WAEC SSCE - General Mathematics - 2009

Swali 1 Ripoti

Express the square root of 0.000144 in the standard form

1.2 x 10^-4

1.2 x 10^-3

1.2 x 10^-2

1.2 x 10^-1

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Number Bases (JAMB)

Number Bases

Tazama Jibu

Swali 2 Ripoti

Using the diagram, find the bearing of X from Y

300^o

240^o

120^o

60^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Bearings (WAEC)

Soma maelezo ya somo kwenye Circles (WAEC)

Bearings

Circles

Tazama Jibu

Swali 3 Ripoti

Arrange the following numbers in descending orders of magnitude: 22_three, 34_five, 21_six

21_six, 22_three, 34_five,

21_six, 34_five, 22_three

22_three, 34_five, 21_six

34_five, 21_six, 22_three

Maelezo ya Majibu

To compare these numbers, we need to convert all of them to the same base. Let's convert them all to base 10 for simplicity: - 22_three = 2\*3¹ + 2\*3⁰ = 6 + 2 = 8 - 34_five = 3\*5¹ + 4\*5⁰ = 15 + 4 = 19 - 21_six = 2\*6¹ + 1\*6⁰ = 12 + 1 = 13 So, in base 10, the numbers are 8, 19, and 13. To arrange them in descending order of magnitude, we simply sort them from largest to smallest: - 19, 13, 8 Therefore, the correct answer is: 34_five, 21_six, 22_three

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

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Swali 4 Ripoti

The following is the graph of a quadratic friction, find the co-ordinates of point P

(0, 4)

(4, 0)

(0, -4)

(-4, 0)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Soma maelezo ya somo kwenye Graphs Of Linear And Quadratic Functions (WAEC)

Quadratic Equations

Graphs Of Linear And Quadratic Functions

Tazama Jibu

Swali 5 Ripoti

If log 2 = x, log 3 = y and log 7 = z, find, in terms of x, y and z, the value of log ($\frac{28}{3}$)

2x + y - z

2x + z - y

x + y - 2x

x + x - y

Maelezo ya Majibu

We can use logarithmic rules to solve this question. Let's first express log($\frac{28}{3}$) in terms of x, y, and z. log($\frac{28}{3}$) = log(28) - log(3) We know that: log(28) = log(4 × 7) = log(4) + log(7) = 2x + z log(3) = y Therefore: log($\frac{28}{3}$) = 2x + z - y So the correct answer is 2x + z - y.

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

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Swali 6 Ripoti

PQRS is a trapezium. QR//PS, /PQ/ = 5cm, /OR/ = 6cm, /PS/ = 10cm and angle QPS = 42^o. Calculate, correct to the nearest cm², the area of the trapezium (h = 3.35cm² )

27cm²

30cm²

36cm²

37cm²

Maelezo ya Majibu

Tazama Jibu

Swali 7 Ripoti

Simplify (x - 3y)² - (x + 3y)²

2(x + 3y)

(2x - 3y)

-12xy

6xy

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

Tazama Jibu

Swali 8 Ripoti

If c and k are the roots of 6 - x - x² = 0, find c + k

-1

-3

Maelezo ya Majibu

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Modular Arithmetic

Quadratic Equations

Tazama Jibu

Swali 9 Ripoti

If 9^2x = $\frac{1}{3}$(27^x), find x

-1

-2

Maelezo ya Majibu

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

Soma maelezo ya somo kwenye Indices (WAEC)

Solution Of Linear Equations

Indices

Tazama Jibu

Swali 10 Ripoti

A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is $\frac{3}{10}$ and the probability of picking a white ball at random is $\frac{2}{5}$. If there are 30 balls in the box, how many of them are red?

Maelezo ya Majibu

The probability of picking a black ball at random from the box is $\frac{3}{10}$ and the probability of picking a white ball at random is $\frac{2}{5}$. Let's assume that there are x red balls in the box. Since there are a total of 30 balls, we can write: number of black balls + number of white balls + number of red balls = total number of balls $\frac{3}{10}(30) + \frac{2}{5}(30) + x = 30$ Simplifying the above equation gives: 9 + 12 + x = 30 x = 30 - 9 - 12 x = 9 Therefore, there are 9 red balls in the box.

Tazama Jibu

Swali 11 Ripoti

The pie chart shows the distribution of 4320 students who graduated from four departments in a university. If a student is picked at random from the four departments, what id the probability that he is not from the education department?

$\frac{3}{10}$

$\frac{2}{9}$

$\frac{5}{18}$

$\frac{7}{10}$

Maelezo ya Majibu

To find the probability that a student picked at random is not from the education department, we need to find the total number of students who are not from the education department and divide it by the total number of students in all departments. From the pie chart, we can see that the education department has 30% of the total students. Therefore, the remaining three departments have a total of 70% of the total students. To find the probability of picking a student who is not from the education department, we divide the percentage of students who are not in the education department by 100%: Probability = $\frac{70}{100}$ = $\frac{7}{10}$ Therefore, the probability that a student picked at random is not from the education department is $\frac{7}{10}$. The correct option is: $\frac{7}{10}$.

Soma maelezo ya somo kwenye Variation (JAMB)

Soma maelezo ya somo kwenye Probability (WAEC)

Soma maelezo ya somo kwenye Mensuration (JAMB)

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

Variation

Probability

Mensuration

Surds (radicals)

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Swali 12 Ripoti

The pie chart shows the distribution of 4320 students who graduated from four departments in a university. How many students graduated from the science department?

840

864

920

960

Maelezo ya Majibu

To find the number of students who graduated from the science department, we need to look at the pie chart and determine the percentage of students that belong to that department. From the pie chart, we can see that the science department occupies 20% of the entire circle. To find the number of students in the science department, we need to calculate 20% of 4320, which can be done by multiplying 4320 by 0.20. 20% of 4320 = 0.20 x 4320 = 864 Therefore, the number of students who graduated from the science department is 864. So, the correct answer is option B: 864.

Soma maelezo ya somo kwenye Mensuration (JAMB)

Mensuration

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Swali 13 Ripoti

PQRS is a trapezuim. QR//PS, /PQ/ = 5cm, /OR/ = 6cm, /PS/ = 10cm and angle QPS = 42^o. Calculate the perpendicular distance between the parallel sides

3.35cm

3.73cm

4.50cm

4.62cm

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 14 Ripoti

If /XY/ = 50m, how far cast of X is Y?

25.5m

40.6m

40.8m

43.3m

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 15 Ripoti

If $\frac{3}{2x} - \frac{2}{3x} = 4$, solve for x

$\frac{4}{5}$

$\frac{4}{13}$

$\frac{5}{24}$

$\frac{13}{24}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Algebraic Fractions

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Swali 16 Ripoti

If (2x + 3)³ = 125, find the value of x

Maelezo ya Majibu

We are given that (2x + 3)³ = 125. We can rewrite 125 as 5³. Therefore, we have: (2x + 3)³ = 5³ Taking the cube root of both sides, we get: 2x + 3 = 5 Solving for x, we get: 2x = 2 x = 1 Therefore, the value of x is 1. Answer: (a) 1.

Soma maelezo ya somo kwenye Indices (WAEC)

Indices

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Swali 17 Ripoti

Two sets are disjoint if

they are both empty

their union is an empty set

their intersection is an empty set

one of them is a subset of the other

Maelezo ya Majibu

Two sets are said to be disjoint if their intersection is an empty set. In other words, if there are no common elements between the sets, they are said to be disjoint. For example, the sets {1,2,3} and {4,5,6} are disjoint since their intersection is an empty set {} or ∅. On the other hand, the sets {1,2,3} and {2,3,4} are not disjoint since they have elements in common, namely 2 and 3.

Soma maelezo ya somo kwenye Sets (WAEC)

Soma maelezo ya somo kwenye Sets (JAMB)

Sets

Tazama Jibu

Swali 18 Ripoti

in the diagram, angle 20^o is subtended at the centre of the circle, find the value of x

30^o

50^o

80^o

100^o

Maelezo ya Majibu

In the given diagram, we have a circle with center O and angle 20^o subtended at the center. We need to find the value of x. Firstly, we know that the angle subtended at the center of a circle is twice the angle subtended at the circumference by the same arc. Therefore, angle AOB = 2 × 20^o = 40^o Also, we know that angle in a semicircle is a right angle. So, angle AOC = 90^o. Using the fact that the angles in a triangle add up to 180^o, we can find angle BOC as follows: angle BOC = 180^o - angle AOB - angle AOC = 180^o - 40^o - 90^o = 50^o Since angle BOC is an angle at the circumference that subtends the arc BC, which is equal to x degrees, we have: x = angle BOC = 50^o Therefore, the value of x is 50^o. Answer is correct.

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

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Swali 19 Ripoti

In an examination, Kofi scored x% in Physics, 50% in Chemistry and 70% in Biology. If his mean score for the three subjects was 55%, find x

Maelezo ya Majibu

Kofi's mean score for the three subjects was 55%, so the total percentage score for the three subjects is 3 x 55 = 165%. Let's assume that Kofi scored x% in Physics. Then, the total percentage score for Physics, Chemistry and Biology would be: x + 50 + 70 = 165 Simplifying the equation, we get: x = 165 - 50 - 70 x = 45 Therefore, Kofi scored 45% in Physics. So the correct option is (B) 45.

Soma maelezo ya somo kwenye Change Of Subject Of A Formula/Relation (WAEC)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Change Of Subject Of A Formula/Relation

Modular Arithmetic

Tazama Jibu

Swali 20 Ripoti

The capacity of a water tank is 1,800 litres. If the tank is in form of a cuboid with base 600cm by 150 cm. Find the height of the tank

2cm

20cm

200cm

2000cm

Maelezo ya Majibu

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Soma maelezo ya somo kwenye Areas (WAEC)

Euclidean Geometry

Areas

Tazama Jibu

Swali 21 Ripoti

Simplify: (3$\frac{1}{2} + 4\frac{1}{3}) \div (\frac{5}{6} - \frac{2}{3}$)

1$\frac{1}{4}$

8$\frac{1}{2}$

Maelezo ya Majibu

We will start by simplifying the expression inside the parenthesis first. 3$\frac{1}{2}$ + 4$\frac{1}{3}$ = (7/2) + (13/3) To add these two fractions, we need a common denominator. Multiplying the denominators together gives us 6, so: (7/2) + (13/3) = (21/6) + (26/6) = 47/6 Now, let's simplify the expression in the denominator: $\frac{5}{6} - \frac{2}{3}$ = $\frac{5}{6} - \frac{4}{6}$ = $\frac{1}{6}$ Finally, we can substitute these values into the original expression: (3$\frac{1}{2}$ + 4$\frac{1}{3}$) ÷ ($\frac{5}{6}$ - $\frac{2}{3}$) = (47/6) ÷ (1/6) When dividing fractions, we can multiply the first fraction by the reciprocal of the second: (47/6) ÷ (1/6) = (47/6) x (6/1) = 47 Therefore, the answer is 47.

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Tazama Jibu

Swali 22 Ripoti

Given that sin 60^o = $\frac{\sqrt{3}}{2}$ and cos 60^o = $\frac{1}{2}$, evaluate $\frac{1 - sin 60^o}{1 + cos 60^o}$

$\frac{2 + \sqrt{3}}{3}$

$\frac{1 - \sqrt{3}}{3}$

$\frac{1 + \sqrt{3}}{3}$

$\frac{2 - \sqrt{3}}{3}$

Maelezo ya Majibu

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

Sine, Cosine And Tangent Of An Angle

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Swali 23 Ripoti

In the diagram, IG is parallel to JE, JEF = 120^o and FHG = 130^o, fins the angle marked t

40^o

70^o

80^o

100^o

Maelezo ya Majibu

Tazama Jibu

Swali 24 Ripoti

If 85% of x is N3230, what is the value of x?

N2745.50

N3714.50

N3800.00

N4845.00

Maelezo ya Majibu

We can solve this problem using a proportion. If 85% of x is N3230, that means we can write: 0.85x = N3230 To solve for x, we need to isolate x on one side of the equation. We can do this by dividing both sides by 0.85: x = N3230 ÷ 0.85 Using a calculator, we get: x ≈ N3800.00 Therefore, the value of x is N3800.00.

Soma maelezo ya somo kwenye Percentages (WAEC)

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

Percentages

Positive And Negative Integers, Rational Numbers

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Swali 25 Ripoti

What is the median of the following scores: 22 35 41 63 74 82

Maelezo ya Majibu

To find the median of a set of numbers, we first need to arrange them in ascending or descending order. In this case, arranging the numbers in ascending order gives us: 22, 35, 41, 63, 74, 82 The median is the middle number in the set when the numbers are arranged in order. Since we have an even number of numbers in this set, there are two middle numbers: 41 and 63. To find the median, we take the average of these two numbers: Median = (41 + 63) / 2 = 104 / 2 = 52 Therefore, the median of the scores is 52.

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Euclidean Geometry

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Swali 26 Ripoti

An arc of a circle subtends an angle of 60^o at the centre. If the radius of the circle is 3cm, find , in terms of $\pi$, the length of the arc

$\pi$cm

2$\pi$cm

3$\pi$cm

6$\pi$cm

Maelezo ya Majibu

When an angle in degrees is subtended at the center of a circle, the length of the arc it cuts out is given by: $$\text{Length of arc} = \frac{\text{angle}}{360^\circ} \times 2\pi r$$ where r is the radius of the circle. In this case, the angle is 60° and the radius is 3 cm. Substituting these values into the formula above, we get: $$\text{Length of arc} = \frac{60}{360^\circ} \times 2\pi (3\text{ cm}) = \frac{1}{6} \times 6\pi = \pi \text{ cm}$$ Therefore, the length of the arc, in terms of π, is π cm. Hence, the correct option is: $\pi$cm.

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

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Swali 27 Ripoti

The interior angles of a pentagon are (2^x + 5)^o, (x + 20)^o, x^o, (3x - 20)^o and (x + 15)^o. Find the value of x

80^o

70^o

65^o

40^o

Maelezo ya Majibu

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

Soma maelezo ya somo kwenye Indices (WAEC)

Solution Of Linear Equations

Indices

Tazama Jibu

Swali 28 Ripoti

In the diagram, /TP/ = 12cm and it is 6cm from O, the centre of the circle, Calculate < TOP

120^o

90^o

60^o

45^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 29 Ripoti

If a positive integer, list the values of x which satisfy the equation 3x - 4 < 6 and x - 1 > 0

{1, 2, 3}

{2, 3}

{2, 3, 4}

{2, 3, 4, 5}

Maelezo ya Majibu

Soma maelezo ya somo kwenye Linear Inequalities (WAEC)

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

Linear Inequalities

Surds (radicals)

Tazama Jibu

Swali 30 Ripoti

In the diagram, \SQ\ = 4cm, \PT\ = 7cm. /TR/ = 5cm and ST//OR. If /SP/ = xcm, find the value of x

5.6

6.5

6.6

6.8

Maelezo ya Majibu

Soma maelezo ya somo kwenye Polynomials (JAMB)

Soma maelezo ya somo kwenye Sets (JAMB)

Polynomials

Sets

Tazama Jibu

Swali 31 Ripoti

Each of the interior angles of a regular polygon is 140^o. Calculate the sum of all the interior angles of the polygon

1080^o

1260^o

1800^o

2160^o

Maelezo ya Majibu

In a regular polygon with n sides, each interior angle measures: \begin{align*} 180^\circ - \frac{360^\circ}{n} \end{align*} Since each interior angle of this polygon is 140^o, we can equate the above formula to 140^o: \begin{align*} 180^\circ - \frac{360^\circ}{n} &= 140^\circ\\ \frac{360^\circ}{n} &= 40^\circ\\ n &= \frac{360^\circ}{40^\circ}\\ n &= 9 \end{align*} Therefore, the given polygon is a nonagon (a polygon with nine sides). The sum of the interior angles of a polygon with n sides can be calculated using the formula: \begin{align*} S &= (n-2)180^\circ \end{align*} Substituting n=9 into this formula, we get: \begin{align*} S &= (9-2)180^\circ\\ &= 7\cdot180^\circ\\ &= 1260^\circ \end{align*} Therefore, the sum of all the interior angles of the given polygon is 1260^o. Hence, the correct option is: - 1260^o

Soma maelezo ya somo kwenye Indices (WAEC)

Indices

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Swali 32 Ripoti

From the diagram which of the following statements are correct? i. XQ is a radius of a circle centre Q. ii. /XQ/ = /QY/. iii. /QX/ = /XY/

i only

inand ii only

ii and iii only

i, ii and iii

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Statistics (WAEC)

Circles

Statistics

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Swali 33 Ripoti

In a particular year, the exchange rate of naira (N) varies directly with the Dollars{$}. If N1122 is equivalent to $8, find the Naira equivalent of $36

N8976

N5049

N140.25

N31.17

Maelezo ya Majibu

The exchange rate of naira (N) varies directly with the Dollars($). This means that the exchange rate is constant, and we can set up a proportion to solve the problem. If N1122 is equivalent to $8, we can write: N1122/$8 = x/$36 where x is the Naira equivalent of $36. To solve for x, we can cross-multiply and simplify: N1122 x 36 = $8 x x 40392 = 8x x = 40392/8 = 5049 Therefore, the Naira equivalent of $36 is N5049. So, the correct option is (B) N5049.

Soma maelezo ya somo kwenye Variation (WAEC)

Soma maelezo ya somo kwenye Variation (JAMB)

Variation

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Swali 34 Ripoti

Find the value to which N3000.00 will amount in 5 years at 6% per annum simple interest

N3,900.00

N3,750.00

N3,600.00

N3,300

Maelezo ya Majibu

Simple interest is calculated as the product of the principal, the rate of interest, and the time duration. From the question, we have a principal of N3000.00, an interest rate of 6%, and a duration of 5 years. Using the formula for simple interest, we can find the interest accrued over the 5 years as: Interest = (P * R * T) / 100 = (3000 * 6 * 5) / 100 = N900.00 The total value to which N3000.00 will amount to after 5 years is the sum of the principal and the interest, which is: Total = Principal + Interest = 3000 + 900 = N3900.00 Therefore, N3000.00 will amount to N3900.00 after 5 years at 6% per annum simple interest. So the correct answer is option A, N3,900.00.

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Soma maelezo ya somo kwenye Ratio, Proportions And Rates (WAEC)

Modular Arithmetic

Ratio, Proportions And Rates

Tazama Jibu

Swali 35 Ripoti

Factorize x² - 2x - 3xy completely

(x - 2)(3x - y)

(x - 3y)(x - 2)

(x - 3y)(x - 3y)

(3x + y)(x - 2)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 36 Ripoti

The angles of triangle are (x + 10)^o, (2x - 40)^o and (3x - 90)^o. Which of the following accurately describes the triangle?

it is a scalene triangle

it is right angled isosceles triangle

t is an equilateral triangle

It is an isosceles triangle but not right angled

Maelezo ya Majibu

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Triangles And Polygons

Tazama Jibu

Swali 37 Ripoti

A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of size 8m x 7m x 5m.(1 litre = 1000cm³)`

280

2800

28000

Maelezo ya Majibu

The volume of the reservoir can be found by multiplying its dimensions: 8m x 7m x 5m = 280 m^3 Since 1 liter is equal to 1000 cubic centimeters (cm^3), 1 cubic meter is equal to 1,000,000 cubic centimeters. Therefore, the reservoir has a volume of: 280 m^3 x 1,000,000 cm^3/m^3 = 280,000,000 cm^3 Each bucket can hold 10 liters of water or 10,000 cubic centimeters (cm^3) of water since 1 liter is equal to 1000 cm^3. Therefore, the number of buckets needed to fill the reservoir is: 280,000,000 cm^3 ÷ 10,000 cm^3/bucket = 28,000 buckets Therefore, the answer is 28,000.

Soma maelezo ya somo kwenye Logical Reasoning (WAEC)

Soma maelezo ya somo kwenye Representation Of Data (JAMB)

Logical Reasoning

Representation Of Data

Tazama Jibu

Swali 38 Ripoti

The following is the graph of a quadratic friction, find the value of x when y = 0

1, 2

1, 4

2, 3

1, 6

Maelezo ya Majibu

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 39 Ripoti

If M and N are two fixed points in a plane. Find the locus L = [P : PM = PN]

a line equal to MN

line parallel to MN

Perpendicular bisector of MN

A circle centre P, radius MN

Maelezo ya Majibu

Soma maelezo ya somo kwenye Loci (JAMB)

Soma maelezo ya somo kwenye Loci (WAEC)

Soma maelezo ya somo kwenye Coordinate Geometry (JAMB)

Loci

Coordinate Geometry

Tazama Jibu

Swali 40 Ripoti

Find the value of x in the diagram

50^o

30^o

22^o

17^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Number Bases (JAMB)

Circles

Number Bases

Tazama Jibu

Swali 41 Ripoti

solve $\frac{2x + 1}{6} - \frac{3x - 1}{4}$ = 0

$\frac{1}{5}$

-$\frac{1}{5}$

-1

Maelezo ya Majibu

To solve the equation $\frac{2x + 1}{6} - \frac{3x - 1}{4} = 0$, we need to simplify the left-hand side and solve for x. First, we need to find a common denominator for the two fractions. The smallest common multiple of 6 and 4 is 12, so we can rewrite the equation as: \[\frac{2x+1}{6}\cdot \frac{2}{2} - \frac{3x-1}{4}\cdot \frac{3}{3} = 0\] Simplifying, we get: \[\frac{4x+2}{12} - \frac{9x-3}{12} = 0\] Combining the fractions, we get: \[\frac{4x+2-(9x-3)}{12} = 0\] Simplifying further, we get: \[\frac{-5x+5}{12} = 0\] Multiplying both sides by 12, we get: \[-5x+5=0\] Adding 5 to both sides, we get: \[-5x=-5\] Dividing both sides by -5, we get: \[x=1\] Therefore, the solution to the equation is x = 1.

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

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

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

Solution Of Linear Equations

Algebraic Fractions

Simple Operations On Algebraic Expressions

Tazama Jibu

Swali 42 Ripoti

The diameter of a bicycle wheel is 42cm. If the wheel makes 16 complete revolution, what will be the total distance covered by the wheel? [Take $\pi \frac{22}{7}$

672cm

1056cm

2112cm

4224cm

Maelezo ya Majibu

The distance covered by the wheel is equal to the circumference of the wheel multiplied by the number of revolutions made. The circumference of the wheel can be calculated using the formula: circumference = diameter x pi circumference = 42cm x 22/7 circumference = 132cm Therefore, the distance covered by the wheel in 16 complete revolutions is: distance = circumference x number of revolutions distance = 132cm x 16 distance = 2112cm So, the answer is (c) 2112cm.

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Areas (WAEC)

Volumes

Areas

Tazama Jibu

Swali 43 Ripoti

Simplify; $\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}$

zero

$\sqrt{2}$

2$\sqrt{2}$

4\(\sqrt{2}\0

Maelezo ya Majibu

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

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

Positive And Negative Integers, Rational Numbers

Surds (radicals)

Tazama Jibu

Swali 44 Ripoti

Express 2.7864 x 10^-3 to 2 significant figures

0.28

0.27

0.0028

0.0027

Maelezo ya Majibu

To express 2.7864 x 10^-3 to 2 significant figures, we need to round off the number to the second significant digit from the left. Since the first significant digit is 2, and the second significant digit is 7, we will look at the third digit, which is 8. Since 8 is greater than or equal to 5, we round up the second significant digit (7) by 1. Therefore, the number becomes 0.0028. So, the answer is 0.0028.

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

Soma maelezo ya somo kwenye Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

Tazama Jibu

Swali 45 Ripoti

Find the quadratic equation whose roots are -$\frac{1}{2}$ and 3

2x² - 2x + 3 = 0

2x² - 2x - 3 = 0

2x² - 5x - 3 = 0

3x² - 5x - 3 = 0

Maelezo ya Majibu

To find the quadratic equation given its roots, we use the fact that for a quadratic equation of the form ax² + bx + c = 0, the roots are given by the formula: x = (-b ± √(b² - 4ac)) / 2a If the roots are given as α and β, then the quadratic equation can be written as: (x - α)(x - β) = 0 Expanding the above equation gives: x² - (α + β)x + αβ = 0 Therefore, to find the quadratic equation whose roots are -$\frac{1}{2}$ and 3, we substitute α = -$\frac{1}{2}$ and β = 3 into the equation: x² - (α + β)x + αβ = 0 x² - (-$\frac{1}{2}$ + 3)x + (-$\frac{1}{2}$ × 3) = 0 Simplifying the above equation, we get: 2x² - 5x - 3 = 0 Therefore, the quadratic equation whose roots are -$\frac{1}{2}$ and 3 is 2x² - 5x - 3 = 0. The correct option is (C) 2x² - 5x - 3 = 0.

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 46 Ripoti

Find the value of x in the diagram

50^o

60^o

70^o

80^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Angles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Circles

Angles

Triangles And Polygons

Tazama Jibu

Swali 47 Ripoti

The marks scored by 50 students in a Geography examination are as follows :

60 54 40 67 53 73 37 55 62 43 44 69 39 32 45 58 48 67 39 51 46 59 40 52 61 48 23 60 59 47 65 58 74 47 40 59 68 51 50 50 71 51 26 36 38 70 46 40 51 42.

(a) Using class intervals 21 - 30, 31 - 40, ..., prepare a frequency distribution table.

(b) Calculate the mean mark of the distribution.

Jibu

None

Soma maelezo ya somo kwenye Percentages (WAEC)

Soma maelezo ya somo kwenye Probability (WAEC)

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

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Percentages (WAEC)

Soma maelezo ya somo kwenye Probability (WAEC)

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

Percentages

Probability

Surds (radicals)

Tazama Jibu

Swali 48 Ripoti

(a) How many numbers between 75 and 500 are divisible by 7?

(b) The 8th term of an Arithmetic Progression (A.P) is 5 times the 3rd term while the 7th term is 9 greater than the 4th term. Write the first 5 terms of the A.P.

Jibu

None

Soma maelezo ya somo kwenye Progression (JAMB)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Progression (JAMB)

Progression

Tazama Jibu

Swali 49 Ripoti

(a) Given that $(\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = a + b\sqrt{6}$, find a and b.

(b) If $\frac{2^{1 - y} \times 2^{y - 1}}{2^{y + 2}} = 8^{2 - 3y}$, find y.

Jibu

None

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

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

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

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

Modular Arithmetic

Surds (radicals)

Tazama Jibu

Swali 50 Ripoti

The table shows the number of children per family in a community.

No of children	0	1	2	3	4	5
No of families	3	5	7	4	3	2

(a) Find the : (i) mode ; (ii) third quartile ; (iii) probability that a family has at least 2 children.

(b) If a pie chart were to be drawn for the data, what would be the sectorial angle representing families with one child?

Jibu

None

Maelezo ya Majibu

None

Tazama Jibu

Swali 51 Ripoti

(a) If $9 \cos x - 7 = 1$ and $0° \leq x \leq 90°$, find x.

(b) Given that x is an integer, find the three greatest values of x which satisfy the inequality $7x < 2x - 13$.

Jibu

None

Soma maelezo ya somo kwenye Change Of Subject Of A Formula/Relation (WAEC)

Soma maelezo ya somo kwenye Inequalities (JAMB)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Change Of Subject Of A Formula/Relation (WAEC)

Soma maelezo ya somo kwenye Inequalities (JAMB)

Change Of Subject Of A Formula/Relation

Inequalities

Tazama Jibu

Swali 52 Ripoti

In the diagram, ABCDEF is a triangular prism. < ABC = < DEF = 90°, /AB/ = 24 cm, /BC/ = 7 cm and /CD/ = 40 cm. Calculate :

(a) /AC/ ;

(b) the total surface area of the prism.

Jibu

None

Maelezo ya Majibu

None

Tazama Jibu

Swali 53 Ripoti

(a) Copy and complete the table of values for $y = \sin x + 2 \cos x$, correct to one decimal place.

x	0°	30°	60°	90°	120°	150°	180°	210°	240°
y		2.2				-1.2	-2.0		-1.9

(b) Using a scale of 2 cm to 30° on the x- axis and 2 cm to 0.5 units on the y- axis, draw the graph of $y = \sin x + 2\cos x$ for $0° \leq x \leq 240°$.

(d) From the graph, find y when x = 171°.

Jibu

None

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

Maelezo ya Majibu

None

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

Sine, Cosine And Tangent Of An Angle

Tazama Jibu

Swali 54 Ripoti

(a) If $\log 5 = 0.6990, \log 7 = 0.8451$ and $\log 8 = 0.9031$, evaluate $\log (\frac{35 \times 49}{40 \div 56})$.

(b) For a musical show, x children were present. There were 60 more adults than children. An adult paid D5 and a child D2. If a total of D1280 was collected, calculate the

(i) value of x ; (ii) ratio of the number of children to the number of adults ; (iii) average amount paid per person ; (iv) percentage gain if the organisers spent D720 on the show.

Jibu

None

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

Soma maelezo ya somo kwenye Logarithms (WAEC)

Maelezo ya Majibu

None

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

Soma maelezo ya somo kwenye Logarithms (WAEC)

Positive And Negative Integers, Rational Numbers

Logarithms

Tazama Jibu

Swali 55 Ripoti

(a) A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100 cm, calculate the radius of the circle. [Take $\pi = \frac{22}{7}$].

(b) A rope 60cm long is made to form a rectangle. If the length is 4 times its breadth, calculate, correct to one decimal place, the :

(i) length ; (ii) diagonal of the rectangle.

Jibu

None

Maelezo ya Majibu

None

Tazama Jibu

Swali 56 Ripoti

(a) A woman looking out from the window of a building at a height of 30m, observed that the angle of depression of the top of a flag pole was 44°. If the foot of the pole is 25m from the foot of the building and on the same horizontal ground, find, correct to the nearest whole number, the (i) angle of depression of the foot of the pole from the woman ; (ii) height of the flag pole.

(b) In the diagram, O is the centre of the circle, < OQR = 32° and < TPQ = 15°. Calculate, (i) < QPR ; (ii) < TQo.

Jibu

None

Maelezo ya Majibu

None

Tazama Jibu

Swali 57 Ripoti

(a) Out of 30 candidates applying for a post, 17 have degrees, 15 have diplomas and 4 neither degree nor diploma. How many of them have both?

(b) In triangle PQR, M and N are points on the side PQ and PR respectively such that MN is parallel to QR. If < PRQ = 75°, PN = QN and < PNQ = 125°, determine :

(i) < NQR ; (ii) < NPM.

Jibu

None

Soma maelezo ya somo kwenye Loci (WAEC)

Soma maelezo ya somo kwenye Sets (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Loci (WAEC)

Soma maelezo ya somo kwenye Sets (WAEC)

Loci

Sets

Tazama Jibu

Swali 58 Ripoti

(a) Using ruler and a pair of compasses only, construct : (i) quadrilateral PQRS such that /PQ/ = 10 cm, /QR/ = 8 cm, /PS/ = 6 cm, < PQR = 60° and < QPS = 75° ;

(ii) the locus $l_{1}$ of points equidistant from QR and RS ; (iii) locus $l_{2}$ of points equidistant from R and S ;

(b) Measure /RS/.

Jibu

None

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Maelezo ya Majibu

None

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Triangles And Polygons

Tazama Jibu

Swali 59 Ripoti

(a) Simplify $\frac{x + 2}{x - 2} - \frac{x + 3}{x - 1}$