WAEC SSCE - General Mathematics - 2018 (Objective)

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To find x : z, we need to have a common ratio between x, y, and z. We can use the given ratios to find a common ratio involving all three. Since x : y = 1/4 : 3/8, we can simplify this ratio by multiplying both terms by 8 to get: x : y = 2 : 3 Similarly, since y : z = 1/3 : 4/9, we can simplify this ratio by multiplying both terms by 3 to get: y : z = 1 : 4/3 Now we have a common ratio of y between the two ratios. We can use this common ratio to find x : z by multiplying the two simplified ratios: x : y = 2 : 3 y : z = 1 : 4/3 Multiplying these ratios gives: x : z = (2/3) * (1/(4/3)) = 2/4 = 1/2 Therefore, x : z = 1 : 2. In summary, x : z = 1 : 2.

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To calculate the probability that a team selected at random scored either 4 or 7 goals, we need to add the frequency of teams that scored 4 goals to the frequency of teams that scored 7 goals and divide by the total number of teams (25). From the table, we can see that 6 teams scored 4 goals and 3 teams scored 7 goals. Therefore, the total number of teams that scored either 4 or 7 goals is: 6 + 3 = 9 The total number of teams in the competition is 25. Therefore, the probability that a team selected at random scored either 4 or 7 goals is: 9/25 This can be simplified as follows: 9/25 = 0.36 Therefore, the probability that a team selected at random scored either 4 or 7 goals is 0.36 or 36%. Hence, the correct option is: - \(\frac{9}{25}\)

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The area of the rectangle WXYZ is 8cm * 6cm = 48 cm\(^2\). The shaded part is made up of four congruent triangles, each of which has an area of 1/2 * base * height = 1/2 * 4cm * 3cm = 6 cm\(^2\). So the total area of the shaded part is 4 * 6 cm\(^2\) = 24 cm\(^2\). The area of the part of the rectangle that is not shaded is 48 cm\(^2\) - 24 cm\(^2\) = 24 cm\(^2\).

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In this question, we are asked to find the value of x for which \(32_{four} = 22_x\). We know that \(32_{four}\) means 3 fours plus 2 ones, which is equal to 14 in the decimal system. So, we have: $$14_{10} = 2\times x^1 + 2\times x^0 = 2x+2$$ Now we can solve for x: $$14_{10} = 2x+2$$ $$12_{10} = 2x$$ $$x = 6_{10}$$ Therefore, \(32_{four} = 22_6\) and the value of x is 6.

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We are given that the curve passes through the points \((-2, 0)\) and \((3, 0)\). Since the curve is a function of \(x\), we can assume that the equation of the curve is of the form \(y = f(x)\). If the curve passes through the point \((-2, 0)\), then we can substitute \(x = -2\) and \(y = 0\) into the equation of the curve to get: $$ 0 = f(-2) $$ Similarly, if the curve passes through the point \((3, 0)\), then we can substitute \(x = 3\) and \(y = 0\) into the equation of the curve to get: $$ 0 = f(3) $$ Therefore, the curve must have at least two roots, namely \(x = -2\) and \(x = 3\). This suggests that the curve is a quadratic function. We can use the information about the roots of the curve to write the equation of the curve in factored form: $$ y = A(x + 2)(x - 3) $$ where \(A\) is a constant. Since the coefficient of \(x^2\) in the equation is 1, we can simplify this equation to: $$ y = Ax^2 + Bx + C $$ where \(A = 1\), and \(B\) and \(C\) are constants. To find the values of \(B\) and \(C\), we can substitute the points \((-2, 0)\) and \((3, 0)\) into the equation: $$ 0 = A(-2)^2 + B(-2) + C \quad \text{and} \quad 0 = A(3)^2 + B(3) + C $$ Simplifying these equations, we get: $$ 4A - 2B + C = 0 \quad \text{and} \quad 9A + 3B + C = 0 $$ We can use these two equations to solve for \(B\) and \(C\). Adding the two equations, we get: $$ 13A + B = 0 $$ Substituting this expression for \(B\) into one of the previous equations, we get: $$ 4A - 2(-13A) + C = 0 $$ Simplifying, we get: $$ 20A + C = 0 $$ Solving these two equations simultaneously, we get: $$ A = \frac{1}{13}, \quad B = -\frac{4}{13}, \quad C = 0 $$ Therefore, the equation of the curve is: $$ y = \frac{1}{13}(x + 2)(x - 3) = \frac{1}{13}(x^2 - x - 6) $$ So the correct answer is \(y = x^2 - x - 6\).

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To find the value of p, we need to determine the slope of the line passing through the two given points. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1) Using the coordinates of the given points, we get: slope = (-2 - 2) / (-8 - 4) = -4 / (-12) = 1/3 Since the equation of the line is given as 3y = px + q, we can rewrite this equation in slope-intercept form, y = (p/3)x + (q/3), by dividing both sides by 3. The slope of the line in slope-intercept form is then (p/3). Since we know the slope of the line passing through the two given points is 1/3, we can set these two expressions equal to each other and solve for p: (p/3) = 1/3 Multiplying both sides by 3, we get: p = 1 Therefore, the value of p is 1.

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The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius and h is the height of the cylinder. In this question, we are given that the height of the cylindrical tank is 10m and its volume is 385 m². Therefore, we can find the radius of the cylinder as follows: 385 = πr² × 10 r² = 38.5/π r = √(38.5/π) = 3.5m (approximately) Finally, we can find the diameter of the cylinder by doubling the radius: Diameter = 2r = 2 × 3.5 = 7m Therefore, the diameter of the tank is 7m.

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To find the distance between two points M(-3, 8) and N(5, -7), we use the distance formula: |MN| = √[(x₂ - x₁)² + (y₂ - y₁)²] where (x₁, y₁) and (x₂, y₂) are the coordinates of M and N, respectively. Substituting the values, we get: |MN| = √[(5 - (-3))² + (-7 - 8)²] |MN| = √[(5 + 3)² + (-15)²] |MN| = √[8² + 15²] |MN| = √(64 + 225) |MN| = √289 |MN| = 17 Therefore, the distance |MN| between the two points is 17 units. So, the correct option is "17 units".

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To find the value of x, we need to use the given information that the mean of 1, 3, 5, 7, and x is 4. The mean of a set of numbers is found by adding up all the numbers in the set and then dividing by the total number of numbers. So, we can write an equation: (1 + 3 + 5 + 7 + x) / 5 = 4 To solve for x, we can first simplify the equation by multiplying both sides by 5: 1 + 3 + 5 + 7 + x = 20 Then, we can solve for x by subtracting the sum of the known numbers from both sides: x = 20 - (1 + 3 + 5 + 7) x = 20 - 16 x = 4 Therefore, the value of x is 4.

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The graph of y = x\(^2\) and y = x intersect at two points where the two curves have the same y-value. To find these points, we need to find the x-values where x\(^2\) = x. We can start by subtracting x from both sides: x\(^2\) - x = 0 Next, we can factor out x: x (x - 1) = 0 This equation tells us that either x = 0 or x - 1 = 0. So, the two points of intersection are (0, 0) and (1, 1).

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To simplify this expression, we need to follow the order of operations (PEMDAS): 1. First, we perform the multiplication of the mixed numbers: 2\(\frac{1}{4} \times 3\frac{1}{2} = \frac{9}{4} \times \frac{7}{2} = \frac{63}{8}\) 2. Then, we perform the division of the mixed numbers: 4 \(\frac{3}{8} = \frac{35}{8}\) \(\frac{63}{8} \div \frac{35}{8} = \frac{63}{8} \times \frac{8}{35} = \frac{9}{5} =\) 1\(\frac{4}{5}\) Therefore, the answer is option (D), 1\(\frac{4}{5}\).

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To simplify \(\frac{2-18m^2}{1+3m}\), we need to factor the numerator and denominator. First, we can factor out a 2 from the numerator: \[\frac{2-18m^2}{1+3m} = \frac{2(1-9m^2)}{1+3m}\] Next, we can factor the numerator further using the difference of squares formula: \[\frac{2(1-9m^2)}{1+3m} = \frac{2(1-3m)(1+3m)}{1+3m}\] Finally, we can cancel out the common factor of \((1+3m)\) in the numerator and denominator: \[\frac{2(1-3m)(1+3m)}{1+3m} = 2(1-3m)\] Therefore, the simplified form of \(\frac{2-18m^2}{1+3m}\) is \(2(1-3m)\).

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The given equation relates the temperature in degrees Celsius (C) to the temperature in degrees Fahrenheit (F). To find C when F = 98.6, we can simply substitute F = 98.6 into the equation and solve for C. So, we have: F = \(\frac{9}{5}\)C + 32 98.6 = \(\frac{9}{5}\)C + 32 (substituting F = 98.6) Subtracting 32 from both sides, we get: 66.6 = \(\frac{9}{5}\)C Multiplying both sides by 5/9, we get: C ≈ 37 Therefore, C is approximately equal to 37 degrees Celsius (not exactly any of the options provided).

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We are given that there are 250 boys and 150 girls in a school. We are also given that 60% of the boys play football, which means that 0.6 x 250 = 150 boys play football. Similarly, 40% of the girls play football, which means that 0.4 x 150 = 60 girls play football. Therefore, the total number of students who play football is 150 + 60 = 210. To find the percentage of the school that plays football, we need to divide the number of students who play football by the total number of students in the school and multiply by 100. The total number of students in the school is 250 + 150 = 400. So, the percentage of the school that plays football is (210/400) x 100 = 52.5%. Therefore, the correct option is 52.5% (option D).

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To solve for x, we can use the following steps: 1. Rewrite the equation using exponential form: 10^(log(6x - 4) - log(2)) = 10^1 2. Use the fact that log(a) - log(b) = log(a/b) to simplify the equation: 10^(log((6x - 4) / 2)) = 10^1 3. Use the definition of logarithms to simplify the equation: (6x - 4) / 2 = 10 4. Solve for x by multiplying both sides of the equation by 2 and then subtracting 4 from both sides: 6x - 4 = 20, 6x = 24, and x = 4 So, the solution to the equation is x = 4.

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To find the value of t, we need to use the information given in the diagram. In a triangle, the sum of all angles is 180 degrees. So, if we know two angles, we can find the third one by subtracting their sum from 180. In this case, we know the angles labeled x and y. So, to find t, we can add x and y and then subtract the sum from 180. That is, t = 180 - (x + y). So, the value of t is 126 degrees.

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To find the median of a set of numbers, we first need to arrange them in order from smallest to largest or largest to smallest. In this case, the numbers are: 0, 0, 1, 1, 1, 2, 2, 3, 4 Next, we determine the middle value(s) of the set. If the set has an odd number of values, there will be one middle value. If the set has an even number of values, there will be two middle values, and the median is the average of these two values. In this case, the set has an even number of values (10), so there are two middle values: 1 and 1. To find the median, we take the average of these two values: (1 + 1)/2 = 1 Therefore, the median of the set {2, 1, 0, 3, 1, 1, 4, 0, 1, 2} is 1. So the answer is 1.0.

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We can solve this problem using trigonometry, specifically the tangent function. Let's draw a diagram to visualize the situation. We have a right triangle with the height of the tree as one of the legs, the distance from the tree to the point on the ground as the other leg, and the angle of elevation (30 degrees) as the angle opposite the height of the tree.  We can use the tangent function to find the height of the tree: $$\tan(30^\circ) = \frac{\text{height of tree}}{27\text{ m}}$$ We know that the tangent of 30 degrees is equal to 1/\(\sqrt{3}\) (or approximately 0.577), so we can substitute that in and solve for the height of the tree: $$\frac{1}{\sqrt{3}} = \frac{\text{height of tree}}{27\text{ m}}$$ Multiplying both sides by 27 m gives: $$\text{height of tree} = \frac{27\text{ m}}{\sqrt{3}} = 9\sqrt{3}\text{ m}$$ Therefore, the height of the tree is 9\(\sqrt{3}\) meters. Answer option (D) is correct.

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To find the value of (x + y), we need to solve for x and y first. We can do this by using two equations: y + 2x = 4 and y - 3x = -1. First, we can isolate y in one of the equations by adding or subtracting the other equation. For example, if we add the two equations, we get: 2y = 3 Then, we can solve for y by dividing both sides by 2: y = 3/2 Next, we can substitute the value of y back into one of the original equations to solve for x. For example, using the equation y + 2x = 4: 3/2 + 2x = 4 Subtracting 3/2 from both sides: 2x = 7/2 And finally, dividing both sides by 2: x = 7/4 Now that we have found the values of x and y, we can add them to find (x + y): x + y = 7/4 + 3/2 Combining the fractional terms: x + y = 7/4 + 6/4 And finally, adding the whole numbers: x + y = 13/4 = 3.25 So, (x + y) is approximately equal to 3.

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The formula for the surface area of a sphere is \(4\pi r^2\), where \(r\) is the radius of the sphere. Given that the surface area of the sphere is \(\frac{792}{7} cm^2\) and \(\pi = \frac{22}{7}\), we can set up an equation: $$ 4\left(\frac{22}{7}\right)r^2 = \frac{792}{7} $$ Simplifying this equation by canceling out the \(7\)s, we get: $$ 4\left(\frac{22}{1}\right)r^2 = 792 $$ Multiplying both sides by \(\frac{1}{4}\) to isolate \(r^2\), we get: $$ \left(\frac{22}{1}\right)r^2 = 198 $$ Dividing both sides by \(\frac{22}{1}\), we get: $$ r^2 = 9 $$ Taking the square root of both sides, we get: $$ r = 3 $$ Therefore, the radius of the sphere is 3 cm. The formula for the volume of a sphere is \(\frac{4}{3}\pi r^3\). Substituting the value of \(r\) into this formula, we get: $$ \frac{4}{3}\left(\frac{22}{7}\right)(3)^3 \approx 113 $$ Therefore, the volume of the sphere is approximately 113\(cm^3\). So the correct answer is 113\(cm^3\).

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Since O is the midpoint of WZ and the diameter of the semicircle, it follows that O lies on the circumference of the semicircle. Let angle WOZ be m. Then angle WXY is also m, since |WX| = |XY|. Similarly, angle YXZ is also m. Since the sum of angles in a triangle is 180 degrees, we have: angle WXY + angle YXZ + angle WYZ = 180 degrees Substituting m for angle WXY and angle YXZ, we get: 2m + angle WYZ = 180 degrees Since WXYZ is a trapezium, we have: angle WYZ + angle WXY = 180 degrees Substituting m for angle WXY, we get: angle WYZ + m = 180 degrees Combining this equation with the previous one, we get: 2m + angle WYZ = angle WYZ + m + 180 degrees Simplifying, we get: m = 60 degrees Therefore, the value of m is 60 degrees.

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