WAEC SSCE - General Mathematics - 2011 (Objective)

Question 1 Report

What is the value of 3 in the number 42.7531?

\(\frac{3}{10000}\)

\(\frac{3}{1000}\) Correct answer

\(\frac{3}{100}\)

\(\frac{1}{10}\)

Answer Details

The digit 3 in the number 42.7531 is in the thousandth place (the digit after the decimal point and three places to the right of it). Therefore, its value is \(\frac{3}{1000}\).

Read lesson note on Number Bases (WAEC)

Number Bases

View Answer

Question 2 Report

Which of these angles can be constructed using ruler and a pair of compasses only?

115^o

125^o

135^o Correct answer

145^o

Answer Details

Read lesson note on Euclidean Geometry (JAMB)

Euclidean Geometry

View Answer

Question 3 Report

The histogram shows the age distribution of members of a club. What is their modal age?

44.5 Correct answer

42.5

41.5

40.5

Answer Details

Read lesson note on Representation Of Data (JAMB)

Representation Of Data

View Answer

Question 4 Report

in a quiz competition, a student answers n questions correctly and was given D(n + 50) for each question correctly answered. If he gets D600.00 altogether, how many questions did he answer correctly?

10 Correct answer

Answer Details

Read lesson note on Number Bases (WAEC)

Read lesson note on Financial Arithmetic (WAEC)

Number Bases

Financial Arithmetic

View Answer

Question 5 Report

What is the value of 3 in the number 42.7531?

\(\frac{3}{10000}\)

\(\frac{3}{1000}\) Correct answer

\(\frac{3}{100}\)

\(\frac{1}{10}\)

Answer Details

The number 42.7531 can be written in expanded form as: 42 + 0.7 + 0.05 + 0.003 + 0.0001 The digit 3 is located in the thousandths place, which represents the decimal value of 0.001. So, the value of 3 in the number 42.7531 is equal to: 3 x 0.001 = 0.003 Therefore, the correct answer is option (A), which is 3 divided by 10000.

Read lesson note on Positive And Negative Integers, Rational Numbers (WAEC)

Read lesson note on Modular Arithmetic (WAEC)

Positive And Negative Integers, Rational Numbers

Modular Arithmetic

View Answer

Question 6 Report

In the diagram, STUV is a straight line. < TSY = < UXY = 40^o and < VUW = 110^o. Calculate < TYW

150^o Correct answer

140^o

130^o

120^o

Answer Details

Read lesson note on Angles (WAEC)

Read lesson note on Triangles And Polygons (WAEC)

Angles

Triangles And Polygons

View Answer

Question 7 Report

Simplify \(\frac{m}{n} + \frac{(m - 1)}{5n} = \frac{(m - 2)}{10n}\) where n \(\neq\) 0

\(\frac{m - 3}{10n}\)

\(\frac{11m}{10n}\) Correct answer

\(\frac{m + 1}{10n}\)

\(\frac{11m + 4}{10n}\)

Answer Details

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Fractions

View Answer

Question 8 Report

The height of a cylinder is equal to its radius. If the volume is 0.216 \(\pi\) m\(^3\). Calculate the radius.

0.46m

0.60m Correct answer

0.87m

1.80m

Answer Details

Let's denote the radius of the cylinder as r and its height as h. We are given that the height of the cylinder is equal to its radius, so h = r. We also know the volume of the cylinder, which is given by: V = \(\pi\)r\(^2\)h Substituting h = r, we get: V = \(\pi\)r\(^2\)r = \(\pi\)r\(^3\) We are given that the volume of the cylinder is 0.216 \(\pi\) m\(^3\). So, we can solve for r as follows: 0.216 \(\pi\) = \(\pi\)r\(^3\) r\(^3\) = 0.216 Taking the cube root of both sides, we get: r = 0.6 Therefore, the radius of the cylinder is 0.6 meters. So, the answer is 0.60m.

Read lesson note on Number Bases (WAEC)

Read lesson note on Coordinate Geometry (WAEC)

Number Bases

Coordinate Geometry

View Answer

Question 9 Report

Find the size of the angle marked x in the diagram.

108^o

112^o

128^o Correct answer

142^o

Answer Details

Read lesson note on Coordinate Geometry (WAEC)

Read lesson note on Angles And Intercepts On Parallel Lines (WAEC)

Read lesson note on Angles (WAEC)

Coordinate Geometry

Angles And Intercepts On Parallel Lines

Angles

View Answer

Question 10 Report

The cross section section of a uniform prism is a right-angled triangle with sides 3cm. 4cm and 5cm. If its length is 10cm. Calculate the total surface area

142cm²

132cm² Correct answer

122cm²

112cm²

Answer Details

Read lesson note on Integration (JAMB)

Read lesson note on Sets (JAMB)

Read lesson note on Mensuration (JAMB)

Integration

Sets

Mensuration

View Answer

Question 11 Report

The perimeter of a sector of a circle of radius 4cm is (\(\pi + 8\))cm. Calculate the anle of the sector

45^o Correct answer

60^o

75^o

90^o

Answer Details

Read lesson note on Circles (WAEC)

Read lesson note on Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

View Answer

Question 12 Report

Using the cumulative frequency curve. What is the 80th percentile?

45.5

46.5

47.5 Correct answer

48.5

Answer Details

Read lesson note on Integration (JAMB)

Integration

View Answer

Question 13 Report

John pours 96 litres of red oil into a rectangular container with length 220cm and breadth 40cm. Calculate, correct to the nearest cm, the height of the oil in the container

11cm Correct answer

18cm

21cm

34cm

Answer Details

To solve this problem, we need to use the formula for the volume of a rectangular container: Volume = Length x Breadth x Height We are given the length and breadth of the container, as well as the volume of the oil. We need to find the height of the oil. First, we need to convert the volume of the oil from litres to cubic centimeters, since the dimensions of the container are given in centimeters. 1 litre = 1000 cubic centimeters Therefore, 96 litres = 96 x 1000 = 96,000 cubic centimeters Now, we can plug in the values we have into the formula for the volume of the container: Volume = Length x Breadth x Height 96,000 = 220 x 40 x Height Simplifying, we get: Height = 96,000 / (220 x 40) Height = 2.18 To round off to the nearest centimeter, we need to look at the first decimal place. If the value in the first decimal place is 5 or more, we round up. If it is less than 5, we round down. In this case, the value in the first decimal place is 1, which is less than 5. Therefore, we round down to 2. So, the height of the oil in the container is approximately 2cm. Therefore, the correct answer is (a) 11cm.

Read lesson note on Lengths And Perimeters (WAEC)

Lengths And Perimeters

View Answer

Question 14 Report

If a number is chosen at random from the set {x: 4 \(\leq x \leq 15\)}. Find the probability that it is a multiple of 3 or a multiple of 4

\(\frac{1}{12}\)

\(\frac{5}{12}\)

\(\frac{7}{12}\) Correct answer

\(\frac{11}{12}\)

Answer Details

Read lesson note on Probability (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Probability

Surds (radicals)

View Answer

Question 15 Report

Given that n(p) = 19, m(P \(\cup\) Q) = 38 and n(P \(\cap\) Q) = 7, Find n(C)

26 Correct answer

Answer Details

Read lesson note on Sets (JAMB)

Read lesson note on Ratio, Proportions And Rates (WAEC)

Sets

Ratio, Proportions And Rates

View Answer

Question 16 Report

a boy looks through a window of a building and sees a mango fruit on the ground 50m away from the foot of the building. If the window is 9m from the ground, calculate, correct to the nearest degree, the angle of depression of the mango from the window

9^o

10^o Correct answer

11^o

12^o

Answer Details

Read lesson note on Angles Of Elevation And Depression (WAEC)

Angles Of Elevation And Depression

View Answer

Question 17 Report

The graph represents the relation y = x\(^2\) - 3x - 3. What is the equation of the line of symmetry of the graph?

y = 0.5

x = 1.0

x = 1.5 Correct answer

y = 4.6

Answer Details

To find the equation of the line of symmetry of the graph, we need to identify the axis of symmetry. The axis of symmetry is a vertical line that passes through the vertex of the parabola. The vertex of the parabola is the point where the parabola changes direction, and it can be found by using the formula: x = -b / (2a) where a and b are the coefficients of the quadratic equation y = ax\(^2\) + bx + c. In the given equation y = x\(^2\) - 3x - 3, a = 1, b = -3, and c = -3. Substituting these values in the formula, we get: x = -(-3) / (2*1) = 3/2 = 1.5 Therefore, the line of symmetry is a vertical line passing through x = 1.5. So, the correct answer is (C) x = 1.5.

Read lesson note on Simple Operations On Algebraic Expressions (WAEC)

Read lesson note on Quadratic Equations (WAEC)

Simple Operations On Algebraic Expressions

Quadratic Equations

View Answer

Question 18 Report

John pours 96 litres of red oil into a rectangular container with length 220cm and breadth 40cm. Calculate, correct to the nearest cm, the height of the oil in the container

11cm Correct answer

18cm

21cm

34cm

Answer Details

To calculate the height of the oil in the container, we need to use the formula for the volume of a rectangular prism: Volume = length x breadth x height First, we need to convert the given volume from liters to cubic centimeters, since the dimensions of the container are in centimeters. 96 liters = 96,000 cubic centimeters Next, we can plug in the given values into the formula: 96,000 = 220 x 40 x height Solving for height, we get: height = 96,000 / (220 x 40) height ≈ 11.0 cm (rounded to the nearest cm) Therefore, the height of the oil in the container is approximately 11 cm. Note: When working with volume, it's important to make sure the units are consistent throughout the problem. In this case, we converted liters to cubic centimeters to match the dimensions of the container.

View Answer

Question 19 Report

In the diagram /Pq//TS//TU, reflex angle QPS = 245^o angle PST = 115^o, , STU = 65^o and < RPS = x. Find the value of x

80^o

70^o

60^o

50^o Correct answer

Answer Details

Read lesson note on Indices (WAEC)

Indices

View Answer

Question 20 Report

If \(\sqrt{72} + \sqrt{32} - 3 \sqrt{18} = x \sqrt{8}\), Find the value of x

\(\frac{3}{4}\)

\(\frac{1}{2}\) Correct answer

\(\frac{1}{4}\)

Answer Details

Read lesson note on Surds (radicals) (WAEC)

Surds (radicals)

View Answer

Question 21 Report

A regular polygon of n sides has each exterior angle to 45^o. Find the value of n

8 Correct answer

Answer Details

In a regular polygon with n sides, each exterior angle measures 360/n degrees. We are given that in this polygon, each exterior angle is 45 degrees. Therefore, we can set up an equation: 360/n = 45 To solve for n, we can cross-multiply and simplify: 360 = 45n n = 360/45 n = 8 Therefore, the regular polygon in question has 8 sides. Answer: 8.

View Answer

Question 22 Report

The venn diagram shows the number of students in a class who like reading(R), dancing(D) and swimming(S). How many students like dancing and swimming?

7 Correct answer

Answer Details

Read lesson note on Circles (WAEC)

Read lesson note on Sets (JAMB)

Circles

Sets

View Answer

Question 23 Report

from the diagram, Which of the following statements are true? i. m = q ii. n = q iii. n + p = 180^o iv. p + m = 180^o

i and iii Correct answer

i and iv

ii and iii

ii and ic

Answer Details

In the given diagram, we can see that lines n and q are parallel and m is a transversal cutting them. Therefore, angles n and q are alternate interior angles and are equal, i.e., statement i is true. Also, we can see that lines n and p are parallel and q is a transversal cutting them. Therefore, angles n and p are corresponding angles and are equal. As the sum of the corresponding angles is equal to 180 degrees, we have n + p = 180 degrees, i.e., statement iii is also true. However, we cannot determine whether statement ii and iv are true or not based on the given information and the diagram. Therefore, the correct answer is (a) i and iii.

Read lesson note on Polynomials (JAMB)

Read lesson note on Measures Of Dispersion (JAMB)

Polynomials

Measures Of Dispersion

View Answer

Question 24 Report

In the diagram /Pq//TS//TU, reflex angle QPS = 245^o angle PST = 115^o, , STU = 65^o and < RPS = x. Find the value of x

80^o

70^o

60^o

50^o Correct answer

Answer Details

Read lesson note on Indices (WAEC)

Read lesson note on Triangles And Polygons (WAEC)

Indices

Triangles And Polygons

View Answer

Question 25 Report

The histogram shows the age distribution of members of a club. How many members are in the club?

52 Correct answer

Answer Details

Read lesson note on Representation Of Data (JAMB)

Read lesson note on Mensuration (JAMB)

Representation Of Data

Mensuration

View Answer

Question 26 Report

Given that cos x^o = \(\frac{1}{r}\), express tan x in terms of r

\(\frac{1}{\sqrt{r}}\)

\(\sqrt{r}\)

\(\sqrt{r^2 + 1}\)

\(\sqrt{r^2 - 1}\) Correct answer

Answer Details

We know that: cos x = adjacent side/hypotenuse So, if cos x = 1/r, then adjacent side = 1 and hypotenuse = r. Using the Pythagorean theorem, we can find the opposite side: opposite side = √(hypotenuse^2 - adjacent side^2) = √(r^2 - 1) Finally, we can find the value of tan x: tan x = opposite side/adjacent side = √(r^2 - 1)/1 = √(r^2 - 1) Therefore, the answer is (d) \(\sqrt{r^2 - 1}\).

Read lesson note on Sine, Cosine And Tangent Of An Angle (WAEC)

Read lesson note on Lengths And Perimeters (WAEC)

Sine, Cosine And Tangent Of An Angle

Lengths And Perimeters

View Answer

Question 27 Report

Factorize the expression: am + bn - an - bm

(a - b)(m + n)

(a - b)(m - n) Correct answer

(a + b)(m - n)

(a + b)(m + n)

Answer Details

We can begin by grouping the first two terms and the last two terms together: am + bn = a(m) + b(n) = (a+b)n - bn an + bm = a(n) + b(m) = (a+b)m - am Now, we can substitute these expressions back into the original equation: am + bn - an - bm = [(a+b)n - bn] - [(a+b)m - am] We can simplify this expression by combining like terms: am + bn - an - bm = (a+b)n - bn - (a+b)m + am am + bn - an - bm = (a+b)n - (a+b)m + am - bn Finally, we can factor out the common factor of (a+b) from the first two terms and the common factor of (-1) from the last two terms: am + bn - an - bm = (a+b)(n-m) - (b-a)(n-m) Therefore, the answer is (a+b)(n-m) - (b-a)(n-m), which can be further simplified to (a-b)(m-n). Thus, the correct option is (a - b)(m - n).

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

View Answer

Question 28 Report

Simplify \(\frac{\log \sqrt{27}}{\log \sqrt{81}}\)

\(\frac{3}{2}\)

\(\frac{3}{4}\) Correct answer

Answer Details

Using the property that \(\log_{a}b = \frac{\log{b}}{\log{a}}\), we can simplify the given expression as follows: \[\frac{\log \sqrt{27}}{\log \sqrt{81}} = \frac{\log 27^{\frac{1}{2}}}{\log 81^{\frac{1}{2}}} = \frac{\frac{1}{2}\log 27}{\frac{1}{2}\log 81} = \frac{\log 3^3}{\log 3^4} = \frac{3\log 3}{4\log 3} = \frac{3}{4}\] Therefore, the simplified form of \(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) is \(\frac{3}{4}\), and the correct option is (D).

Read lesson note on Logarithms (WAEC)

Logarithms

View Answer

Question 29 Report

The graph represents the relation y = x^o2 - 3x - 3. Find the value of x for which x² - 3x = 7

-1.55, 4.44 Correct answer

1.55, -4.55

-1.55, -4.55

1.55, 4.55

Answer Details

Read lesson note on Solution Of Linear Equations (WAEC)

Read lesson note on Quadratic Equations (WAEC)

Solution Of Linear Equations

Quadratic Equations

View Answer

Question 30 Report

A rectangular garden measures 18.6m by 12.5m. Calculate, correct to three significant figures, the area of the garden

230m²

231m²

232m²

233m² Correct answer

Answer Details

The area of a rectangle is given by multiplying the length by the width. Therefore, the area of the garden is: Area = length × width Area = 18.6m × 12.5m Area = 232.5m² Rounding to three significant figures gives 233m². Therefore, the answer is (d) 233m².

Read lesson note on Lengths And Perimeters (WAEC)

Lengths And Perimeters

View Answer

Question 31 Report

One of the factors of (mn - nq - n2 + mq) is (m - n). The other factor is?

(n - q)

(q - n)

(n + q) Correct answer

(q - m)

Answer Details

Read lesson note on Number Bases (WAEC)

Number Bases

View Answer

Question 32 Report

If 27^x = 9^y. Find the value of \(\frac{x}{y}\)

\(\frac{1}{3}\)

\(\frac{2}{3}\) Correct answer

1\(\frac{1}{2}\)

Answer Details

If we can find the value of x and y, then we can calculate x/y by dividing x by y. Given: 27^x = 9^y We can rewrite 27 as 3³ and 9 as 3² to get: (3³)^x = (3²)^y Applying the power of a power rule, we get: 3^3x = 3^2y For two exponential expressions to be equal, their bases must be equal. Therefore: 3^3x = 3^2y implies 3x = 2y Dividing both sides by y, we get: \(\frac{x}{y} = \frac{2}{3}\) Therefore, the answer is \(\frac{2}{3}\).

Read lesson note on Indices (WAEC)

Indices

View Answer

Question 33 Report

Simplify 1\(\frac{3}{4} - (2 \frac{1}{3} + 4)\)

3\(\frac{5}{12}\)

2\(\frac{7}{12}\)

-4 \(\frac{7}{12}\) Correct answer

-5 \(\frac{7}{12}\)

Answer Details

Read lesson note on Solution Of Linear Equations (WAEC)

Read lesson note on Algebraic Expressions (WAEC)

Solution Of Linear Equations

Algebraic Expressions

View Answer

Question 34 Report

The perpendicular bisectors of the sides of an acute-angled triangle are drawn. Which of these statements is correct? They intersect

on one of the vertices

at a midpoint of a side

inside the triangle Correct answer

outside the triangle

Answer Details

The perpendicular bisectors of the sides of an acute-angled triangle intersect at a point inside the triangle. This point is called the circumcenter, which is equidistant from the three vertices of the triangle. To see why this is true, consider two sides of the triangle, and let their perpendicular bisectors intersect at a point O. Since O lies on the perpendicular bisector of each of the two sides, it is equidistant from the endpoints of each of those sides. Therefore, O is equidistant from two vertices of the triangle. Similarly, O is equidistant from the third vertex, so it must be the circumcenter of the triangle. Since the triangle is acute-angled, the circumcenter lies inside the triangle.

Read lesson note on Polynomials (JAMB)

Read lesson note on Euclidean Geometry (JAMB)

Read lesson note on Triangles And Polygons (WAEC)

Polynomials

Euclidean Geometry

Triangles And Polygons

View Answer

Question 35 Report

If N112.00 exchanges for D14.95, calculate the value of D1.00 in naira

0.13

7.49 Correct answer

8.00

13.00

Answer Details

To calculate the value of D1.00 in naira, we can use the given exchange rate of N112.00 to D14.95. We can find the value of 1 D in Naira by dividing N112.00 by the equivalent value of D14.95. So, 1 D = N112.00/D14.95 To simplify this, we can first convert D14.95 to its decimal equivalent by dividing by 100: D14.95 = 14.95/100 = 0.1495 Now we can substitute this value into the equation: 1 D = N112.00/0.1495 Simplifying this expression, we get: 1 D = N748.16 Therefore, the value of D1.00 in Naira is N748.16. Answer: 7.49.

Read lesson note on Positive And Negative Integers, Rational Numbers (WAEC)

Read lesson note on Areas (WAEC)

Positive And Negative Integers, Rational Numbers

Areas

View Answer

Question 36 Report

A cylindrical container has a base radius of 14cm and height 18cm. How many litres of liquid can it hold? correct to the nearest litre [Take \(\pi = \frac{22}{7}\)]

11 Correct answer

Answer Details

The volume of a cylinder can be calculated using the formula: V = πr²h, where r is the radius of the base and h is the height of the cylinder. Substituting the given values, we have: V = π(14)²(18) V = 11088 cm³ To convert cm³ to litres, we divide by 1000: V = 11088/1000 V = 11.088 litres Rounding to the nearest litre, we get: V ≈ 11 litres Therefore, the answer is 11.

Read lesson note on Volumes (WAEC)

Read lesson note on Inequalities (JAMB)

Volumes

Inequalities

View Answer

Question 37 Report

The diagram shows a cyclic quadrilateral PQRS with its diagonals intersecting at K. Which of the following triangles is similar to triangle QKR?

\(\bigtriangleup\) PQK

\(\bigtriangleup\) PKS

\(\bigtriangleup\) SKR Correct answer

\(\bigtriangleup\) PSR

Answer Details

Read lesson note on Statistics (WAEC)

Read lesson note on Angles (WAEC)

Read lesson note on Triangles And Polygons (WAEC)

Statistics

Angles

Triangles And Polygons

View Answer

Question 38 Report

Using the cumulative frequency curve, estimate the median of the data represented on the graph.

35.5

36.5 Correct answer

37.5

38.5

Answer Details

View Answer

Question 39 Report

Esther was facing S 20° W. She turned 90° in the clock wise direction. What direction is she facing?

N 70^o W Correct answer

S 70^o W

N 20^o W

S 20^o E

Answer Details

If Esther was initially facing S 20° W and then turned 90° clockwise, she would end up facing in a new direction. To determine the new direction, we can add 90° to her initial direction. When we add 90° to S 20° W, we rotate the direction clockwise by 90°, which means the new direction will be to the right of the initial direction. To find the new direction, we need to subtract the initial angle from 90°: 90° - 20° = 70° Therefore, Esther is facing in the direction of N 70° W after turning 90° clockwise from her initial direction of S 20° W.

Read lesson note on Introductory Calculus (WAEC)

Read lesson note on Trigonometry (JAMB)

Introductory Calculus

Trigonometry

View Answer

Question 40 Report

Solve for x in the equation; \(\frac{3}{5}\)(2x - 1) = \(\frac{1}{4}\)(5x - 3)

zero

3 Correct answer

Answer Details

Read lesson note on Fractions, Decimals And Approximations (WAEC)

Read lesson note on Solution Of Linear Equations (WAEC)

Read lesson note on Algebraic Expressions (WAEC)

Fractions, Decimals And Approximations

Solution Of Linear Equations

Algebraic Expressions

View Answer

Question 41 Report

What must be added to (2x - 3y) to get (x - 2y)?

5y - x

y - x Correct answer

x - 5x

x - y

Answer Details

To get from (2x - 3y) to (x - 2y), we need to subtract x from 2x and add 2y to -3y. Therefore, we need to add (x - 2y) - (2x - 3y) to (2x - 3y) to get (x - 2y). Simplifying (x - 2y) - (2x - 3y), we have: (x - 2y) - (2x - 3y) = x - 2y - 2x + 3y = -x + y Therefore, we need to add (-x + y) to (2x - 3y) to get (x - 2y). Simplifying (2x - 3y) + (-x + y), we have: (2x - 3y) + (-x + y) = 2x - 3y - x + y = x - 2y So, we need to add (-x + y) to (2x - 3y) to get (x - 2y). Therefore, the answer is (B) y - x.

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

View Answer

Question 42 Report

In the diagram, PO and OR are radii, |PQ| = |QR| and reflex < PQR is 240^o. Calculate the value x

60^o Correct answer

55^o

50^o

45^o

Answer Details

In the given diagram, we have a circle with center O and radii OP and OR. The reflex angle PQR is 240° and |PQ| = |QR|. We need to find the value of x. Since |PQ| = |QR|, we know that triangle PQR is an isosceles triangle. Therefore, the angles opposite to PQ and QR are equal. Let's denote the angle PQR by y. Then we have: 2y + 60° = 360° (sum of angles in a triangle) 2y = 300° y = 150° Therefore, each of the angles opposite to PQ and QR is equal to (180° - 150°)/2 = 15°. Now, consider the triangle OQP. We know that the sum of angles in a triangle is 180°. Therefore: ∠OQP + ∠QOP + ∠OPQ = 180° Since OP and OQ are radii, ∠QOP = ∠OPQ. Let's denote this angle by z. Then we have: z + z + 15° = 180° 2z = 165° z = 82.5° Finally, consider the triangle OXR. We know that the sum of angles in a triangle is 180°. Therefore: ∠OXR + ∠ORX + ∠ROX = 180° Since OR and OX are radii, ∠ORX = ∠ROX. Let's denote this angle by x. Then we have: x + x + 60° = 180° 2x = 120° x = 60° Therefore, the value of x is 60°. Answer: 60°.

Read lesson note on Circles (WAEC)

Read lesson note on Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

View Answer

Question 43 Report

G varies directly as the square of H, If G is 4 when H is 3, find H when G = 100

15 Correct answer

225

Answer Details

In this problem, we are given that G varies directly as the square of H. This means that if H is multiplied by some factor, then G will be multiplied by the square of that factor. Mathematically, we can write this as: G ∝ H^2 where the symbol "∝" means "varies directly as". We are also given that G is 4 when H is 3. Using this information, we can write: 4 ∝ 3^2 To find H when G = 100, we can use the same relationship: G ∝ H^2 If we let the constant of proportionality be k, we can write: G = kH^2 To solve for k, we can use the initial condition where G is 4 when H is 3: 4 = k(3^2) Simplifying, we get: k = 4/9 Now we can use this value of k to find H when G is 100: 100 = (4/9)H^2 Multiplying both sides by 9/4, we get: 225 = H^2 Taking the square root of both sides, we get: H = 15 Therefore, the correct answer is (a) 15. In summary, we used the direct variation relationship between G and H^2 to find the constant of proportionality, and then used that constant and the given value of G to solve for H.

View Answer

Question 44 Report

Solve the equation; 3x - 2y = 7, x + 2y = -3

x = 1, y = -2 Correct answer

x = 1, y = 3

x = -2, y = -1

x = 4, y = -3

Answer Details

To solve this system of equations, we can use the method of elimination. We will add the two equations together, which will eliminate the y variable: (3x - 2y) + (x + 2y) = 7 + (-3) Simplifying, we get: 4x = 4 Dividing both sides by 4, we get: x = 1 Substituting x = 1 into one of the equations, we get: 1 + 2y = -3 Solving for y, we get: y = -2 Therefore, the solution to the system of equations is x = 1, y = -2. So, the correct option is (a) x = 1, y = -2.

Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

View Answer

Question 45 Report

The height of a cylinder is equal to its radius. If the volume is 0.216 \(\pi m^3\) Calculate the radius.

0.46m Correct answer

0.60m

0.87m

1.80m

Answer Details

Read lesson note on Representation Of Data (JAMB)

Read lesson note on Modular Arithmetic (WAEC)

Representation Of Data

Modular Arithmetic

View Answer

Question 46 Report

Find the smaller value of x that satisfies the equation x₂ + 7x + 10 = 0

-5 Correct answer

-2

Answer Details

We are given a quadratic equation x² + 7x + 10 = 0 and we need to find the smaller value of x that satisfies the equation. To solve the equation, we can factorize it by finding two numbers whose product is 10 and whose sum is 7. We can see that the two numbers are 2 and 5, since 2 × 5 = 10 and 2 + 5 = 7. So, we can write the equation as (x + 2)(x + 5) = 0. For this equation to be true, either (x + 2) = 0 or (x + 5) = 0. Therefore, we get x = -2 or x = -5. Since we are asked to find the smaller value of x, we choose x = -5 as the answer. Hence, the smaller value of x that satisfies the equation x² + 7x + 10 = 0 is -5.

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

View Answer

Question 47 Report

The length of a piece of stick is 1.75m. A girl measured it as 1.80m. Find the percentage error

\(\frac{28}{7}\)%

\(\frac{29}{7}\)%

\(\frac{20}{7}\)% Correct answer

Answer Details

The actual length of the stick is 1.75m and the measured length is 1.80m. The error is the difference between the actual and measured length: 1.80m - 1.75m = 0.05m To find the percentage error, we divide the error by the actual length and multiply by 100%: \frac{0.05}{1.75} \times 100\% \approx 2.857\% \approx \frac{20}{7}\% Therefore, the percentage error is approximately \frac{20}{7}\%.

Read lesson note on Percentages (WAEC)

Percentages

View Answer

Question 48 Report

From the equation whose roots are x = \(\frac{1}{2}\) and -\(\frac{2}{3}\)

6x² - x + 2 = 0

6x² - x - 2 = 0

6x² + x + 2 = 0

6x² + x - 2 = 0 Correct answer

Answer Details

When a quadratic equation has roots at x = a and x = b, it can be written in factored form as (x-a)(x-b) = 0. Therefore, from the given roots, the factors are (x - \(\frac{1}{2}\)) and (x + \(\frac{2}{3}\)). To get the quadratic equation, we can expand the factors by multiplying them together, which gives us: (x - \(\frac{1}{2}\))(x + \(\frac{2}{3}\)) = x² - \(\frac{1}{2}\)x + \(\frac{2}{3}\)x - \(\frac{1}{2}\)\(\frac{2}{3}\) = x² + \(\frac{1}{6}\)x - \(\frac{1}{3}\) Therefore, the correct option is 6x² + x - 2 = 0.

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

View Answer

Question 49 Report

In the diagram, /MN/, /OP/, /QOP/ = 125^o. What is the size of < MQR?

11^o

120^o Correct answer

130^o

160^o

Answer Details

Read lesson note on Angles (WAEC)

Read lesson note on Triangles And Polygons (WAEC)

Angles

Triangles And Polygons

View Answer






Press & Hold to Drag Around
Click Here to Close