WAEC SSCE - General Mathematics - 2002 (Objective)

Question 1 Report

Points X, Y and Z are located in the same horizontal plane such that Y is 12 km north of X and Z is on a bearing of 270° from X. If |XZ| = 6km, calculate, correct to one decimal place, lYZl

18km

13.4km Correct answer

13km

10.4km

Answer Details

Read lesson note on Circles (WAEC)

Read lesson note on Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

View Answer

Question 2 Report

If (x + 3) varies directly as y and x = 3 when y = 12, what is the value of x when y = 8?

1 Correct answer

$\frac{1}{2}$

$-\frac{}{}$

-1

Answer Details

In a direct variation, two variables are related by a constant ratio. This can be expressed mathematically as: x ∝ y which means that x is directly proportional to y, or that x and y vary directly. We can also write this relationship as an equation: x = ky where k is the constant of proportionality. In this problem, we are given that (x + 3) varies directly as y. So we can write: x + 3 = ky where k is some constant of proportionality that we don't know yet. We are also given that x = 3 when y = 12. We can use this information to solve for k: x + 3 = ky 3 + 3 = k(12) 6 = 12k k = 0.5 Now that we know k, we can use the equation x + 3 = ky to find x when y = 8: x + 3 = ky x + 3 = 0.5(8) x + 3 = 4 x = 1 Therefore, when y = 8, x = 1. The answer is (a) 1.

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

Read lesson note on Variation (JAMB)

Sine, Cosine And Tangent Of An Angle

Variation

View Answer

Question 3 Report

In the diagram, |SR| = |RQ| and ?PRQ = 58^o ?VQT = 19^o, PQT, SQV and PSR are straight lines. Find ?QPS

42^o Correct answer

39^o

38^o

30^o

Answer Details

Read lesson note on Triangles And Polygons (WAEC)

Triangles And Polygons

View Answer

Question 4 Report

The lengths of the parallel sides of a trapezium are 9 cm and 12 cm. lf the area of the trapezium is 105 cm², find the perpendicular distance between the parallel sides.

5cm

7cm

10cm Correct answer

15cm

Answer Details

The formula for the area of a trapezium is given as: Area = 1/2 × (sum of the parallel sides) × (perpendicular distance between them) In this case, we have the lengths of the parallel sides as 9 cm and 12 cm, and the area as 105 cm². Substituting these values in the formula, we get: 105 = 1/2 × (9 + 12) × (perpendicular distance) 105 = 1/2 × 21 × (perpendicular distance) 105 = 10.5 × (perpendicular distance) Dividing both sides by 10.5, we get: Perpendicular distance = 105/10.5 Perpendicular distance = 10 Therefore, the perpendicular distance between the parallel sides is 10 cm. Hence, the correct option is (c) 10cm.

Read lesson note on Lengths And Perimeters (WAEC)

Read lesson note on Areas (WAEC)

Lengths And Perimeters

Areas

View Answer

Question 5 Report

The diagram is the graph of $y = 6 + x - x^2$. The graph intercepts the x- axis at P and R and the y- axis at Q.

When $y = 3\frac{1}{3}$, what is the positive value of x?

$ 2\frac{1}{2}$

$ 2\frac{1}{5}$ Correct answer

$ 1\frac{1}{5}$

zero

Answer Details

The given function is $y = 6 + x - x^2$. We are required to find the value of x when y is equal to $3\frac{1}{3}$, which is also equal to $\frac{10}{3}$. Substituting $y = \frac{10}{3}$ in the given equation, we get \[\frac{10}{3} = 6 + x - x^2\] Rearranging the terms, we get \[x^2 - x + \frac{8}{3} = 0\] Solving the quadratic equation, we get two solutions for x, which are $\frac{4}{3}$ and $1\frac{1}{2}$. However, we are asked to find the positive value of x, which is $\boxed{2\frac{1}{5}}$.

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

View Answer

Question 6 Report

The ratio of the number of men to the number of women in a 20 member committee is 3:1. How many women must be added to the 20-member committee so as to make the ratio of men to women 3:2?

5 Correct answer

Answer Details

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

Read lesson note on Financial Arithmetic (WAEC)

Ratio, Proportions And Rates

Financial Arithmetic

View Answer

Question 7 Report

A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is $2\sqrt{3}$ cm. Calculate the volume of the pyramid

$5\frac{1}{3}cm^3$

$10\frac{2}{3}cm^3$ Correct answer

$16cm^3$

$32cm^3$

Answer Details

A right pyramid is a pyramid in which the apex is directly above the center of the base. In this case, the base is a square and the pyramid is right, so each triangular face of the pyramid is an isosceles right triangle. The slanting side of the pyramid is a hypotenuse of one of the triangular faces. By the Pythagorean theorem, the length of each leg of the right triangle is equal to the length of the base of the square, which is 4cm. Therefore, each leg has length 4cm and the hypotenuse has length $2\sqrt{3}$ cm. To find the height of the pyramid, we draw a perpendicular line from the apex of the pyramid to the center of the base. This line divides the square base into four congruent right triangles, each with legs of length 2cm and hypotenuse of length $2\sqrt{2}$ cm. By the Pythagorean theorem, the height of each of these triangles is $\sqrt{(2\sqrt{2})^{2} - 2^{2}} = \sqrt{8} = 2\sqrt{2}$. Therefore, the height of the pyramid is also 2$\sqrt{2}$cm. The volume of the pyramid is given by the formula: \[\frac{1}{3} \times (\text{area of base}) \times (\text{height})\] The area of the square base is $4^{2}$ cm$^{2}$ = 16 cm$^{2}$, and the height is 2$\sqrt{2}$ cm. Substituting these values into the formula, we get: \[\frac{1}{3} \times (16) \times (2\sqrt{2}) = \frac{32\sqrt{2}}{3} \approx 10.67 \text{ cm}^{3}\] Therefore, the volume of the pyramid is approximately 10.67 cm$^{3}$. Hence, the correct option is $\mathbf{(b)}$ $10\frac{2}{3}$ cm$^{3}$.

View Answer

Question 8 Report

In the diagram, |QR| = 10cm, PR⊥QS, angle PSR = 30° and angle PQR = 45°. Calculate in meters |QS|

$10(1+\sqrt{3})$ Correct answer

$20\sqrt{3}$

$10\sqrt{3}$

$(10+\sqrt{3})$

Answer Details

Read lesson note on Circles (WAEC)

Read lesson note on Number Bases (WAEC)

Circles

Number Bases

View Answer

Question 9 Report

In the diagram, LMT is a straight line. lf O is the centre of circle LMN, OMN = 20°, LTN = 32° and |NM| = |MT|, find LNM.

44^o

46^o Correct answer

52^o

70^o

Answer Details

Read lesson note on Circles (WAEC)

Circles

View Answer

Question 10 Report

A number is selected at random from the set Y = {18, 19, 20, . . . 28, 29}. Find the probability that the number is prime.

$\frac{1}{4}$ Correct answer

$\frac{3}{11}$

$\frac{1}{2}$

$\frac{3}{4}$

Answer Details

To find the probability of selecting a prime number from the set Y = {18, 19, 20, ..., 28, 29}, we need to first identify the prime numbers in this set. The prime numbers in this set are 19, 23, and 29. The total number of elements in the set Y is 12. Therefore, the probability of selecting a prime number from the set Y is 3/12 or 1/4. Therefore, the correct option is (a) $\frac{1}{4}$.

Read lesson note on Probability (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Probability

Surds (radicals)

View Answer

Question 11 Report

The number of goals scored by a school team in 10 netball matches are as follows: 3, 5, 7, 7, 8, 8, 8, 11, 11, 12. Find the probability that in a match, the school team will score at most 8 goals.

$\frac{7}{10}$ Correct answer

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{1}{5}$

Answer Details

Read lesson note on Probability (WAEC)

Probability

View Answer

Question 12 Report

Which of the following is represented by the above sketch?

y = x² + x - 6

y = x² - x - 6 Correct answer

y = x² - x + 6

y = x² + x + 6

Answer Details

The given sketch is a quadratic function graph. From the graph, we can see that the parabola intersects the x-axis at two points which are (-3, 0) and (2, 0). Therefore, the roots or zeros of the quadratic function are -3 and 2. By comparing the options given, we can see that only option B, y = x² - x - 6, has roots of -3 and 2. Thus, option B is the correct answer.

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

View Answer

Question 13 Report

In the diagram, QRT is a straight line. If angle PTR = 90°, angle PRT = 60°, angle PQR = 30° and |PQ| = $6\sqrt{3}cm$, calculate |RT|

0.3cm

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

3cm Correct answer

$3\sqrt{3}cm$

Answer Details

View Answer

Question 14 Report

In the diagram above, ∠PQU=36°, ∠QRT = 29°, PQ||RT. Find ∠PQR

94^o

65^o Correct answer

61^o

54^o

Answer Details

Read lesson note on Angles (WAEC)

Read lesson note on Triangles And Polygons (WAEC)

Angles

Triangles And Polygons

View Answer

Question 15 Report

In the diagram O is the center of the circle, ∠SOR = 64° and ∠PSO = 36°. Calculate ∠PQR

100^o

96^o

94^o

86^o Correct answer

Answer Details

View Answer

Question 16 Report

For what values of x is the expression $\frac{3x-2}{4x^2+9x-9}$ undefined?

$\frac{-3}{4} \hspace{1mm}or \hspace{1mm}3$

$\frac{-2}{3} \hspace{1mm}or \hspace{1mm}-3$

$\frac{2}{3} \hspace{1mm}or \hspace{1mm}3$

$\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3$ Correct answer

Answer Details

The expression $\frac{3x-2}{4x^2+9x-9}$ is undefined when the denominator is equal to zero. Therefore, we need to find the values of x that make the denominator zero. We can factor the denominator as follows: \[4x^2 + 9x - 9 = (4x - 3)(x + 3)\] So, the denominator is equal to zero when: \begin{align*} 4x - 3 &= 0 &\text{or} && x + 3 &= 0 \\ 4x &= 3 &&& x &= -3 \\ x &= \frac{3}{4} \end{align*} Therefore, the expression is undefined when $x = \frac{3}{4}$ or $x = -3$. So, the answer is $\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3$.

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Fractions

View Answer

Question 17 Report

If $M5_{ten} = 1001011_{two}$ find the value of M

7 Correct answer

Answer Details

To convert a number from base 2 to base 10, we multiply each digit by its corresponding power of 2 and sum the results. For example, in the binary number 1001, the first digit (from the right) represents 2^0 (1), the second digit represents 2^1 (2), the third digit represents 2^2 (4), and the fourth digit represents 2^3 (8). So, to convert 1001 to base 10, we compute: 1*2^0 + 0*2^1 + 0*2^2 + 1*2^3 = 1 + 0 + 0 + 8 = 9 Using this method, we can convert the binary number 1001011 to base 10: 1*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 0*2^4 + 0*2^5 + 1*2^6 = 1 + 2 + 0 + 8 + 0 + 0 + 64 = 75 Therefore, M5 in base 10 is 75, and since M5 is in base 10, M is simply 7. So the answer is 7.

Read lesson note on Number Bases (JAMB)

Number Bases

View Answer

Question 18 Report

The base diameter of a cone is 14cm, and its volume is 462 cm³. Find its height. [Taken $\pi = \frac{22}{7}$]

3.5cm

5cm

7cm

9cm Correct answer

Answer Details

The formula for the volume of a cone is given by V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. Since we are given the base diameter, which is 14cm, we can find the radius by dividing it by 2: radius, r = 14/2 = 7cm Also, we are given the volume of the cone, which is 462 cm^3. Substituting these values into the formula for the volume of a cone, we get: 462 = (1/3)π(7^2)h Simplifying this equation, we get: 22h = 198 h = 198/22 h = 9cm Therefore, the height of the cone is 9cm. Hence, the correct option is (d) 9cm.

Read lesson note on Integration (JAMB)

Integration

View Answer

Question 19 Report

In the diagram, $QR||TP and W\hat{P}T = 88^{\circ} $. Find the value of x

92^o

68^o

67^o Correct answer

23^o

Answer Details

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

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

Read lesson note on Angles (WAEC)

Angles And Intercepts On Parallel Lines

Simple Operations On Algebraic Expressions

Angles

View Answer

Question 20 Report

Find the value of x in the diagram

31^o

35^o Correct answer

37^o

41^o

Answer Details

Read lesson note on Circles (WAEC)

Read lesson note on Angles (WAEC)

Circles

Angles

View Answer

Question 21 Report

Simplify $\frac{2^{\frac{1}{2}}\times 8^{\frac{1}{2}}}{4}$

1 Correct answer

Answer Details

Read lesson note on Number Bases (WAEC)

Read lesson note on Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

View Answer

Question 22 Report

In the diagram, $\bar{PS}\hspace{1mm} and \hspace{1mm}\bar{QT}$ are two altitudes of ?PQR. Which of the following is equal to ∠RQT?

?PQT

?SRP

?PQR

?SPR Correct answer

Answer Details

In a triangle, an altitude is a line segment drawn from a vertex perpendicular to the opposite side. In the given diagram, $\bar{PS}$ and $\bar{QT}$ are two altitudes of triangle PQR. By definition, the altitude $\bar{QT}$ is perpendicular to the side $\bar{PR}$. Therefore, ∠QTR is a right angle. Also, we know that the sum of the angles in a triangle is 180 degrees. So, we can find the measure of ∠RQT as follows: ∠RQT = 180° - ∠QTR - ∠QRT We don't know the value of either ∠QTR or ∠QRT, but we can find one of them using the fact that $\bar{PS}$ is an altitude. Since $\bar{PS}$ is perpendicular to $\bar{QR}$, ∠QPS is a right angle. Therefore, ∠QTR = ∠QTP + ∠RTP Since ∠QTP and ∠RTP are both complementary to ∠QPR, which is a known angle in the diagram, we can find their values: ∠QTP = ∠RTP = 90° - ∠QPR Now we can substitute these values into our equation for ∠RQT: ∠RQT = 180° - (90° - ∠QPR) - (90° - ∠QPR) Simplifying this expression gives: ∠RQT = 2∠QPR - 90° Therefore, the answer is option (B) ?SRP, since ∠QPR and ∠SRP are corresponding angles and thus equal to each other.

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

Read lesson note on Triangles And Polygons (WAEC)

Angles And Intercepts On Parallel Lines

Triangles And Polygons

View Answer

Question 23 Report

Factorize m(2a-b)-2n(b-2a)

(2a-b)(2n-m)

(2a+b)(m-2n)

(2a-b)(m+2n) Correct answer

(2a-b)(m-2n)

Answer Details

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

View Answer

Question 24 Report

The range of the distribution is

25 Correct answer

Answer Details

Read lesson note on Measures Of Location (JAMB)

Measures Of Location

View Answer

Question 25 Report

The median of the distribution is

17.5

15 Correct answer

12.5

Answer Details

Read lesson note on Integration (JAMB)

Read lesson note on Measures Of Location (JAMB)

Integration

Measures Of Location

View Answer

Question 26 Report

Find the nth term of the sequence 4, 10, 16 ,...

2(3n- 1) Correct answer

2(2 + 3 ^n-1)

2 ⁿ + 2

2(3n+2)

Answer Details

The sequence 4, 10, 16,... is an arithmetic sequence because there is a common difference between every pair of consecutive terms. To find the common difference, we can subtract any term from the following term. For example: - The common difference between the first and second terms is 10 - 4 = 6. - The common difference between the second and third terms is 16 - 10 = 6. Since the common difference is 6, we can find the nth term of the sequence using the formula: nth term = first term + (n - 1) * common difference The first term is 4 and the common difference is 6, so we get: nth term = 4 + (n - 1) * 6 Simplifying this expression, we get: nth term = 6n - 2 Therefore, the correct answer is (A) 2(3n-1).

Read lesson note on Sequence And Series (WAEC)

Sequence And Series

View Answer

Question 27 Report

Simplify $5\frac{1}{4}\div \left(1\frac{2}{3}- \frac{1}{2}\right)$

$1\frac{3}{4}$

$3\frac{1}{2}$

$4\frac{1}{2}$ Correct answer

$8\frac{1}{2}$

Answer Details

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

Fractions, Decimals And Approximations

View Answer

Question 28 Report

The length, in cm, of the sides of a right angled triangle are x, (x+2) and (x+1) where x > 0. Find , in cm, the length of its hypotenuse

5 Correct answer

Answer Details

In a right-angled triangle, the hypotenuse is the longest side, and it is opposite to the right angle. Using the Pythagorean theorem, we know that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. So, we have: \begin{align*} x^2 + (x+2)^2 &= (x+1)^2 \\ x^2 + x^2 + 4x + 4 &= x^2 + 2x + 1 \\ x^2 + 2x^2 + 4x + 4 &= x^2 + 2x + 1 \\ 3x^2 + 4x + 4 &= x^2 + 2x + 1 \\ 2x^2 + 2x + 3 &= 0 \end{align*} We can solve this quadratic equation using the quadratic formula: \begin{align*} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\ &= \frac{-2 \pm \sqrt{2^2 - 4(2)(3)}}{2(2)} \\ &= \frac{-2 \pm \sqrt{-8}}{4} \\ &= \frac{-1}{2} \pm \frac{\sqrt{2}}{2}i \end{align*} Since x must be greater than 0, the only valid solution is: \begin{align*} x &= \frac{-1}{2} + \frac{\sqrt{2}}{2}i \end{align*} However, we are asked to find the length of the hypotenuse, which is given by: \begin{align*} \sqrt{x^2 + (x+2)^2} &= \sqrt{\left(\frac{-1}{2} + \frac{\sqrt{2}}{2}i\right)^2 + \left(\frac{1}{2} + \frac{\sqrt{2}}{2}i\right)^2} \\ &= \sqrt{\frac{1}{4} - \frac{1}{2}\sqrt{2}i - \frac{1}{4} - \frac{1}{2}\sqrt{2}i + \frac{1}{4} + \frac{\sqrt{2}}{2}i + \frac{1}{4} - \frac{\sqrt{2}}{2}i} \\ &= \sqrt{\frac{1}{2}} \\ &= \frac{\sqrt{2}}{2} \approx 0.707 \end{align*} Therefore, the length of the hypotenuse is approximately 0.707 cm, which is closest to 5 cm.

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

View Answer

Question 29 Report

If (-3, -4) is a point on the line y = mx + 2 find the value of m.

-2

$\frac{7}{4}$

2 Correct answer

$\frac{8}{3}$

Answer Details

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In this question, we are given that the point (-3, -4) lies on the line y = mx + 2. This means that when x = -3, y = -4. We can substitute these values into the equation to get: -4 = m(-3) + 2 Simplifying this expression, we get: -4 = -3m + 2 Subtracting 2 from both sides, we get: -6 = -3m Dividing both sides by -3, we get: m = 2 Therefore, the value of m is 2.

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

View Answer

Question 30 Report

Simplify $\frac{1}{1-x} + \frac{2}{1+x}$

$\frac{x+3}{1-x^2}$

$\frac{x-3}{1+x^2}$

$\frac{3-x}{1-x^2}$ Correct answer

$\frac{3-x}{1+x^2}$

Answer Details

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

Read lesson note on Algebraic Fractions (WAEC)

Positive And Negative Integers, Rational Numbers

Algebraic Fractions

View Answer

Question 31 Report

The upper quartile of the distribution is

27.5

17.75 Correct answer

Answer Details

Read lesson note on Measures Of Dispersion (JAMB)

Measures Of Dispersion

View Answer

Question 32 Report

Find the value of x in 0.5x + 2.6 = 5x + 0.35

0.5 Correct answer

2.6

Answer Details

To find the value of x in the equation 0.5x + 2.6 = 5x + 0.35, we need to isolate x on one side of the equation. We can start by subtracting 0.5x from both sides to get rid of the x-term on the left side: 0.5x + 2.6 - 0.5x = 5x + 0.35 - 0.5x Simplifying the left side and combining like terms on the right side, we get: 2.6 = 4.5x + 0.35 Subtracting 0.35 from both sides, we get: 2.6 - 0.35 = 4.5x Simplifying and dividing both sides by 4.5, we get: x = (2.6 - 0.35)/4.5 = 0.5 Therefore, the value of x is 0.5.

Read lesson note on Solution Of Linear Equations (WAEC)

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

Solution Of Linear Equations

Simple Operations On Algebraic Expressions

View Answer

Question 33 Report

The height of a right circular cone is 4cm. The radius of its base is 3cm. Find the curved surface area

$9\pi cm^2$

$15\pi cm^2$ Correct answer

$16\pi cm^2$

$20\pi cm^2$

Answer Details

The curved surface area of a cone is given by the formula: \[\text{Curved surface area} = \pi rl,\] where $r$ is the radius of the base, $l$ is the slant height, and $\pi$ is the constant pi (approximately 3.14). In this case, the height of the cone is 4 cm and the radius of the base is 3 cm. To find the slant height, we can use the Pythagorean theorem: \[l^2 = r^2 + h^2.\] Plugging in the values we get, \[l^2 = 3^2 + 4^2 = 9 + 16 = 25.\] So, $l = 5$ cm. Now, we can use the formula for curved surface area, substituting $r=3$ cm and $l=5$ cm: \[\text{Curved surface area} = \pi \cdot 3 \cdot 5 = 15\pi \text{ cm}^2.\] Therefore, the answer is (B) $15\pi cm^2$.

Read lesson note on Areas (WAEC)

Read lesson note on Angles (WAEC)

Areas

Angles

View Answer

Question 34 Report

In the diagram, calculate the value of x

35^o

80^o

100^o Correct answer

115^o

Answer Details

View Answer

Question 35 Report

In the diagram O and O' are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OO'|.

8.46cm

19.04cm Correct answer

20.81cm

26.16cm

Answer Details

View Answer

Question 36 Report

In the diagram, SQ is a tangent to the circle at P, XP||YQ, ∠XPY = 56 o and ∠PXY = 80 o.Find angle PQY

34^o Correct answer

13.36^o

44^o

46^o

Answer Details

Read lesson note on Circles (WAEC)

Circles

View Answer

Question 37 Report

In the diagram O is the centre of the circle. Which of the following is/are not true? I. a = b II. b + c = 180^o III. a + b = c

I and II only Correct answer

II and III only

II only

III only

Answer Details

Read lesson note on Introductory Calculus (WAEC)

Read lesson note on Circles (WAEC)

Introductory Calculus

Circles

View Answer

Question 38 Report

In the diagram O is the center of the circle. Reflex angle XOY = 210° and the length of the minor arc is 5.5m. Find, correct to the nearest meter, the length of the major arc.

8m Correct answer

10m

13m

Answer Details

View Answer

Question 39 Report

From the diagram, find the bearing of Q from P.

236^o Correct answer

214^o

146^o

124^o

Answer Details

Read lesson note on Bearings (WAEC)

Bearings

View Answer

Question 40 Report

If q oranges are sold for t Naira, how many oranges can be bought for p naira?

$\frac{p}{2}t$

$\frac{qt}{p}$

$\frac{q}{pt}$

$\frac{pq}{t}$ Correct answer

Answer Details

The correct answer is $\frac{qp}{t}$. Since q oranges are sold for t Naira, we can say that the cost of one orange is $\frac{t}{q}$ Naira. To find how many oranges can be bought for p Naira, we need to divide p by the cost of one orange: Number of oranges = $\frac{p}{\frac{t}{q}}$ Simplifying, we get: Number of oranges = $\frac{pq}{t}$

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

Read lesson note on Modular Arithmetic (WAEC)

Fractions, Decimals And Approximations

Modular Arithmetic

View Answer

Question 41 Report

Simplify $3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}$

$7\sqrt{3}$

$10\sqrt{3}$

$14\sqrt{3}$ Correct answer

$18\sqrt{3}$

Answer Details

We can start by simplifying each term separately before adding them up: $3\sqrt{12} = 3\sqrt{4\cdot3} = 3\cdot2\sqrt{3} = 6\sqrt{3}$ $10\sqrt{3}$ is already in its simplest form. $\frac{6}{\sqrt{3}} = \frac{6}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3}$ Now we can substitute these values back into the original expression: $3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}} = 6\sqrt{3} + 10\sqrt{3} - 2\sqrt{3} = 14\sqrt{3}$ Therefore, the simplified form of the expression is $14\sqrt{3}$, which is.

Read lesson note on Surds (radicals) (WAEC)

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

Surds (radicals)

Simple Operations On Algebraic Expressions

View Answer

Question 42 Report

The angle of depression of a point Q from a vertical tower PR, 30m high, is 40°. If the foot P of the tower is on the same horizontal level as Q, find, correct to 2 decimal places, |PQ|.

35.75m Correct answer

25.00m

22.98m

19.28

Answer Details

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

Angles Of Elevation And Depression

View Answer

Question 43 Report

To arrive on schedule, a train is to cover a distance of 60km at 72km/hr. If it starts 10 minutes late, at what speed must it move to arrive on schedule?

60km/hr

80km/hr

90km/hr Correct answer

108km/hr

Answer Details

To arrive on schedule, the train needs to cover a distance of 60 km at a speed of 72 km/hr. However, the train starts 10 minutes late, which means it has lost 10 minutes of travel time. We need to find the speed the train needs to travel to make up for the lost time and arrive on schedule. We can use the formula: distance = speed x time Let's first calculate the time taken to cover the distance of 60 km at the speed of 72 km/hr. time = distance / speed time = 60 km / 72 km/hr time = 0.8333 hours or 50 minutes (rounded to the nearest minute) Since the train is starting 10 minutes late, it has only 40 minutes to cover the distance of 60 km to arrive on schedule. We can use the same formula to find the speed the train needs to travel to cover the distance in 40 minutes. speed = distance / time speed = 60 km / (40/60) hours speed = 90 km/hr Therefore, the correct answer is 90 km/hr.

Read lesson note on Algebraic Fractions (WAEC)

Read lesson note on Quadratic Equations (WAEC)

Algebraic Fractions

Quadratic Equations

View Answer

Question 44 Report

If log 2 = 0.3010 and log 2$^y$ = 1.8062, find; correct to the nearest whole number, the value of y.

6 Correct answer

-5

Answer Details

We can use the rule that log a^n = n log a to solve this problem. Since we are given log 2 = 0.3010 and log 2^y = 1.8062, we can use the second equation to get:


log 2^y = 1.8062
y log 2 = 1.8062     (using the above rule)
y = 1.8062 / log 2
y = 5.9889

Rounding to the nearest whole number, we get y = 6. Therefore, the answer is option A.

Read lesson note on Logarithms (WAEC)

Logarithms

View Answer

Question 45 Report

The diagram is the graph of $y = 6 + x - x^2$. The graph intercepts the x- axis at P and R and the y- axis at Q.

What is the value of y at Q?

$6\frac{1}{3}$ Correct answer

zero

Answer Details

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Graphs Of Linear And Quadratic Functions (WAEC)

Algebraic Expressions

Graphs Of Linear And Quadratic Functions

View Answer

Question 46 Report

The volume of a cylinder of radius 14cm is 210cm³. What is the curved surface area of the cylinder?

15cm²

30cm² Correct answer

616cm²

1262cm²

Answer Details

Read lesson note on Volumes (WAEC)

Read lesson note on Angles (WAEC)

Volumes

Angles

View Answer

Question 47 Report

Given that $p = x-\frac{1}{x} and\hspace{1mm}q = x^2 + \frac{1}{x^2}$ express q in terms of p.

(p² + 2) Correct answer

(p - 2) ²

(p + 2) ²

(p² - 2)

Answer Details

View Answer

Question 48 Report

Which of the following is not a rational number?

-5

$\sqrt{4}$

$3\frac{3}{4}$

$\sqrt{90}$ Correct answer

Answer Details

A rational number is any number that can be expressed as a ratio of two integers (where the denominator is not zero). - -5 can be expressed as -5/1, which is a ratio of two integers, so it is rational. - $\sqrt{4}$ is equal to 2, which can be expressed as the ratio 2/1, so it is rational. - $3\frac{3}{4}$ is equal to 15/4, which is a ratio of two integers, so it is rational. - $\sqrt{90}$ cannot be expressed as a ratio of two integers. It is irrational. Therefore, the number that is not rational is $\sqrt{90}$.

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

Read lesson note on Surds (radicals) (WAEC)

Positive And Negative Integers, Rational Numbers

Surds (radicals)

View Answer

Question 49 Report

Calculate and correct to two significant figures, the percentage error in approximating 0.375 to 0.4

2.0

2.5

6.6

6.7 Correct answer

Answer Details

To calculate the percentage error, we first need to find the absolute error, which is the difference between the actual value and the approximate value. In this case, the actual value is 0.375, and the approximate value is 0.4. Absolute error = |actual value - approximate value| Absolute error = |0.375 - 0.4| Absolute error = 0.025 To find the percentage error, we divide the absolute error by the actual value and multiply by 100. Percentage error = (absolute error / actual value) x 100 Percentage error = (0.025 / 0.375) x 100 Percentage error = 6.67 Rounding to two significant figures, the percentage error in approximating 0.375 to 0.4 is 6.7%. Therefore, the correct answer is option D.

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

Read lesson note on Number Bases (JAMB)

Fractions, Decimals And Approximations

Number Bases

View Answer






Press & Hold to Drag Around
Click Here to Close