WAEC SSCE - General Mathematics - 2011

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

11^o

12^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Angles Of Elevation And Depression (WAEC)

Angles Of Elevation And Depression

Tazama Jibu

Swali 5 Ripoti

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

y = 4.6

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Simple Operations On Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Simple Operations On Algebraic Expressions

Quadratic Equations

Tazama Jibu

Swali 6 Ripoti

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

x = 1, y = -2

x = 1, y = 3

x = -2, y = -1

x = 4, y = -3

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Tazama Jibu

Swali 7 Ripoti

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

0.87m

1.80m

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Coordinate Geometry (WAEC)

Number Bases

Coordinate Geometry

Tazama Jibu

Swali 8 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Indices (WAEC)

Indices

Tazama Jibu

Swali 9 Ripoti

Factorize the expression: am + bn - an - bm

(a - b)(m + n)

(a - b)(m - n)

(a + b)(m - n)

(a + b)(m + n)

Maelezo ya Majibu

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).

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

Tazama Jibu

Swali 10 Ripoti

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

i and iv

ii and iii

ii and ic

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Polynomials (JAMB)

Soma maelezo ya somo kwenye Measures Of Dispersion (JAMB)

Polynomials

Measures Of Dispersion

Tazama Jibu

Swali 11 Ripoti

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

(n - q)

(q - n)

(n + q)

(q - m)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 12 Ripoti

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

$\frac{28}{7}$%

$\frac{29}{7}$%

$\frac{20}{7}$%

Maelezo ya Majibu

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}\%.

Soma maelezo ya somo kwenye Percentages (WAEC)

Percentages

Tazama Jibu

Swali 13 Ripoti

What is the value of 3 in the number 42.7531?

$\frac{3}{10000}$

$\frac{3}{1000}$

$\frac{3}{100}$

$\frac{1}{10}$

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Positive And Negative Integers, Rational Numbers

Modular Arithmetic

Tazama Jibu

Swali 14 Ripoti

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

-1.55, 4.44

1.55, -4.55

-1.55, -4.55

1.55, 4.55

Maelezo ya Majibu

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Solution Of Linear Equations

Quadratic Equations

Tazama Jibu

Swali 15 Ripoti

What is the value of 3 in the number 42.7531?

$\frac{3}{10000}$

$\frac{3}{1000}$

$\frac{3}{100}$

$\frac{1}{10}$

Maelezo ya Majibu

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 $\frac{3}{1000}$.

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 16 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Representation Of Data (JAMB)

Soma maelezo ya somo kwenye Mensuration (JAMB)

Representation Of Data

Mensuration

Tazama Jibu

Swali 17 Ripoti

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

35.5

36.5

37.5

38.5

Maelezo ya Majibu

Tazama Jibu

Swali 18 Ripoti

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

$\frac{1}{12}$

$\frac{5}{12}$

$\frac{7}{12}$

$\frac{11}{12}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Probability (WAEC)

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Probability

Surds (radicals)

Tazama Jibu

Swali 19 Ripoti

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

$\frac{m - 3}{10n}$

$\frac{11m}{10n}$

$\frac{m + 1}{10n}$

$\frac{11m + 4}{10n}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Algebraic Fractions

Tazama Jibu

Swali 20 Ripoti

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

outside the triangle

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Polynomials (JAMB)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Polynomials

Euclidean Geometry

Triangles And Polygons

Tazama Jibu

Swali 21 Ripoti

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

122cm²

112cm²

Maelezo ya Majibu

Soma maelezo ya somo kwenye Integration (JAMB)

Soma maelezo ya somo kwenye Sets (JAMB)

Soma maelezo ya somo kwenye Mensuration (JAMB)

Integration

Sets

Mensuration

Tazama Jibu

Swali 22 Ripoti

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

44.5

42.5

41.5

40.5

Maelezo ya Majibu

Soma maelezo ya somo kwenye Representation Of Data (JAMB)

Representation Of Data

Tazama Jibu

Swali 23 Ripoti

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

$\frac{1}{3}$

$\frac{2}{3}$

1$\frac{1}{2}$

Maelezo ya Majibu

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 $\frac{2}{3}$.

Soma maelezo ya somo kwenye Indices (WAEC)

Indices

Tazama Jibu

Swali 24 Ripoti

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

18cm

21cm

34cm

Maelezo ya Majibu

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.

Tazama Jibu

Swali 25 Ripoti

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

108^o

112^o

128^o

142^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Coordinate Geometry (WAEC)

Soma maelezo ya somo kwenye Angles And Intercepts On Parallel Lines (WAEC)

Soma maelezo ya somo kwenye Angles (WAEC)

Coordinate Geometry

Angles And Intercepts On Parallel Lines

Angles

Tazama Jibu

Swali 26 Ripoti

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

$\bigtriangleup$ PSR

Maelezo ya Majibu

Soma maelezo ya somo kwenye Statistics (WAEC)

Soma maelezo ya somo kwenye Angles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Statistics

Angles

Triangles And Polygons

Tazama Jibu

Swali 27 Ripoti

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?

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Sets (JAMB)

Circles

Sets

Tazama Jibu

Swali 28 Ripoti

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

60^o

55^o

50^o

45^o

Maelezo ya Majibu

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°.

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

Tazama Jibu

Swali 29 Ripoti

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

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{1}{4}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Surds (radicals)

Tazama Jibu

Swali 30 Ripoti

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

Maelezo ya Majibu

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.

Tazama Jibu

Swali 31 Ripoti

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

150^o

140^o

130^o

120^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Angles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Angles

Triangles And Polygons

Tazama Jibu

Swali 32 Ripoti

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 $\pi = \frac{22}{7}$]

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Inequalities (JAMB)

Volumes

Inequalities

Tazama Jibu

Swali 33 Ripoti

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

45.5

46.5

47.5

48.5

Maelezo ya Majibu

Soma maelezo ya somo kwenye Integration (JAMB)

Integration

Tazama Jibu

Swali 34 Ripoti

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

115^o

125^o

135^o

145^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Euclidean Geometry

Tazama Jibu

Swali 35 Ripoti

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

5y - x

y - x

x - 5x

x - y

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

Tazama Jibu

Swali 36 Ripoti

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

$\frac{1}{\sqrt{r}}$

$\sqrt{r}$

$\sqrt{r^2 + 1}$

$\sqrt{r^2 - 1}$

Maelezo ya Majibu

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) $\sqrt{r^2 - 1}$.

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Soma maelezo ya somo kwenye Lengths And Perimeters (WAEC)

Sine, Cosine And Tangent Of An Angle

Lengths And Perimeters

Tazama Jibu

Swali 37 Ripoti

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

-5

-2

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 38 Ripoti

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

zero

Maelezo ya Majibu

Soma maelezo ya somo kwenye Fractions, Decimals And Approximations (WAEC)

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Fractions, Decimals And Approximations

Solution Of Linear Equations

Algebraic Expressions

Tazama Jibu

Swali 39 Ripoti

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

N 70^o W

S 70^o W

N 20^o W

S 20^o E

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Introductory Calculus (WAEC)

Soma maelezo ya somo kwenye Trigonometry (JAMB)

Introductory Calculus

Trigonometry

Tazama Jibu

Swali 40 Ripoti

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

11^o

120^o

130^o

160^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Angles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Angles

Triangles And Polygons

Tazama Jibu

Swali 41 Ripoti

Simplify $\frac{\log \sqrt{27}}{\log \sqrt{81}}$

$\frac{3}{2}$

$\frac{3}{4}$

Maelezo ya Majibu

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).

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 42 Ripoti

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

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 43 Ripoti

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

18cm

21cm

34cm

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Lengths And Perimeters (WAEC)

Lengths And Perimeters

Tazama Jibu

Swali 44 Ripoti

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

45^o

60^o

75^o

90^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

Tazama Jibu

Swali 45 Ripoti

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

0.13

7.49

8.00

13.00

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Soma maelezo ya somo kwenye Areas (WAEC)

Positive And Negative Integers, Rational Numbers

Areas

Tazama Jibu

Swali 46 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Indices (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Indices

Triangles And Polygons

Tazama Jibu

Swali 47 Ripoti

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?

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Financial Arithmetic (WAEC)

Number Bases

Financial Arithmetic

Tazama Jibu

Swali 48 Ripoti

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

225

Maelezo ya Majibu

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.

Tazama Jibu

Swali 49 Ripoti

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

230m²

231m²

232m²

233m²

Maelezo ya Majibu

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.

Soma maelezo ya somo kwenye Lengths And Perimeters (WAEC)

Lengths And Perimeters

Tazama Jibu

Swali 50 Ripoti

Using ruler and a pair of compasses only,

(a) construct a rhombus PQRS of side 7 cm and < PQR = 60°;

(b) locate point X such that X lies on the locus of points equidistant from PQ and QR and also equidistant from Q and R ;

Jibu

None

Soma maelezo ya somo kwenye Loci (WAEC)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Loci (WAEC)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Loci

Euclidean Geometry

Tazama Jibu

Swali 51 Ripoti

(a) The area of trapezium PQRS is 60$cm^{2}$. PQ // RS, /PQ/ = 15 cm, /RS/ = 25 cm and < PSR = 60°. Calculate the : (i) perpendicular height of PQRS ; (ii) |PS|.

(b) Ade received $\frac{3}{5}$ of a sum of money, Nelly $\frac{1}{3}$ of the remainder while Austin took the rest. If Austin's share is greater than Nelly's share by N3,000, how much did Ade get?

Jibu

None

Soma maelezo ya somo kwenye Mensuration (JAMB)

Soma maelezo ya somo kwenye Areas (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Mensuration (JAMB)

Soma maelezo ya somo kwenye Areas (WAEC)

Mensuration

Areas

Tazama Jibu

Swali 52 Ripoti

(a) Given that $\sin x = 0.6, 0° \leq x \leq 90°$, evaluate $2\cos x + 3\sin x$, leaving your answer in the form $\frac{m}{n}$, where m and n are integers.

(b)

In the diagram, a semi-circle WXYZ with centre O is inscribed in an isosceles triangle ABC. If /AC/ = /BC/, |OC| = 30 cm and < ACB = 130°, calculate, correct to one decimal place, the (i) radius of the circle ; (ii) area oc the shaded portion. [Take $\pi = \frac{22}{7}$].

Jibu

None

Soma maelezo ya somo kwenye Coordinate Geometry (WAEC)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Soma maelezo ya somo kwenye Coordinate Geometry (JAMB)

Soma maelezo ya somo kwenye Statistics (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Coordinate Geometry (WAEC)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Soma maelezo ya somo kwenye Coordinate Geometry (JAMB)

Soma maelezo ya somo kwenye Statistics (WAEC)

Coordinate Geometry

Euclidean Geometry

Coordinate Geometry

Statistics

Tazama Jibu

Swali 53 Ripoti

(a)

In the diagram, PQRST is a quadrilateral. PT // QS, < PTQ = 42°, < TSQ = 38° and < QSR = 30°. If < QTS = x and < POT = y, find: (i) x ; (ii) y.

(b)

In the diagram, PQRS is a circle centre O. If POQ = 150°, < QSR = 40° and < SQP = 45°, calculate < RQS.

Jibu

None

Soma maelezo ya somo kwenye Introductory Calculus (WAEC)

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Introductory Calculus (WAEC)

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Introductory Calculus

Circles

Triangles And Polygons

Tazama Jibu

Swali 54 Ripoti

(a) The total surface area of two spheres are in the ratio 9 : 49. If the radius of the smaller sphere is 12 cm, find, correct to the nearest $cm^{3}$, the volume of the bigger sphere.

(b) A cyclist starts from a point X and rides 3 km due West to a point Y. At Y, he changes direction and rides 5 km North- West to a point Z.

(i) How far is he from the starting point, correct to the nearest km? ; (ii) Find the bearing of Z from X, to the nearest degree.

Jibu

None

Maelezo ya Majibu

None

Tazama Jibu

Swali 55 Ripoti

In a class of 40 students, 18 passed Mathematics, 19 passed Accounts, 16 passed Economics, 5 passed Mathematics and Accounts only, 6 Mathematics only, 9 Accounts only, 2 Accounts and Economics only. If each student offered at least one of the subjects,

(a) how many students failed in all subjects?

(b) find the percentage number that failed in at least one of Economics and Mathematics

Jibu

None

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Soma maelezo ya somo kwenye Sets (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Soma maelezo ya somo kwenye Sets (WAEC)

Positive And Negative Integers, Rational Numbers

Sets

Tazama Jibu

Swali 56 Ripoti

A sector of a circle with radius 21 cm has an area of 280$cm^{2}$.

(a) Calculate, correct to 1 decimal place, the perimeter of the sector.

(b) If the sector is bent such that its straight edges coincide to form a cone, calculate, correct to the nearest degree, the vertical angle of the cone. [Take $\pi = \frac{22}{7}$].

Jibu

None

Maelezo ya Majibu

None

Tazama Jibu

Swali 57 Ripoti

(a) Make q the subject of the relation $t = \sqrt{\frac{pq}{r} - r^{2}q}$.

(b) If $9^{(1 - x)} = 27^{y}$ and $x - y = -1\frac{1}{2}$, find the value of x and y.

Jibu

None

Maelezo ya Majibu

None

Tazama Jibu

Swali 58 Ripoti

(a) Simplify : $\frac{\frac{1}{2} of \frac{1}{4} \div \frac{1}{3}}{\frac{1}{6} - \frac{3}{4} + \frac{1}{2}}$.

(b) Given that $\sqrt{x} = 10^{\bar{1}.6741}$, without using calculators, find the value of x.

Jibu

None

Soma maelezo ya somo kwenye Fractions, Decimals And Approximations (WAEC)

Soma maelezo ya somo kwenye Number Bases (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Fractions, Decimals And Approximations (WAEC)

Soma maelezo ya somo kwenye Number Bases (WAEC)

Fractions, Decimals And Approximations

Number Bases

Tazama Jibu

Swali 59 Ripoti

A library received $1,300 grant. It spends 10% of the grant on magazine subscriptions, 35% on new books, 15% to repair damaged books, 30% to buy new furniture and 10% to train library staff.

(a) Represent this information on a pie chart.

(b) Calculate, correct to the nearest whole number, the percentage increase of the amount for buying books over that of new furniture.

Jibu

None

Soma maelezo ya somo kwenye Percentages (WAEC)

Soma maelezo ya somo kwenye Financial Arithmetic (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Percentages (WAEC)

Soma maelezo ya somo kwenye Financial Arithmetic (WAEC)

Percentages

Financial Arithmetic

Tazama Jibu

Swali 60 Ripoti

The table shows the scores obtained when a fair die was thrown a number of times.

Score	1	2	3	4	5	6
Frequency	2	5	x	11	9	10

If the probability of obtaining a 3 is 0.26, find the (a) median

(b) standard deviation of the distribution.

Jibu

None

Soma maelezo ya somo kwenye Probability (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Probability (WAEC)

Probability

Tazama Jibu

Swali 61 Ripoti

(a) P varies directly as Q and inversely as the square of R. If P = 1 when Q = 8 and R = 2, find the value of Q when P = 3 and R = 5.

(b) An aeroplane flies from town A(20°N, 60°E) to town B(20°N, 20°E). (i) if the journey takes 6 hours, calculate, correct to 3 significant figures, the average speed of the aeroplane. (ii) if it then flies due North from town B to town C, 420 km away, calculate correct to the nearest degree, the latitude of town C. [Take radius of the earth = 6400 km and $\pi$ = 3.142].

Jibu

None

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Soma maelezo ya somo kwenye Variation (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Soma maelezo ya somo kwenye Variation (WAEC)

Sine, Cosine And Tangent Of An Angle

Variation

Tazama Jibu

Swali 62 Ripoti