WAEC SSCE - General Mathematics - 1995 (Objective)

Question 1 Report

Given that log₂a = log₈4, find a

2^1/3

4^2/3

8 2/3

2^2/3

2³

Answer Details

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Number Bases

Logarithms

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Question 2 Report

In the diagram above, ?PRQ = 90°, ?QPR = 30° and /PQ/ = 10 cm. Find y.

6cm

5cm

4cm

3cm

2cm

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.

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Question 3 Report

Express 0.000834 in standard form

8.34 x 10^-4

8.34 x 10^-3

8.34 x 10³

8.34 x 10⁴

8.34 x 10⁶

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.

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Fractions, Decimals And Approximations

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Question 4 Report

Find the nth term Un of the A.P., 11, 4, -3,....... .

Un=19+7n

Un=19-7n

Un=18+7n

Un= 18-7n

Un= 17-7n

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.

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Sequence And Series

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Question 5 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.

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Variation

Ratio, Proportions And Rates

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Question 6 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.

13m

11m

Answer Details

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Bearings

Triangles And Polygons

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Question 7 Report

In the diagram above, the value of angles b + c is

180^o

90^o

45^o

a^o

d^o

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) 180^o.

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Read lesson note on Angles (WAEC)

Angles And Intercepts On Parallel Lines

Angles

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Question 8 Report

Find the value(s) of x for which the expression is undefined: $\frac{6x - 1}{x^2 + 4x - 5}$

+4 or+1

-5 or +1

-5 or -1

+5 or -1

$\frac{1}{6}$

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

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Algebraic Fractions

Simple Operations On Algebraic Expressions

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Question 9 Report

Solve the equation 3x$^2$ + 25x -18 = 0

-3,2

-2,3

-2,9

-9,2/3

2/3, 9.

Answer Details

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Quadratic Equations

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Question 10 Report

If three children shares N10.50 among themselves in ratio 6:7:8, how much is the largest share?

N3.00

N3.50

N4.00

N4.50

N5.00

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.

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Sine, Cosine And Tangent Of An Angle

Positive And Negative Integers, Rational Numbers

Modular Arithmetic

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Question 11 Report

Solve the inequality: $\frac{1}{3}(2x - 1) < 5$

x < - 5

X<-6

X<7

x <8

x < 16

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.

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Question 12 Report

The locus of a point which is equidistant from two given fixed points is the

perpendicular bisector of the straight line joining them

angle bisector of the straight lines joining the points to the origin

perpendiculars to the straight line joining them

parallel-line to the straight line joining them

a line making an acute angle with the line joining the two points

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.

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Loci

Statistics

Triangles And Polygons

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Question 13 Report

In the diagram above, AB//CD, the bisector of ?BAC and ?ACD meet at E. Find the value of ?AEC

30^o

45^o

60^o

75^o

90^o

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 $\boxed{90^\circ}$.

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Angles And Intercepts On Parallel Lines

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Question 14 Report

Which of the following angles is an exterior angle of a regular polygon?

95^o

85^o

78^o

75^o

72^o

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: 72^o.

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Triangles And Polygons

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Question 15 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

6 3/5cm

6 4/5cm

7 1/10cm

10 2/5cm

13 3/5cm,

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.

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Circles

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Question 16 Report

A water tank of height $\frac{1}{2}$ m has a square base of side $1\frac{1}{2}$ m. lf it is filled with water from a water tanker holding 1500 litres, how many litres of water are left in the water tanker? [1000 litres = 1m$^3$]

37.5litres

375 litres

3750 litres

37500 litres

375000 litres

Answer Details

The volume of the water tank can be calculated as follows: Volume of tank = Base area x Height = (1.5m x 1.5m) x 0.5m = 1.125 m$^3$ Since 1000 litres = 1 m$^3$, the volume of the tank is equivalent to 1,125 litres. Therefore, the amount of water left in the water tanker after filling the tank is: 1500 - 1125 = 375 litres. Hence, the answer is 375 litres.

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Positive And Negative Integers, Rational Numbers

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Question 17 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?

2/13

5/13

5/11

5/6

11/13

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.

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Probability

Surds (radicals)

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Question 18 Report

In the diagram above; O is the centre of the circle and |BD| = |DC|. If ?DCB = 35°, find ?BAO.

20^o

25^o

30^o

35^o

40^o

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.

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Circles

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Question 19 Report

The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.

24cm²

36cm²

48cm²

60cm²

96cm²

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.

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Integration

Indices

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Question 20 Report

Solve the following simultaneous equations: x+ y = 3/2; x - y = 5/2 and use your result to find the value of 2y + x

-2

-1

¹/₂

3¹/₂

Answer Details

To solve the simultaneous equations x + y = 3/2 and x - y = 5/2, we can use the method of elimination. First, we need to eliminate y. We can do this by adding the two equations: (x + y) + (x - y) = 3/2 + 5/2 Simplifying, we get: 2x = 4 Dividing both sides by 2, we get: x = 2 Now that we have solved for x, we can substitute this value into one of the original equations to solve for y. Let's use the first equation: 2 + y = 3/2 Subtracting 2 from both sides, we get: y = -1/2 So the solution to the simultaneous equations is x = 2 and y = -1/2. To find the value of 2y + x, we can simply substitute the values we found: 2y + x = 2(-1/2) + 2 = 1 Therefore, the answer is 1.

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Solution Of Linear Equations

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Question 21 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.

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Probability

Linear Inequalities

Statistics

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Question 22 Report

A 120° sector of a circle of radius 21cm is bent to form a cone. What is the base radius of the cone?

3¹/₂cm

7cm

1O¹/₂cm

14cm

21cm

Answer Details

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Circles

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Question 23 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

1.0 And -1.2

1.1and-1.3

1.4and-1.7

2.0 and -1.9

2.4 and -2.0

Answer Details

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Quadratic Equations

Graphs Of Linear And Quadratic Functions

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Question 24 Report

Two fair dice are tossed together once. Find the probability that the sum of the outcome is at least 10.

1/12

5/ 36

1/ 6

1/4

5/18

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.

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Representation Of Data

Probability

Surds (radicals)

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Question 25 Report

Find (101$_2$)$^2$, expressing the answer in base 2.

10101

11001

10010

11101

10110

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.

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Number Bases

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Question 26 Report

In the diagram above, PQ is parallel to TU, ?PQR = 50°, ?QRS = 86° and ?STU = 64°. Calculate the value of x.

136^o

120^o

108^o

100^o

96^o

Answer Details

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Question 27 Report

The positions of two countries P and Q are (15°N, 12°E) and (65°N, 12°E) respectively. What is the difference in latitude?

104^o

100^o

80^o

50^o

24^o

Answer Details

Latitude is a measure of the north-south position of a point on the Earth's surface, measured in degrees from the Equator. In this case, country P is located at 15°N and country Q is located at 65°N. To find the difference in latitude between the two countries, we simply subtract the latitude of P from the latitude of Q: Difference in latitude = 65°N - 15°N = 50°N Therefore, the answer is 50°.

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Circles

Angles

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Question 28 Report

Use the graph of y = 3x$^2$ + x - 7 above to answer the question

What is the minimum value of y?

-10

-7

-4

-1

Answer Details

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Quadratic Equations

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Question 29 Report

Solve the equation (x +2)(x - 7) = 0

x = 1 or 8

x = -2 or 7

x = -4 or 5

x = -3 or 6

x= -5 or -2

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.

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Solution Of Linear Equations

Quadratic Equations

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Question 30 Report

Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. [Take π = 22/7]

37 5/7cm²

66cm²

75 3/7cm²

78 2/7cm²

88cm²

Answer Details

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Question 31 Report

A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere.

3cm

6cm

9cm

12cm

More information is needed

Answer Details

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Question 32 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?

O.117

0.118

0.903

O.944

0.946

Answer Details

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Logarithms

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Question 33 Report

Find the median of the following numbers 2.64, 2.50, 2.72, 2.91 and 2.35.

2.91

2.72

2.64

2.50

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.

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Representation Of Data

Measures Of Location

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Question 34 Report

If R = [2, 4, 6, 7] and S = [1, 2, 4, 8], then R∪S equal

[1,2,4,6,7,8]

[1,2,4,7,8]

[1,4.7,8]

[2.6.7]

[2.4]

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].

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Sets

Ratio, Proportions And Rates

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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?

N1,200.00

N900.00

N450.00

N400.00

N200.00

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.

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Financial Arithmetic

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Question 36 Report

In the diagram above, AB//CD. What is the size of the angle marked x?

103^o

93^o

77^o

62^o

52^o

Answer Details

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Angles And Intercepts On Parallel Lines

Angles

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Question 37 Report

In the diagram above. |AB| = 12cm, |AE| = 8cm, |DCl = 9cm and AB||DC. Calculate |EC|

10cm

9cm

8cm

7cm

6cm

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.

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Volumes

Triangles And Polygons

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Question 38 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?

35cm³

154cm³

220cm³

528cm³

770cm³

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).

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Volumes

Number Bases

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Question 39 Report

The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.

12cm

15cm

18cm

24cm

30cm

Answer Details

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Mensuration

Areas

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Question 40 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

35cm³

154cm³

220cm²

528cm²

770cm²

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.

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Question 41 Report

lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y.

9/16

3/4

4/3

16/6

Answer Details

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Sequence And Series

Progression

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Question 42 Report

In the diagram above, AO is perpendicular to OB. Find x

7.5^o

15^o

22.5^o

30^o

38.6^o

Answer Details

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Loci

Euclidean Geometry

Coordinate Geometry

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Question 43 Report

Without using tables, find the value of $\frac{\sin 20°}{\cos 70°} + \frac{\cos 25°}{\sin 65°}$

-1

-2

Answer Details

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Sine, Cosine And Tangent Of An Angle

Trigonometry

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Question 44 Report

In ?ABC above, BC is produced to D, /AB/ = /AC/ and ?BAC = 50^o. Find ?ACD

50^o

60^o

65^o

100^o

115^o

Answer Details

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Question 45 Report

Which of the following could be the inequality illustrated in the sketch graph above?

y?2x+3

y?-3x+3

y < 3x+2

y?x +3

y?3x+2.

Answer Details

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Linear Inequalities

Progression

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Question 46 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.

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Solution Of Linear Equations

Quadratic Equations

Graphs Of Linear And Quadratic Functions

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Question 47 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.

2.85

2.60

2.56

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.

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Measures Of Location

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Question 48 Report

Factorize the expression x(a - c) + y(c - a)

(a - c)(y - x)

(a - c)(x - y)

(a + c)(x - y)

(a + c)(x + y)

(a - c)(x + y)

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).

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Algebraic Expressions

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