o.
Question 31 Report
What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, 8, 10, 9, 8 and 14?
Answer Details
The mode is the number that appears most frequently in the given set of numbers. In this case, we can see that the number 8 appears 4 times, while the other numbers appear either 2 or 1 times. Therefore, the mode of the set is 8. So, the answer is 8.
Question 32 Report
Factorize the expression x(a - c) + y(c - a)
Answer Details
Given expression is x(a - c) + y(c - a). Rearranging this expression, we get: x(a - c) - y(a - c) We can factorize (a - c) from both terms to get: (a - c)(x - y) Therefore, the factorization of the expression x(a - c) + y(c - a) is (a - c)(x - y). The correct option is (b) (a - c)(x - y).
Question 34 Report
In the diagram above, AB//CD. What is the size of the angle marked x?
Answer Details
Question 35 Report
By selling some crates of soft drinks for N600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?
Answer Details
If the dealer makes a 50% profit, it means that the selling price is 150% (100% cost price + 50% profit) of the cost price. Let the cost price of the crates of soft drinks be x. Then, 150% of x is equal to N600.00. Mathematically, we can write it as: 150/100 * x = N600.00 Simplifying the equation, we have: x = N600.00 * 100/150 x = N400.00 Therefore, the dealer paid N400.00 for the crates of soft drinks.
Question 36 Report
If log\(_{10}\) x = \(\bar{2}.3675\) and log\(_{10}\) y = \(\bar{2}.9738\), what is the value of x + y, correct lo three significant figures?
Answer Details
Question 38 Report
Find (101\(_2\))\(^2\), expressing the answer in base 2.
Answer Details
To find (1012)2, we need to square the binary number 1012. We can use the standard multiplication method taught in primary school, but we only need to remember two things: 1) 0 x anything = 0, and 2) 1 x anything = the same anything. Here's the calculation:
101 (this is 1012) x 101 (this is also 1012) ----- 101 101 --- 11001 (this is the result of (1012)2 in binary)
Therefore, the answer is 11001, which is (2510)2.
Question 39 Report
Which of the following could be the inequality illustrated in the sketch graph above?
Answer Details
Question 40 Report
The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.
Answer Details
In a rhombus, the diagonals are perpendicular bisectors of each other and they divide the rhombus into four congruent right-angled triangles. Therefore, each triangle has a base of 6cm and a height of 8cm (half the length of the diagonals). The area of each triangle is given by: Area = 1/2 x base x height = 1/2 x 6cm x 8cm = 24cm^2 Since there are four such triangles in the rhombus, the total area of the rhombus is given by: Area = 4 x 24cm^2 = 96cm^2 Therefore, the area of the rhombus is 96cm^2, which corresponds to the last option.
Question 41 Report
The mean of 20 observations in an experiment is 4, lf the observed largest value is 23, find the mean of the remaining observations.
Answer Details
To find the mean of the remaining observations, we need to subtract the largest value from the sum of all the observations and then divide it by the number of observations minus one. Number of observations = 20 Mean of 20 observations = 4 Largest value = 23 Sum of all observations = Mean x Number of observations = 4 x 20 = 80 Sum of remaining observations = Sum of all observations - Largest value = 80 - 23 = 57 Number of remaining observations = Number of observations - 1 = 20 - 1 = 19 Mean of remaining observations = Sum of remaining observations / Number of remaining observations = 57 / 19 = 3 Therefore, the mean of the remaining observations is 3. Hence, the correct option is (b) 3.
Question 42 Report
From a box containing 2 red, 6 white and 5 black balls, a ball is randomly selected. What is the probability that the selected ball is black?
Answer Details
There are a total of 2 + 6 + 5 = 13 balls in the box. Out of these, 5 are black. The probability of selecting a black ball is the number of black balls divided by the total number of balls, which is 5/13. Therefore, the answer is 5/13.
Question 43 Report
A 120° sector of a circle of radius 21cm is bent to form a cone. What is the base radius of the cone?
Answer Details