WAEC SSCE - General Mathematics - 1996 (Objective)

Question 1 Report

In the diagram above, AB, CD and XY are straight lines intersecting at W. Find ?CWX

20^o

80^o

100^o

120^o

140^o

Answer Details

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Question 2 Report

In the diagram above, PQ is a tangent to the circle MTN at T. What is the size of ?MTN?

52^o

54^o

66^o

72^o

128^o

Answer Details

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Circles

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Question 3 Report

Each interior angle of a regular nonagon(nine sided polygon) is equal to

160^o

144^o

140^o

132^o

36^o

Answer Details

A nonagon has nine sides and nine interior angles. In a regular nonagon, all the sides and angles are equal. To find the measure of each interior angle of a regular nonagon, we can use the formula: Interior angle = (n - 2) x 180° / n where n is the number of sides of the polygon. Substituting n = 9 in the formula, we get: Interior angle = (9 - 2) x 180° / 9 = 7 x 20° = 140° Therefore, each interior angle of a regular nonagon is equal to 140°. So the correct answer is option (C) 140^o.

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Euclidean Geometry

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Question 4 Report

The trapezium PQRS parallel to SR,?PQS = 34^o and ?SPQ = 2 ?SRQ. Find the size of, SQR

58^o

68^o

78^o

90^o

112^o

Answer Details

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Question 5 Report

Make p the subject if formula y =

a + p/a - p

2a + y/a + y

= p

ay - y/y + 1

= p

a(y -1)/y + 1

= p

ay/y + 1

= p

2y -1/y - 1

= p

Answer Details

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Solution Of Linear Equations

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Question 6 Report

A town P is 150km from a town Q in the direction 050^o. What is the bearing of Q from P?

050^o

130^o

230^o

270^o

310^o

Answer Details

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Bearings

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Question 7 Report

The angle of elevation of the top X of a vertical pole from a point P on a level ground is 60^o. The distance from P to the foot of the pole is 55m. Without using tables, find the height of the pole.

50/3m

50m

55√3m

60m

65m

Answer Details

We can use trigonometry to solve this problem. Let's draw a diagram to help us visualize the situation:

We know that the angle of elevation of X from P is 60 degrees, which means that the angle XPX' is also 60 degrees, where X' is the foot of the pole. We also know that the distance from P to X' is 55m.

Let H be the height of the pole. Then we have:

tan 60 = H / PX'

We can simplify this expression using trigonometric ratios:

√3 = H / 55

Solving for H, we get:

H = 55√3

Therefore, the height of the pole is 55√3 meters. So the correct option is (c).

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Bearings

Angles Of Elevation And Depression

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Question 8 Report

Find, correct to 1 decimal place, the volume of cylinder of height 8cm and base radius 3cm. [Take π = 3.142]

503.0cm³

300.0cm³

250.0cm³

226.2cm³

150.9cm³

Answer Details

The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base of the cylinder and h is the height of the cylinder. Substituting the given values in the formula, we have: V = π(3cm)²(8cm) V = 72π cm³ V ≈ 226.1cm³ (rounded to 1 decimal place, using π ≈ 3.142) Therefore, the correct option is (D) 226.2cm³.

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Question 9 Report

The marks obtained by pupils of class are grouped as shown below; 0 - 4, 5 - 9,10 -14, 15 -19. Which of the following is/are not true? l. The mid values of the grouped marks are 2, 7, 12 and 17. II The class interval is 4. III The class boundaries are 0.5, 4.5, 9.5, 14.5 and 19.5

I only

II only

III only

I and II only

II and III only

Answer Details

The mid values of the grouped marks can be found by taking the average of the upper and lower limits of each class interval. For example, the mid value of the first class interval (0 - 4) is (0+4)/2 = 2. Similarly, the mid values of the other class intervals can be calculated as 7, 12, and 17. The class interval is the difference between the upper limit of a class interval and the lower limit of the previous class interval. For example, the class interval between 0-4 and 5-9 is 5-4 = 1. The class interval in this case is not 4, but rather it is 5-0 = 5. The class boundaries are the values that separate one class interval from another. They are found by adding and subtracting half of the class interval from the upper and lower limits of each class interval. For example, the lower class boundary of the first class interval (0 - 4) is 0 - 0.5 = -0.5, and the upper class boundary of the second class interval (5 - 9) is 9 + 0.5 = 9.5. Therefore, the class boundaries for the given grouped marks are -0.5, 4.5, 9.5, 14.5, and 19.5. Therefore, the statement that is not true is II only, since the class interval is not 4. The correct class interval is 5, as explained above. So the answer is (B) II only.

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Sets

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Question 10 Report

Simplify: \((2\frac{1}{6} - 1\frac{2}{3}) \div 2\frac{2}{3}\).

3/16

7/16

1 13/24

2 11/24

10 2/5

Answer Details

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Fractions, Decimals And Approximations

Positive And Negative Integers, Rational Numbers

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Question 11 Report

A bag contains 3 red, 4 black and 5 green identical balls. Two balls are picked at random, one after the other without replacement. Find the probability that one is red and the other is green

2/3

5/11

5/22

5/24

5/48

Answer Details

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Probability

Surds (radicals)

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Question 12 Report

The angle of a sector of a circle of radius 35cm is 288^o. Find the perimeter of the sector. [Take π = 22/7]

246cm

211cm

141cm

114cm

44cm

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Circles

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Question 13 Report

The 6th term of a G.P is -2 and its first term is 18. What is the common ratio?

-¹/₂

-1/3

1/4

Answer Details

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Sequence And Series

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Question 14 Report

Solve the equation

4/a

1/5a

= 3

2¹/₅

1²/₅

1¹/₃

1⁴/₁₅

¹/₃

Answer Details

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Solution Of Linear Equations

Quadratic Equations

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Question 15 Report

M varies directly as n and inversely as the square of p. If M = 3, when n = 2 and p = 1, find M in terms of n and p.

M = 2n/3p

M = 3n²/2p²

M = n²/2p

M = 3n/2p²

M = 2n/3p²

Answer Details

We are given that "M varies directly as n and inversely as the square of p." This means that M is directly proportional to n and inversely proportional to the square of p. We can represent this relationship mathematically as: M ∝ n/p^2 where the symbol ∝ means "is proportional to". We are also given that M = 3 when n = 2 and p = 1. We can use this information to find the constant of proportionality k: M ∝ n/p^2 3 ∝ 2/1^2 3 ∝ 2 To find k, we can write: M = k(n/p^2) Substituting the values we know: 3 = k(2/1^2) k = 3/2 Now we can use k to find M in terms of n and p: M = (3/2)(n/p^2) Simplifying, we get: M = (3n)/(2p^2) Therefore, the answer is option D: M = 3n/2p^2.

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Sine, Cosine And Tangent Of An Angle

Variation

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Question 16 Report

In the diagram above, TRQ is a straight line. Find p, if p = 1/3(a + b + c)

45^o

60^o

90^o

120sup>o

150^o

Answer Details

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Solution Of Linear Equations

Number Bases

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Question 17 Report

Two angles (a + 31) and (b - 49^o) are adjacent angles on a straight line. Which of the following is true

a + b = 198^o

a + b = 180^o

a + b = 162^o

a + b = 100^o

a + b = 80^o

Answer Details

We are given that the angles (a + 31) and (b - 49) are adjacent angles on a straight line. When two adjacent angles form a straight line, they add up to 180 degrees. This is known as the straight angle theorem. Therefore, we can write: (a + 31) + (b - 49) = 180 Simplifying the expression, we get: a + b - 18 = 180 Adding 18 to both sides, we get: a + b = 198 Therefore, the sum of the angles a and b is 198 degrees. Hence, the answer is: a + b = 198°.

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Angles And Intercepts On Parallel Lines

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Question 18 Report

If 3p - q = 6 and 2p + 3q = 4, find q

¹/₂

2/3

3³/₇

Answer Details

To find the value of q, we need to solve the given system of equations:

3p - q = 6 ...(1)

2p + 3q = 4 ...(2)

One way to solve this system is to use the method of elimination, where we eliminate one of the variables by adding or subtracting the equations.

Multiplying equation (1) by 3, we get:

9p - 3q = 18 ...(3)

Now, we can eliminate q by adding equations (2) and (3):

2p + 3q = 4

9p - 3q = 18

-----------

11p = 22

Dividing both sides by 11, we get:

p = 2

Substituting this value of p in equation (1), we get:

3(2) - q = 6

Simplifying this, we get:

6 - q = 6

Subtracting 6 from both sides, we get:

-q = 0

Dividing both sides by -1, we get:

q = 0

Therefore, q = 0 is the solution of the given system of equations.

In summary, to find the value of q, we used the method of elimination by multiplying equation (1) by 3 and adding it to equation (2) to eliminate q. This resulted in finding the value of p as 2. Substituting this value of p in equation (1), we found the value of q as 0.

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Solution Of Linear Equations

Algebraic Expressions

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Question 19 Report

The table gives the distribution of outcomes obtained when a die was rolled 100 times.

What is the experimental probability that it shows at most 4 when rolled again?

8/25

12/25

13/25

2/3

17/25

Answer Details

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Integration

Probability

Sets

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Question 20 Report

Factorize 32x³ - 8xy²

4(4x + y)(2x - y)

(16x - y)(2x + y)

8x(2x - y)

8x(2x + y)(2x - y)

4(2x + y)(4x - y)

Answer Details

We can factorize the given expression by first finding the greatest common factor (GCF) of the two terms, which is 8x. We can factor out the GCF from the given expression as: 32x³ - 8xy² = 8x(4x² - y²) We can then use the identity a² - b² = (a + b)(a - b) to factorize the expression further: 8x(4x² - y²) = 8x(2x + y)(2x - y) Therefore, the fully factorized form of 32x³ - 8xy² is 8x(2x + y)(2x - y). So, the correct option is: - 8x(2x + y)(2x - y)

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Polynomials

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Question 21 Report

Simplify: \(\frac{5}{x - y} - \frac{4}{y - x}\)

9/x - y

9/y - x

1/x - y

1/y - x

y - 9x/x - y

Answer Details

To simplify \(\frac{5}{x-y}-\frac{4}{y-x}\), we first notice that \(y-x=-(x-y)\). Thus, we can rewrite the expression as \(\frac{5}{x-y}+\frac{4}{x-y}\). Now, we can combine the fractions by finding a common denominator, which is \(x-y\). Thus, we have \[\frac{5}{x-y}+\frac{4}{x-y}=\frac{5+4}{x-y}=\frac{9}{x-y}.\] Therefore, the simplified expression is \(\boxed{\frac{9}{x-y}}\).

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Algebraic Fractions

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Question 22 Report

If sin\(\theta\) cos\(\theta\), for 0^o \(\leq\) θ \(\leq\) 360^o, find the value of \(\theta\)

45^o, 225^o

135^o, 315^o

45^o, 315^o

135^o, 225^o

45^o, 135^o

Answer Details

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Introductory Calculus

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Question 23 Report

A boy measured the length and breath of a rectangular lawn as 59.6m and 40.3m respectively instead of 60m and 40m. What is the percentage error in his calculation of the perimeter of the lawn?

10%

1.4%

0.2%

0.1%

Answer Details

The correct perimeter of the rectangular lawn can be calculated by adding twice the length and twice the breadth, i.e., 2 × length + 2 × breadth = 2 × 60m + 2 × 40m = 120m + 80m = 200m The perimeter calculated by the boy would be: 2 × 59.6m + 2 × 40.3m = 119.2m + 80.6m = 199.8m The difference between the correct perimeter and the calculated perimeter is: 200m - 199.8m = 0.2m To find the percentage error, we divide the difference by the correct perimeter and multiply by 100: (0.2m / 200m) × 100% = 0.1% Therefore, the percentage error in the boy's calculation of the perimeter of the lawn is 0.1%. The correct option is: 0.1%.

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Percentages

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Question 24 Report

Simplufy Log₁₀4 + Log₁₀25

Answer Details

Using the logarithmic identity Log_b(MN) = Log_bM + Log_bN, we can simplify Log₁₀4 + Log₁₀25 as follows: Log₁₀4 + Log₁₀25 = Log₁₀(4 x 25) = Log₁₀100 Since 100 is 10 raised to the power of 2, we can rewrite this as: Log₁₀100 = Log₁₀(10²) = 2 Therefore, the simplified expression is 2.

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Logarithms

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Question 25 Report

In the diagram above, find x correct to the nearest degree

15^o

25^o

26^o

36^o

72^o

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Trigonometry

Circles

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Question 26 Report

If x is a real number which of the following is more illustrated on the number line?

x < 4

x > -2

-2 < x ? 4

-3 ? x < 4

-2 ? x < 4

Answer Details

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Bearings

Linear Inequalities

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Question 27 Report

What percentage of observation lie outside interquartile range of any distribution?

12¹/₂%

25%

50%

62¹/₂ %

75%

Answer Details

The interquartile range (IQR) is the range between the first quartile (25th percentile) and the third quartile (75th percentile) of a distribution. Half of the observations lie within this range, which means that the other half lie outside of it. Therefore, the percentage of observations that lie outside the IQR is 100% - 50% = 50%. So, the answer is 50%.

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Sine, Cosine And Tangent Of An Angle

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Question 28 Report

The graph of 2y = 5x² - 3x² - 2 cuts the y axis at the point

(1,0)

(-2/5, 0)

(0, -1)

(0, -2)

(0, 1)

Answer Details

To find where the graph of the equation 2y = 5x² - 3x² - 2 intersects the y-axis, we substitute x = 0 and solve for y: 2y = 5(0)^2 - 3(0)^2 - 2 2y = -2 y = -1 Therefore, the graph of the equation intersects the y-axis at the point (0, -1). Hence, the correct option is (c) (0, -1).

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Quadratic Equations

Graphs Of Linear And Quadratic Functions

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Question 29 Report

In the diagram above, ?SPQ = 79^o. Find ?SRQ

11^o

39¹/₂

79^o

90^o

101^o

Answer Details

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Angles

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Question 30 Report

In the diagram above, /PQ/ = /PS/ and /QR/ = /SR/. Which of the following is/are true? i. the line PR bisects ?QRS ii. The line PR is the perpendicular bisector of the line segment QS iii. Every point on PR is equidistant from SP and QP

I only

III only

I and II only

I and III only

I, II and III

Answer Details

Given that /PQ/ = /PS/ and /QR/ = /SR/, we can see that triangle QPR and SPR are congruent by the Side-Side-Side (SSS) criterion. Hence, we have ∠QPR = ∠SPR and ∠PQR = ∠PSR. i. From the above statement, we can say that the line PR bisects ∠QRS and ∠QSR, but it does not necessarily bisect the whole angle ∠QSRQ. Hence, statement (i) is true. ii. As triangle QPR and SPR are congruent, we can say that /QP/ = /SP/ and /QR/ = /SR/. Hence, the line PR is the perpendicular bisector of the line segment QS. Therefore, statement (ii) is also true. iii. Every point on the perpendicular bisector of a line segment is equidistant from the endpoints of the line segment. As we have already proved that line PR is the perpendicular bisector of the line segment QS, every point on PR is equidistant from SP and QP. Hence, statement (iii) is true. Therefore, all the three statements are true, and the correct answer is (v) I, II and III.

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Polynomials

Triangles And Polygons

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Question 31 Report

Find the 9th term of the arithmetic progression 18, 12, 6, 0, -6 .........

-54

-30

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Sequence And Series

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Question 32 Report

two towns X and Y both on latitude 60^oS have longitude 27^oE and 33^oW respectively. Find to the nearest kilometers, the distance between X and Y measured along the parallel of latitude. [Take 2πR = 4 x 10⁴km, where R is the Radius of the earth]

28850km

16667km

8333km

6667km

3333km

Answer Details

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Coordinate Geometry

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Question 33 Report

If tan x = \(2\frac{2}{5}\), find the value of sin x; 0 \(\leq\) x \(\leq\) 90^o

5/13

5/12

144/169

12/13

13/12

Answer Details

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Sine, Cosine And Tangent Of An Angle

Trigonometry

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Question 34 Report

The roots of a quadratic equation are -¹/₄ and 3. The quadratic equation is

4x² - 13x - 3 = 0

4x² - 11x - 3 = 0

4x² + 11x - 3 = 0

3x² - 11x - 3 = 0

3x² - 11x + 3 = 0

Answer Details

We know that if a quadratic equation has roots α and β, then the equation can be written as: (x - α)(x - β) = 0 Expanding the above expression, we get: x² - (α + β)x + αβ = 0 Here, the roots of the quadratic equation are -¹/₄ and 3. Therefore, α = -¹/₄ and β = 3. Substituting these values in the above equation, we get: x² - (α + β)x + αβ = 0 x² - (-¹/₄ + 3)x + (-¹/₄ × 3) = 0 x² - ¹¹/₄ x - ³/₄ = 0 Hence, the quadratic equation is 4x² - 11x - 3 = 0. Therefore, the correct option is: 4x² - 11x - 3 = 0

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Quadratic Equations

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Question 35 Report

Simplify 56x\(^{-4}\) \(\div\) 14x\(^{-8}\)

2x^-12

3x^-3

4x^-4

4x^-3

4x⁴

Answer Details

To simplify the expression, we can use the rule of dividing powers with the same base. We divide the coefficients and subtract the exponents: 56x^-4 ÷ 14x^-8 = (56/14)x^(-4)-(-8) = 4x^-4+8 = 4x⁴ Therefore, the simplified expression is 4x⁴.

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Solution Of Linear Equations

Indices

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Question 36 Report

The number of goals scored by a football team in 20 matches is shown in the table above

What is the mean goal scored?

0.75

1.75

1.9

2.15

Answer Details

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Linear Inequalities

Euclidean Geometry

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Question 37 Report

The cumulative frequency curve may be used to find the

variance

standard deviation

mode

median

mean

Answer Details

The cumulative frequency curve can be used to find the median. A cumulative frequency curve represents the cumulative frequencies of a dataset in ascending order, with the class boundaries on the x-axis and the cumulative frequency on the y-axis. To find the median from a cumulative frequency curve, we need to locate the point on the curve where the cumulative frequency is half of the total frequency. This point will correspond to the median class, and we can then use the formula for finding the median of grouped data to calculate the exact value of the median. Therefore, the answer is median.

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Fractions, Decimals And Approximations

Percentages

Number Bases

Sets

Inequalities

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Question 38 Report

The number of goals scored by a football team in 20 matches is shown in the table above

What is the modal goal scored?

Answer Details

The modal score is the score that occurs most frequently. Looking at the table, we can see that the score of 2 occurs the most frequently, appearing 6 times. Therefore, the modal goal scored is 2.

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Question 39 Report

In the diagram above, KLMN is a cyclic quadrilateral. /KL/ = /KN/, ?NKM = 55^o and ?KML = 40^o. Find ?LKM

35^o

40^o

45^o

50^o

55^o

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Circles

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Question 40 Report

In the diagram above, O is the center of the circle of radius 3.5cm, ?POQ = 60^o

Use the information to answer the question below [Take ? = 22/7]

What is the length of the arc PXQ?

22cm

18¹/₃cm

11cm

9¹/₆cm

7¹/₃cm

Answer Details

The length of an arc is given by the formula L = 2πr(θ/360), where r is the radius of the circle and θ is the central angle of the arc in degrees. In this case, the radius of the circle is 3.5cm and the central angle of the arc PXQ is 60 degrees. Substituting these values into the formula, we have: L = 2 x (22/7) x 3.5 x (60/360) L = 11cm Therefore, the length of the arc PXQ is 11cm. Answer (C)

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Question 41 Report

In the diagram above, O is the center of the circle of radius 3.5cm, ∠POQ = 60°. What is the area of the minor sector POQ?

[Take π = 22/7].

148¹/₂cm²

77cm²

32¹/₁₂cm²

6⁵/₁₂cm²

1⁵/₆cm²

Answer Details

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Circles

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Question 42 Report

Expand (2x - 5)(x - 3)

x² - 1x -15

2x² - 11x + 15

2² - 5x - 8

x² - 5x - 15

2x² - 6x + 15

Answer Details

To expand the expression (2x - 5)(x - 3), we need to apply the distributive property, which states that the product of a sum (or difference) and a term is equal to the sum (or difference) of the products of each term with the given term. So, we start by multiplying the first term of the first factor, 2x, by each term of the second factor, x and -3, and then do the same for the second term of the first factor, -5: (2x)(x) + (2x)(-3) + (-5)(x) + (-5)(-3) Simplifying this expression by multiplying and adding the terms, we get: 2x² - 6x - 5x + 15 Combining like terms, we have: 2x² - 11x + 15 Therefore, the correct answer is 2x² - 11x + 15.

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Algebraic Expressions

Coordinate Geometry

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Question 43 Report

In the diagram above, PQ is parallel to RST. /RS/ = /SQ/ = /TQ/ and ?PQR = 35^o.Calculate ?SQT

30^o

35^o

40^o

70^o

110^o

Answer Details

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Angles

Triangles And Polygons

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Question 44 Report

In the diagram below, PMN=PRQ and PNM=PQR.If /PM/=3cm, /MQ/=7cm and /PN/=5cm, find /NR/ - Brainly.in

In the diagram, ?PMN = ?PRQ and ?PNM = ?PQR. If /Pm/ = 3cm, /MQ/ = 7cm and /PN/ = 5cm, find /NR/

1cm

3cm

3¹/₂

5cm

6cm

Answer Details

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Change Of Subject Of A Formula/Relation

Coordinate Geometry

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Question 45 Report

Convert the decimal number 89 to a binary number

101101

111001

1001001

1001101

1011001

Answer Details

To convert a decimal number to binary, we need to continuously divide the decimal number by 2, until the quotient becomes 0. The binary number is obtained by writing the remainders (0 or 1) obtained in reverse order. Here's the step-by-step process: - Divide 89 by 2. Quotient is 44 and remainder is 1. - Divide 44 by 2. Quotient is 22 and remainder is 0. - Divide 22 by 2. Quotient is 11 and remainder is 0. - Divide 11 by 2. Quotient is 5 and remainder is 1. - Divide 5 by 2. Quotient is 2 and remainder is 1. - Divide 2 by 2. Quotient is 1 and remainder is 0. - Divide 1 by 2. Quotient is 0 and remainder is 1. So the remainders obtained in reverse order are: 1 0 1 1 0 0 0 Therefore, the binary representation of 89 is 1011001.

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Number Bases

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Question 46 Report

One side of a rectangle is 8cm and the diagonal is 10cm. What is the area of the rectangle?

80cm²

48cm²

40cm²

36cm²

24cm²

Answer Details

We know that the diagonal of a rectangle divides it into two right triangles with the diagonal as the hypotenuse, and the sides of the rectangle as the legs of the right triangles. Let's call the other side of the rectangle "x". Using the Pythagorean theorem, we have: 10² = 8² + x² Simplifying and solving for x, we get: x = √(10² - 8²) = √36 = 6 Therefore, the area of the rectangle is: 8 x 6 = 48 cm² Hence, the answer is 48cm².

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Read lesson note on Areas (WAEC)

Sets

Areas

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Question 47 Report

Which of the following is not true? You may construct a

triangle given all the three sides

triangle given one side and two angles

triangle given two sides and the included angle

quatrilateral given all the four sides

parallelogram given two adjacent sides and the diagonal joining them

Answer Details

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Question 48 Report

If the hypotenuse of a right-angle isosceles triangle is 2, what is the length of each of the other side?

1/√2

√2 - 1

√2

√3

Answer Details

In a right-angle isosceles triangle, the two legs are congruent to each other. Let x be the length of each leg. By the Pythagorean theorem, we know that: x² + x² = 2² Simplifying the equation gives: 2x² = 4 Dividing both sides by 2, we have: x² = 2 Taking the square root of both sides gives: x = √2 Therefore, the length of each leg is √2, which is approximately 1.41. So, the correct answer is not in the options given, but it is approximately equal to, √2.

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Number Bases

Surds (radicals)

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Question 49 Report

How many sides has a polygon if the sum of its interior angle is 1440^o?

Answer Details

To find the number of sides of a polygon given the sum of its interior angles, we can use the formula: Sum of interior angles = (n - 2) × 180° where "n" is the number of sides of the polygon. We are given that the sum of the interior angles of the polygon is 1440°. Substituting this value into the formula, we get: 1440° = (n - 2) × 180° Simplifying this equation, we can divide both sides by 180: 8 = n - 2 Adding 2 to both sides, we get: n = 10 Therefore, the polygon has 10 sides.

Read lesson note on Triangles And Polygons (WAEC)

Triangles And Polygons

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