JAMB UTME - Mathematics - 2000

Question 1 Report

If 31410 - 2567 = 340x, find x.

Answer Details

31410 - 2567 = 340x,
Convert 2567 and 340x to base 10, such that:
314 - 139 = 3x2 + 4x
=> 3x2 + 4x - 175 = 0 (quadratic)
Factorising, (x - 7) (3x + 25) = 0,
either x = 7 or x = -25/3 ( but x cannot be negative)
Therefore, x = 7.

Read lesson note on Number Bases (WAEC)

Number Bases

View Answer

Question 2 Report

Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 10, 9, 7, 10, 6, 5

Answer Details

To find the range, we need to subtract the smallest number from the largest number in the set. The smallest number in the set is 4 and the largest number is 10. So, the range is 10 - 4 = 6. To find the mode, we need to determine the number that occurs the most frequently in the set. In this case, the number 10 occurs the most frequently, appearing 7 times. So, the mode is 10. To find the sum of the range and the mode, we simply add the two values together. Thus, the sum of the range and the mode is 6 + 10 = 16. Therefore, the answer is option (A) 16.

Read lesson note on Representation Of Data (JAMB)

Read lesson note on Sets (WAEC)

Read lesson note on Measures Of Location (JAMB)

Read lesson note on Statistics (WAEC)

Representation Of Data

Sets

Measures Of Location

Statistics

View Answer

Question 3 Report

In the diagram, PQRS is a circle center O. PQR is a diameter and ∠PRQ = 40o. Calculate ∠QSR.

30o

40o

45o

50o

Answer Details

Read lesson note on Circles (WAEC)

Circles

View Answer

Question 4 Report

If the volume of a hemisphere is increasing at a steady rate of 18π m/s, at what rate is its radius changing when its is 6m?

2.30m/s

2.00 m/s

0.25 m/s

0.20 m/s

Answer Details

We can solve this problem using the formula for the volume of a hemisphere, which is given by V = (2/3)πr^3. To find the rate of change of the radius, we need to differentiate this equation with respect to time t. Thus, we have: dV/dt = (2/3)π(3r^2)(dr/dt) where dV/dt is the rate of change of volume (18π m/s), and r = 6 m is the radius of the hemisphere. Solving for dr/dt, we get: dr/dt = (3dV/dt)/(4πr^2) = (3(18π))/(4π(6)^2) = 0.25 m/s Therefore, the rate of change of the radius when the volume of the hemisphere is increasing at a steady rate of 18π m/s and its radius is 6 m is 0.25 m/s. Thus, the correct option is: 0.25 m/s.

View Answer

Question 5 Report

A predator moves in a circle of radius $ \sqrt{2} $ centre $(0,0)$, while a prey moves along the line $y = x$. If $0 \le x \le 2$, at which point(s) will they meet?

(1,1) only

(1,1) and (1,2)

(0,0) and (1,1)

(√2,√2) only

Answer Details

The predator moves in a circular path with a radius of √2 centered at the origin (0,0), while the prey moves along the line y = x. The prey's movement is restricted between x = 0 and x = 2. At some point, the predator will catch up to the prey, and they will meet. The predator will catch the prey when the distance between them is less than or equal to √2. We can find the equation of the circle centered at (0,0) with a radius of √2: x^2 + y^2 = (√2)^2 x^2 + y^2 = 2 We can substitute y = x into the equation to get: x^2 + x^2 = 2 2x^2 = 2 x^2 = 1 x = ±1 Therefore, the possible points of intersection are (1,1) and (-1,-1), but we know that the prey can only be at x values between 0 and 2, so the only possible point of intersection is (1,1). Therefore, the answer is (1,1) only.

Read lesson note on Coordinate Geometry (WAEC)

Read lesson note on Statistics (WAEC)

Coordinate Geometry

Statistics

View Answer

Question 6 Report

If $U = \{x : x\text{ is an integer and }1 \le x \le 20\}$

$E_1 = \{x : x\text{ is a multiple of }3\}$

$E_2 = \{x : x\text{ is a multiple of }4\}$

and an integer is picked at random from $U$, find the probability that it is not in $E_2$

3/4

3/10

1/4

1/20

Answer Details

U = {1, 2, 3, 4, 5,..., 20}
E1 = {3, 6, 9, 12, 15, 18}
E2 = {4, 8, 12, 16, 20}
P(E1) = 5/20
P(not E1) = 1 - (5/20) = 15/20 = 3/4

View Answer

Question 7 Report

Simplify 3(2n+1) - 4(2n-1) 2n+1 - 2n

2n+1

2n-1

1/4

Answer Details

Start by expanding 3(2n+1) - 4(2n-1) 2n+1 - 2n:
3 x 2n x 21 - 22 x 2n x 2-1 2n x 2 -2n
Solving the equation above gives;
2n x 21 x 2 2n = 2 x 2 = 4

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

View Answer

Question 8 Report

In how many ways can the word MATHEMATICS be arranged?

11!/(9! 2!)

11!/(9! 2! 2!)

11!/(2! 2! 2!)

11!/(2! 2!)

Answer Details

Number of letter in MATHEMATICS = 11
Number of letter M = 2
Number of letter E = 2
Number of letter A = 2
Arrangement = 11!/(2! 2! 2!) ways

Read lesson note on Permutation And Combination (JAMB)

Permutation And Combination

View Answer

Question 9 Report

If the mean of the numbers 0, (x+2), (3x+6), and (4x+8) is 4, find their mean deviation.

zero

Answer Details

The mean deviation of a set of numbers is the average of the absolute deviations from their mean. To find the mean deviation of the given set of numbers, we need to first find their mean. Mean = (0 + (x+2) + (3x+6) + (4x+8))/4 Mean = (8x + 16)/4 Mean = 2x + 4 We are given that the mean is 4. Therefore, 2x + 4 = 4 2x = 0 x = 0 Substituting x = 0 in the set of numbers, we get: 0, 2, 6, 8 Mean = (0+2+6+8)/4 = 4 To find the mean deviation, we need to find the deviation of each number from the mean and then take the average of their absolute values. Deviations from the mean: 0-4 = -4 2-4 = -2 6-4 = 2 8-4 = 4 Mean deviation = (|-4| + |-2| + |2| + |4|)/4 Mean deviation = (12/4) Mean deviation = 3 Therefore, the answer is 3.

Read lesson note on Representation Of Data (JAMB)

Read lesson note on Number Bases (WAEC)

Representation Of Data

Number Bases

View Answer

Question 10 Report

The cumulative frequency curve represents the ages of ages of students in a school. What age group do 70% of the students belongs?

17.5 - 20.5

16.5 - 19.5

15.5 - 19.5

15.5 - 18.5

Answer Details

Read lesson note on Representation Of Data (JAMB)

Read lesson note on Algebraic Expressions (WAEC)

Representation Of Data

Algebraic Expressions

View Answer

Question 11 Report

If α and β are the roots of the equation 3x2 + 5x - 2 = 0, find the value of 1/α + 1/β

-5/3

-2/3

1/2

5/2

Answer Details

We know that if α and β are the roots of the quadratic equation ax^2 + bx + c = 0, then α + β = -b/a and α × β = c/a. In this equation, 3x^2 + 5x - 2 = 0, we have a = 3, b = 5, and c = -2. So, α + β = -b/a = -5/3 And, α × β = c/a = -2/3 We need to find the value of 1/α + 1/β = (α + β)/(α × β) = (-5/3) / (-2/3) = 5/2. Therefore, the value of 1/α + 1/β is 5/2.

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

View Answer

Question 12 Report

A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)?

y = (3x2/)2 + 2x

y = (3x2)/2 + x

y = 3x2 + (x/2)

y = 3x2 +2x

Answer Details

Hints:
1. Integrate the given first derivative of f(x) at the boundaries, (0,0)
Then solve accordingly to get f(x) = y = (3x2/)2 + 2x

Read lesson note on Functions And Relations (WAEC)

Functions And Relations

View Answer

Question 13 Report

Evaluate (1/2 - 1/4 - 1/8 - 1/16 + ...) - 1

2/3

zero

-2/3

-1

Answer Details

The given expression is a geometric series with the first term as 1/2 and the common ratio as -1/2. Using the formula for the sum of an infinite geometric series with |r| < 1, we can find that the sum of the series is: S = a/(1-r) = (1/2)/(1-(-1/2)) = (1/2)/(3/2) = 1/3 Therefore, the expression (1/2 - 1/4 - 1/8 - 1/16 + ...) - 1 simplifies to: 1/3 - 1 = -2/3 So, the answer is -2/3.

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

Read lesson note on Representation Of Data (JAMB)

Read lesson note on Number Bases (WAEC)

Fractions, Decimals And Approximations

Representation Of Data

Number Bases

View Answer

Question 14 Report

Find the inverse of p under the binary operation * defined by p*q = p + q - pq, where p and q are real numbers and zero is the identity

p -1

p/(p-1)

p/(p+1)

Answer Details

If P-1 is the inverse of P and O is the identity, Then P-1 * P = P * P-1 = 0
i.e. P-1 + P - P-1.P = 0
P-1 - P-1.P = -P
P-1(1 - P) = -P
P-1 = -P/(P-1)
= P/(P-1)

Read lesson note on Matrices And Determinants (JAMB)

Read lesson note on Binary Operations (JAMB)

Matrices And Determinants

Binary Operations

View Answer

Question 15 Report

Solve the inequality 2 - x > x2.

x < -2 or x > 1

x > 2 or x< -1

-1 < x < 2

-2 < x < 1

Answer Details

2 - x > x2
2 - x - x2 > 0
(x+2)(x-1) < 0

Read lesson note on Statistics (WAEC)

Statistics

View Answer

Question 16 Report

The variance of x, 2x, 3x, 4x and 5x is

x√2

2x2

Answer Details

Hint: prepare a three-columned table, one for (x), another for the (deviation), and the last for the (squared-deviation).
Sum of (x) = 15x, algebraic sum of (deviation) = zero (0)
Sum of (squared-deviation) = 10x2
Variance = ∑(squared-deviation)/n = 10x2/5 = 2x2

Read lesson note on Measures Of Dispersion (JAMB)

Measures Of Dispersion

View Answer

Question 17 Report

Let P = {1, 2, u, v, w, x}; Q = {2, 3, u, v, w, 5, 6, y} and R = {2, 3, 4, v, x, y}.

Determine (P-Q) ? R

{1, x}

{x y}

{x}

Answer Details

To determine (P-Q) ? R, we need to first find the set difference (P-Q), which is the set of elements that are in P but not in Q. So, we need to remove all the elements in Q from P. (P-Q) = {1, w, x} Then, we take the intersection of (P-Q) and R, which means we need to find all the elements that are common to both (P-Q) and R. (P-Q) ? R = {x} Therefore, the answer is {x}.

Read lesson note on Sets (WAEC)

Read lesson note on Sets (JAMB)

Sets

View Answer

Question 18 Report

A trader realizes 10x - x2 naira profit from the sale of x bags on corn. How many bags will give him the desired profit?

Answer Details

The trader's profit function can be represented as P(x) = 10x - x^2, where x is the number of bags sold and P(x) is the profit obtained from selling x bags of corn. To find the number of bags that will give him the desired profit, we need to maximize the profit function P(x). We can do this by finding the derivative of P(x) with respect to x, and then setting it to zero to find the critical point(s) of the function. P'(x) = 10 - 2x Setting P'(x) to zero gives: 10 - 2x = 0 Solving for x gives: x = 5 Therefore, the trader will make the maximum profit when he sells 5 bags of corn. This means that the answer is, 5.

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

View Answer

Question 19 Report

3y = 4x - 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.

-4/3

-3/4

3/4

4/3

Answer Details

Grad of 3y = 4x - 1
y = 4x/3 - 1/3
Grad = 4/3
Grad of Ky = x + 3
y = x/k + 3/4
Grad = 1/k
Since two lines are perpendicular,
1/k = -3/4
-3k = 4
k = -4/3

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Differentiation (JAMB)

Algebraic Expressions

Differentiation

View Answer

Question 20 Report

In the diagram, POS and ROT are straight lines, OPQR is a parallelogram. |OS| = |OT| and ∠OST = 50o. Calculate ∠OPQ.

160o

140o

120o

100o

Answer Details

View Answer

Question 21 Report

In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?

Answer Details

Use a venn diagram:
60-3x+3x+50-3x = 94-x.
110-3x+x = 94
-2x = 94-110
=>-2x = -16, this x = -8.
Members that like only one game:
= 60 - 3x + 50 - 3x
= 60 - 3x8 + 50 - 3x8
= 60 - 24 + 50 - 24
= 36 + 26 = 62

Read lesson note on Sets (JAMB)

Sets

View Answer

Question 22 Report

X and Y are two events. The probability of X or Y is 0.7 and that of X is 0.4. If X and Y are independent, find the probability of Y.

0.30

0.50

0.57

1.80

Answer Details

P (X or Y) = P(X) + P(Y), when they are independent as given.
0.7 = 0.4 + P(Y)
P(Y) = 0.7 - 0.4 = 0.30

Read lesson note on Probability (WAEC)

Probability

View Answer

Question 23 Report

A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for ₦150,000. How much does he need to deposit?

₦112,000.50

₦96,000.00

₦85,714.28

₦76,800.00

Answer Details

Amount A = P(1+r)n;
A = ₦150,000, r = 25%, n = 3.
150,000 = P(1+0.25)3 = P(1.25)3
P = 150,000/1.253 =₦76,800.00

Read lesson note on Sets (WAEC)

Read lesson note on Quadratic Equations (WAEC)

Sets

Quadratic Equations

View Answer

Question 24 Report

If y = 2x - sin2x, find dy/dx when x = π/4

-π

π/2

-π/2

Answer Details

y = 2x cos2x - sin2x
dy/dx = 2 cos2x +(-2x sin2x) - 2 cos2x
= 2 cos2x - 2x sin2x - cos2x
= -2x sin2x
= -2 x (π/4) sin2 x (π/4)
= -(π/2) x 1 = -(π/2)

Read lesson note on Differentiation (JAMB)

Differentiation

View Answer

Question 25 Report

If P3446 - 23P26 = 2PP26, find the value of the digit P.

Answer Details

Covert everything to base 10 and collect like terms, such that:
210P - 42P = 434 + 406
168P = 840
P = 840/168 = 5

Read lesson note on Number Bases (WAEC)

Number Bases

View Answer

Question 26 Report

In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.

Answer Details

2x + x = 180°, => 3x = 180°, and thus x = 60°
Each exterior angle = 60° but size of ext. angle = 360°/n
Therefore 60° = 360°/n
n = 360°/60° = 6 sides

Read lesson note on Triangles And Polygons (WAEC)

Triangles And Polygons

View Answer

Question 27 Report

In how many ways can a delegation of 3 be chosen from 5 men and 3 women. If at least 1 man and 1 woman must be included?

Answer Details

Read lesson note on Permutation And Combination (JAMB)

Permutation And Combination

View Answer

Question 28 Report

Simplify $ \frac{1}{1+\sqrt{5}} - \frac{1}{1-\sqrt{5}} $

\frac{1}{2} \sqrt{5}

\frac{1}{2} \sqrt{5}

\frac{1}{4} \sqrt{5}

Answer Details

\frac{1}{1 + \sqrt{5}}

\frac{1}{1 - \sqrt{5}}

\frac{3 - \sqrt{5} - 3 - \sqrt{5}}{(3 + \sqrt{5}) (3 - \sqrt{5}}

\frac{- 2 \sqrt{5}}{9 - 5}

\frac{- 2 \sqrt{5}}{4}

= -

\frac{1}{2} \sqrt{5}

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 29 Report

Two chords PQ and RS of a circle when produced meet at K. If ∠KPS = 31o and ∠PKR = 42o, find ∠KQR

11o

73o

107o

138o

149o

Answer Details

QPS - QRK = 31o
QRK + RKQ + KQR = 180
31 + 42 + KQR = 180o
KQR = 180 - 73 = 107o

Read lesson note on Polynomials (JAMB)

Polynomials

View Answer

Question 30 Report

A ship sails a distance of 50km in the direction S50°E and then sails a distance of 50km in the direction ₦40°E. FInd the bearing of the ship from the original position.

S90°E

₦40°E

S95°E

₦85°E

Answer Details

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

View Answer

Question 31 Report

The expression ax2 + bx + c equals 5 at x = 1. If its derivative is 2x + 1, what are the values of a, b, c respectively?

1, 3, 1

1, 2, 1

2, 1, 1

1, 1, 3

Answer Details

At x = 1, substituting x = 1 in the equation: ax2 + bx + c = 5;
f(1) => a + b + c = 5 .....(1)
Taking the first derivative of f(x) in the original equation gives dy/dx = 2ax + b = 2x + 1 (given)....(2)
From (2),=> b = 1, and 2ax = 2x, => a = 1.
substituting into (1) 1 + 1 + c = 5, => c = 5 - 2 = 3
Thus a = 1, b = 1 and c = 3

Read lesson note on Differentiation (JAMB)

Differentiation

View Answer

Question 32 Report

If the diagram is the graph of y = x2, the shaded area is

64 square units

\frac{126}{4}

square units

32 square units

\frac{64}{3}

square units

Answer Details

A =

\int_{x = 0}^{x = 4}

ydx =

\int_{0}^{4}

x2dx = [

\frac{x^{3}}{3} + c]_{0}^{4}

= $\frac{64}{3}$ square units

View Answer

Question 33 Report

If the population of a town was 240,000 in January 1998 and it increased by 2% each year, what would be the population of the town in January, 2000?

480,000

249,696

249,600

244,800

Answer Details

To solve this problem, we can use the formula for exponential growth, which is: A = P(1 + r)^t where A is the final amount, P is the initial amount, r is the annual growth rate as a decimal, and t is the time in years. In this problem, we are given P = 240,000, r = 0.02, and t = 2 (since we want to find the population after two years). We can plug these values into the formula and simplify: A = 240,000(1 + 0.02)^2 A = 240,000(1.02)^2 A = 240,000(1.0404) A = 249,696 Therefore, the population of the town in January 2000 would be 249,696. So the answer is 249,696.

Read lesson note on Representation Of Data (JAMB)

Representation Of Data

View Answer

Question 34 Report

If $\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})}=m+n\sqrt{6}$, find the values of m and n respectively.

1, -2

-2, 1

\frac{- 2}{5}

, 1

2, 3/5

Answer Details

Rationalize

\frac{(2 \sqrt{3} - \sqrt{2})}{(\sqrt{3} + 2 \sqrt{2})}

and equate to

m + n \sqrt{6}

. Such that m = -2, and n = 1.

View Answer

Question 35 Report

if P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X is

A straight line

a circle

the bisector of angle PXQ

the perpendicular bisector of PQ

Answer Details

Given two fixed points P and Q, the locus of points X which are equidistant from P and Q is the perpendicular bisector of PQ. This is because any point on the perpendicular bisector of PQ will be equidistant from both P and Q by definition. Therefore, if X is a point which moves so that XP = XQ, it must lie on the perpendicular bisector of PQ. Therefore, the correct answer is "the perpendicular bisector of PQ".

Read lesson note on Circles (WAEC)

Read lesson note on Euclidean Geometry (JAMB)

Circles

Euclidean Geometry

View Answer

Question 36 Report

if (x - 1), (x + 1) and (x - 2) are factors of the polynomial ax3 + bx2 + cx - 1, find a, b, c in that order.

-1/2, 1., 1/2

1/2, 1, 1/2

1/2, 1, -1/2

1/2, -1, 1/2

Answer Details

This is a polynomial of the 3rd order, thus x should have three answers. Use the factors given to get values of x as 1, -1 and -2.
Form three equations, and carry out elimination and subsequent substitution to get a = -1/2, b = 1, and c = 1/2

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

View Answer

Question 37 Report

A frustrum of pyramid with square base has its upper and lower sections as squares of sizes 2m and 5m respectively and the distance between them 6m. Find the height of the pyramid from which the frustrum was obtained.

8.0 m

8.4 m

9.0 m

10.0 m

Answer Details

Read lesson note on Polynomials (JAMB)

Polynomials

View Answer

Question 38 Report

An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle.

2/3 cm

2 cm

1 cm

3 cm

Answer Details

In an equilateral triangle, all the sides are of equal length and each angle is 60 degrees. Let's draw an equilateral triangle with side √3 cm inscribed in a circle. Since the triangle is equilateral, we know that the circumcenter (center of the circle that passes through all the vertices of the triangle) is also the centroid (point of intersection of the medians). The median of an equilateral triangle is the line segment from a vertex to the midpoint of the opposite side. Therefore, the circumcenter is also the midpoint of any side of the triangle. Let's choose one side of the triangle and label its midpoint as point M. We can draw a perpendicular line from M to the opposite vertex of the triangle, which will bisect the side and form a right triangle with one leg being half of the side of the triangle and the other leg being the radius of the circle. Using the Pythagorean theorem, we can solve for the radius: (radius)^2 = (√3/2)^2 + (1/2)^2 (radius)^2 = 3/4 + 1/4 (radius)^2 = 1 radius = 1 cm Therefore, the radius of the circle is 1 cm. Answer: 1 cm.

Read lesson note on Trigonometry (JAMB)

Read lesson note on Differentiation (JAMB)

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

Read lesson note on Triangles And Polygons (WAEC)

Trigonometry

Differentiation

Simple Operations On Algebraic Expressions

Triangles And Polygons

View Answer

Question 39 Report

Evaluate (2.813 x 10-3 x 1.063) (5.637 x 10-2)

0.056

0.055

0.054

0.54

Answer Details

Read lesson note on Number Bases (WAEC)

Number Bases

View Answer

Question 40 Report

Find the value of $ \displaystyle \int_{0}^{\pi}\frac{\cos^{2}\theta-1}{\sin^{2}\theta}\,d\theta $

π/2

-π/2

-π

Answer Details

\int_{0}^{π} \frac{c o s^{2} θ - 1}{s i n^{2} θ} d θ = \int_{0}^{π} \frac{- s i n^{2} θ}{s i n^{2} θ} = \int_{0}^{π} d θ = - π

Read lesson note on Integration (JAMB)

Integration

View Answer

Question 41 Report

A bowl is designed by revolving completely the area enclosed by y = x2 - 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?

7π cubic units

15π/2 cubic units

8π cubic units

17π/2 cubic units

Answer Details

∫30 π(y+1) dy = π[y2 + y30
= π(9/2 + 3) = 15π/2

Read lesson note on Volumes (WAEC)

Read lesson note on Areas (WAEC)

Volumes

Areas

View Answer

Question 42 Report

Given that the various faces of a fair dice 1, 2, 3, 4, 5, 6 appeared 30, 43, 54, 40, 41, 32 times respectively in a single toss. Picture the figures as being represented in a simple table with number (X) against frequency (f).

If a pie chart is used to depict the data, the angle corresponding to 4 is?

10°

16°

40°

60°

Answer Details

To find the angle corresponding to 4 in the pie chart, we need to calculate the percentage of times 4 appeared in the toss. Total frequency = 30 + 43 + 54 + 40 + 41 + 32 = 240 Frequency of 4 = 40 Percentage of times 4 appeared = (Frequency of 4 / Total frequency) x 100% = (40/240) x 100% = 16.67% The pie chart represents a circle of 360°. Therefore, to find the angle corresponding to 4 in the pie chart, we need to calculate 16.67% of 360°. Angle corresponding to 4 = (16.67/100) x 360° = 60° Therefore, the angle corresponding to 4 in the pie chart is 60°. Option (d) is the correct answer.

Read lesson note on Probability (WAEC)

Read lesson note on Linear Inequalities (WAEC)

Probability

Linear Inequalities

View Answer

Question 43 Report

A binary operation * is defined by a*b = ab. If a*2 = 2-a, find the possible values of a.

1, -1

1, 2

2, -2

1, -2

Answer Details

a * b = ab
a * 2 = a2 = 2 - a
a2 + 2a - a - 2 = 0
a(a+2) - 1(a+2) = 0
(a-1)(a+2) = 0
a = 1, -2

Read lesson note on Binary Operations (JAMB)

Binary Operations

View Answer

Question 44 Report

P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and angle VUS = 60°, find angle UST.

310°

130°

80°

50°

Answer Details

Make a good sketch of the question, and follow this steps.
Since ST is parallel to UV => angle USR = 50°(alternate to VUS.
Angle UST = 180° - 50° = 130° (angle on a straight line)

Read lesson note on Loci (WAEC)

Read lesson note on Euclidean Geometry (JAMB)

Loci

Euclidean Geometry

View Answer

Question 45 Report

Evaluate 5-3log52 x 22log23

11/8

2/5

1/8

Answer Details

5-3log52 x 22log23i Let -3log52 = p => log52-3 = p
∴2-3 = 5p
∴5-3log52 = 5log52-3 = 5pii 22log23 = q => log532 = q
∴32 = 2q
∴222log23 = 2q
= 32 = 9
i x ii = 2-3 x 9 = 1/23 x 9
= 1/8 x 9
= 9/8 = 11/8

Read lesson note on Logarithms (WAEC)

Logarithms

View Answer

Question 46 Report

The 3rd term of an A.P is 4x - 2y and the 9th term is 10x - 8y. Find the common difference.

19x - 17y

8x - 4y

x - y

Answer Details

In an Arithmetic Progression (A.P), the difference between any two adjacent terms is constant. Let d be the common difference of the A.P, then: - The 3rd term is the first term plus two common differences, i.e. a + 2d = 4x - 2y - The 9th term is the first term plus eight common differences, i.e. a + 8d = 10x - 8y We can now solve for d by subtracting the first equation from the second: a + 8d - (a + 2d) = 10x - 8y - (4x - 2y) 6d = 6x - 6y d = (x - y) Therefore, the common difference is x - y, which is option (C).

Read lesson note on Sequence And Series (WAEC)

Sequence And Series

View Answer

Question 47 Report

In the diagram above, EFGH is a circle center O. Fh is a diameter and GE is a chord which meets FH at right angle at the point N. If NH = 8cm and EG = 24cm, calculate FH.

16 cm

20 cm

26 cm

32 cm

Answer Details

To solve this problem, we need to use the property of a circle that states that a diameter is twice the radius of the circle. Since FH is a diameter, then FH = 2OH, where OH is the radius of the circle. Since GE is a chord that meets FH at right angle at the point N, then N is the midpoint of FH. Therefore, NH = NF = 8 cm. Let's use the Pythagorean theorem to find OH. Since GE is a chord of the circle, we can draw radii from the center O to the endpoints of the chord so that we have a right triangle. Let x be the length of OE. Then, HG = 2x, and OH = x + 12 (since FH = 2OH = 2(x + 12) = 2x + 24). Using the Pythagorean theorem, we have: x^2 + 12^2 = (2x)^2 x^2 + 144 = 4x^2 3x^2 = 144 x^2 = 48 x = sqrt(48) = 4sqrt(3) Therefore, OH = x + 12 = 4sqrt(3) + 12. Finally, we can calculate FH: FH = 2OH = 2(4sqrt(3) + 12) = 8sqrt(3) + 24 ≈ 32.39 cm. Therefore, the answer is 32 cm.

Read lesson note on Circles (WAEC)

Read lesson note on Coordinate Geometry (WAEC)

Circles

Coordinate Geometry

View Answer






Press & Hold to Drag Around
Click Here to Close