WAEC SSCE - Further Mathematics - 2021…

Ibeere 1 Ìròyìn

Solve (\(\frac{1}{9}\))\(^{x + 2}\) = 243\(^{x - 2}\)

\(\frac{7}{5}\) Ìdáhùn tó tọ́

\(\frac{6}{7}\)

\(\frac{-7}{6}\)

\(\frac{-6}{7}\)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Surds (WAEC)

Surds

Wo Idahun

Ibeere 2 Ìròyìn

Using binomial expansion of ( 1 + x)\(^6\) = 1 + 6x + 15x\(^2\) + 20x\(^3\) + 6x\(^5\) + x)\(^6\), find, correct to three decimal places, the value of (1.998))\(^6\)

63.616

63.167 Ìdáhùn tó tọ́

62.628

62.629

Awọn alaye Idahun

To use the binomial expansion of (1 + x)\(^6\), we substitute x = 1.998, which gives: (1 + 1.998)\(^6\) = 1 + 6(1.998) + 15(1.998)\(^2\) + 20(1.998)\(^3\) + 6(1.998)\(^5\) + (1.998)\(^6\) We are interested in finding the value of (1.998)\(^6\), which is the last term on the right-hand side of the equation. We can solve for it by subtracting the other terms from both sides of the equation: (1.998)\(^6\) = (1 + 1.998)\(^6\) - 1 - 6(1.998) - 15(1.998)\(^2\) - 20(1.998)\(^3\) - 6(1.998)\(^5\) Using a calculator, we can evaluate the right-hand side of the equation to get: (1.998)\(^6\) ≈ 63.167 Therefore, the correct answer is option B, 63.167, rounded to three decimal places. Explanation: The binomial expansion of (1 + x)\(^6\) is a formula that allows us to expand the expression into a sum of terms involving powers of x. By substituting x = 1.998, we can use the formula to find the value of (1.998)\(^6\). We then use a calculator to evaluate the expression to obtain the final answer.

Ka ìwé ẹ̀kọ́ nípa Binomial Theorem (WAEC)

Binomial Theorem

Wo Idahun

Ibeere 3 Ìròyìn

A body of mass 15kg is placed on a smooth plane which is inclined at 60° to the horizontal. If the box is at rest,

calculate the normal reaction to the plane. [ Take g = 10m/s\(^2\) ]

129.9N

75N Ìdáhùn tó tọ́

60.0N

7.5N

Awọn alaye Idahun

To find the normal reaction to the plane, we can use the following approach: Step 1: Draw a diagram of the situation. In this case, we have a body of mass 15kg on a smooth plane inclined at 60° to the horizontal. The weight of the body acts vertically downwards and is equal to mg, where m is the mass of the body and g is the acceleration due to gravity. Step 2: Resolve the weight of the body into two components, one perpendicular to the plane and the other parallel to the plane. The component of the weight perpendicular to the plane is equal to mg cos 60°, which is equal to (15 kg) x (10 m/s\(^2\)) x cos 60° = 75 N. Step 3: The normal reaction to the plane is equal in magnitude but opposite in direction to the component of the weight perpendicular to the plane. Therefore, the normal reaction to the plane is 75 N in the upward direction. Step 4: Check the options given in the question and select the one that matches the value obtained in Step 3. In this case, the correct option is 75N. Therefore, the normal reaction to the plane is 75 N.

Ka ìwé ẹ̀kọ́ nípa Statics (WAEC)

Statics

Wo Idahun

Ibeere 4 Ìròyìn

g(x) = 2x + 3 and f(x) = 3x\(^2\) - 2x + 4

37 Ìdáhùn tó tọ́

-3

-179

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Functions (WAEC)

Functions

Wo Idahun

Ibeere 5 Ìròyìn

If α and β are the roots of 3x\(^2\) - 7x + 6 = 0, find \(\frac{1}{α}\) + \(\frac{1}{β}\)

\(\frac{7}{6}\) Ìdáhùn tó tọ́

\(\frac{7}{3}\)

\(\frac{14}{5}\)

\(\frac{14}{3}\)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Polynomial Functions (WAEC)

Polynomial Functions

Wo Idahun

Ibeere 6 Ìròyìn

A bag contains 8 red, 4 blue and 2 green identical balls. Two balls are drawn randomly from the bag without replacement. Find the probability that the balls drawn are red and blue.

A. 12/91 B. C. D.

12/91

16/91

30/91

32/91 Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Probability

Wo Idahun

Ibeere 7 Ìròyìn

Three forces, F\(_1\) (8N, 030°), F\(_\2) (10N, 150° ) and F\(_\3) ( KN, 240° )are in equilibrium. Find the value of N

5√3

6√2

6√3 Ìdáhùn tó tọ́

9√3

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Vectors (WAEC)

Vectors

Wo Idahun

Ibeere 8 Ìròyìn

Simplify \(\frac{1}{3}\) log8 + \(\frac{1}{3}\) log 64 - 2 log6

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

log 2

log \(\frac{2}{9}\) Ìdáhùn tó tọ́

log 9

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Indices And Logarithmic Functions (WAEC)

Indices And Logarithmic Functions

Wo Idahun

Ibeere 9 Ìròyìn

For what range of values of x is x\(^2\) - 2x - 3 ≤ 0

{x: -1 ≤ x ≤ 3} Ìdáhùn tó tọ́

{ x: -3 ≤ x ≤ 1}

{ x: -3 ≤ x ≤ -1}

{ x: 1 ≤ x ≤ 3}

Awọn alaye Idahun

To solve the inequality x\(^2\) - 2x - 3 ≤ 0, we can use factoring or the quadratic formula. Factoring gives us (x - 3)(x + 1) ≤ 0, which means that the expression is less than or equal to zero when x is between or equal to -1 and 3, since the factors change sign at these values. Therefore, the correct answer is {x: -1 ≤ x ≤ 3}. Alternatively, we can use the quadratic formula to find the roots of the equation x\(^2\) - 2x - 3 = 0, which are x = -1 and x = 3. Since the quadratic function is a parabola that opens upward, it is negative in the interval between these two roots. Therefore, the expression x\(^2\) - 2x - 3 is less than or equal to zero when x is between or equal to -1 and 3.

Ka ìwé ẹ̀kọ́ nípa Polynomial Functions (WAEC)

Polynomial Functions

Wo Idahun

Ibeere 10 Ìròyìn

Given that \( M = \begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix} \) and \( N = \begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix} \), calculate \( (3M - 2N) \)

\(\begin{pmatrix} 1 & 6 \\ 1 & 18 \end{pmatrix}\)

\(\begin{pmatrix} -1 & -6 \\ 1 & 18 \end{pmatrix}\) Ìdáhùn tó tọ́

\(\begin{pmatrix} 1 & 6 \\ -1 & -18 \end{pmatrix}\)

\(\begin{pmatrix} -1 & -6 \\ -1 & -18 \end{pmatrix}\)

Awọn alaye Idahun

To calculate 3M - 2N, we need to multiply each matrix by its scalar factor and then subtract the results. First, we have: 3M = 3 x \(\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}\) = \(\begin{pmatrix} 9 & 6 \\ -3 & 12 \end{pmatrix}\) Next, we have: 2N = 2 x \(\begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix}\) = \(\begin{pmatrix} 10 & 12 \\ -4 & -6 \end{pmatrix}\) Now we can subtract these two matrices to get: 3M - 2N = \(\begin{pmatrix} 9 & 6 \\ -3 & 12 \end{pmatrix}\) - \(\begin{pmatrix} 10 & 12 \\ -4 & -6 \end{pmatrix}\) = \(\begin{pmatrix} -1 & -6 \\ 1 & 18 \end{pmatrix}\) Therefore, the correct answer is (B) \(\begin{pmatrix} -1 & -6 \\ 1 & 18 \end{pmatrix}\).

Ka ìwé ẹ̀kọ́ nípa Matrices And Linear Transformation (WAEC)

Matrices And Linear Transformation

Wo Idahun

Ibeere 11 Ìròyìn

Find the radius of the circle 2x\(^2\) - 4x + 2y\(^2\) - 6y -2 = 0.

17/4

17/2

17/√2 Ìdáhùn tó tọ́

√17/2

Awọn alaye Idahun

To find the radius of a circle from its equation in general form, we need to rewrite the equation in the standard form of a circle, which is: (x - h)\(^2\) + (y - k)\(^2\) = r\(^2\) Where (h, k) is the center of the circle, and r is its radius. To do this, we complete the square for both x and y terms in the given equation. We start by rearranging the terms as follows: 2x\(^2\) - 4x + 2y\(^2\) - 6y -2 = 0 2x\(^2\) - 4x + 2y\(^2\) - 6y = 2 Now, we need to add and subtract appropriate constants to complete the square for x and y terms separately. For the x terms, we take half of the coefficient of x (-4/2 = -2) and square it to get 4. So, we add and subtract 4 to the equation: 2x\(^2\) - 4x + 4 - 4 + 2y\(^2\) - 6y = 2 We can now group the first three terms and factor it as a perfect square: 2(x - 1)\(^2\) + 2y\(^2\) - 6y - 2 = 0 For the y terms, we take half of the coefficient of y (-6/2 = -3) and square it to get 9. So, we add and subtract 9 to the equation: 2(x - 1)\(^2\) + 2(y - 3)\(^2\) - 2 - 9 = 0 2(x - 1)\(^2\) + 2(y - 3)\(^2\) = 11 Now, we have the equation in the standard form of a circle, where the center is at (1, 3) and the radius is the square root of 11/2. We can simplify this expression to get: sqrt(11/2) = sqrt(11)/sqrt(2) = sqrt(2)*sqrt(11)/2 Therefore, the answer is option (C), 17/√2.

Wo Idahun

Ibeere 12 Ìròyìn

Find the value of the derivative of y = 3x\(^2\) (2x +1) with respect to x at the point x = 2.

84 Ìdáhùn tó tọ́

120

Awọn alaye Idahun

Wo Idahun

Ibeere 13 Ìròyìn

If √5 cosx + √15sinx = 0, for 0° < x < 360°, find the values of x.

30° and 150°

150° and 210°

150° and 330° Ìdáhùn tó tọ́

210° and 330°

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Surds (WAEC)

Surds

Wo Idahun

Ibeere 14 Ìròyìn

The table shows the distribution of marks obtained by some students in a test

Marks	0-9	10-19	20-29	30-39	40-49
Frequency	4	12	16	6	2

Find the modal class mark.

4.5

14.5

24.5 Ìdáhùn tó tọ́

34.5

Awọn alaye Idahun

To find the modal class mark, we need to first identify the class with the highest frequency, which in this case is the class with marks 20-29 (16 students). The modal class mark is the midpoint of this class, which is calculated by adding the lower and upper limits of the class and dividing by 2: Modal class mark = (20 + 29) / 2 = 24.5 Therefore, the modal class mark is 24.5, which is option (C).

Ka ìwé ẹ̀kọ́ nípa Statistics (WAEC)

Statistics

Wo Idahun

Ibeere 15 Ìròyìn

The table shows the distribution of marks obtained by some students in a test

Marks	0-9	10-19	20-29	30-39	40-49
Frequency	4	12	16	6	2

What is the upper class boundary of the upper quartile class?

49.5

39.5

29.5 Ìdáhùn tó tọ́

19.5

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Statistics (WAEC)

Statistics

Wo Idahun

Ibeere 16 Ìròyìn

A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t + \(\frac{5}{2t^2}\) - t\(^3\).

Calculate the distance travelled in the third second.

5.5m Ìdáhùn tó tọ́

14.5m

26.0m

30.0m

Awọn alaye Idahun

Wo Idahun

Ibeere 17 Ìròyìn

If f(x) = 4x\(^3\) + px\(^2\) + 7x - 23 is divided by (2x -5), the remainder is 7. find the value of p

-7.0

-8.0 Ìdáhùn tó tọ́

-9.6

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Polynomial Functions (WAEC)

Polynomial Functions

Wo Idahun

Ibeere 18 Ìròyìn

In how many ways can 8 persons be seated on a bench if only three seats are available?

100

125

336 Ìdáhùn tó tọ́

427

Awọn alaye Idahun

The first person has 8 choices for a seat, the second person has 7 choices remaining, and the third person has 6 choices. However, the order in which they choose their seats does not matter, so we need to divide by the number of ways that the three people can be arranged. This is given by 3 factorial (3!), which is 3 x 2 x 1 = 6. Therefore, the total number of ways that 8 persons can be seated on a bench if only three seats are available is: 8 x 7 x 6 / 3! = 336 So the correct answer is (C) 336.

Ka ìwé ẹ̀kọ́ nípa Permutation And Combinations (WAEC)

Permutation And Combinations

Wo Idahun

Ibeere 19 Ìròyìn

The first term of an AP is 4 and the sum of the first three terms is 18. Find the product of the first three terms

292

272

192 Ìdáhùn tó tọ́

172

Awọn alaye Idahun

Let the common difference of the AP be denoted by d. Then, the first three terms of the AP are 4, 4 + d, and 4 + 2d, respectively. The sum of the first three terms of the AP is given as 18. Therefore, we have: 4 + (4 + d) + (4 + 2d) = 18 Simplifying the above equation, we get: 3d + 12 = 18 3d = 6 d = 2 Hence, the common difference of the AP is 2. Therefore, the first three terms of the AP are: 4, 6, 8 The product of the first three terms is: 4 x 6 x 8 = 192 Therefore, the answer is 192.

Ka ìwé ẹ̀kọ́ nípa Sequences And Series (WAEC)

Sequences And Series

Wo Idahun

Ibeere 20 Ìròyìn

Consider the following statements:

X: Benita is polite

y: Benita is neat

z: Benita is intelligent

Which of the following symbolizes the statement: "Benita is neat if and only if she is neither polite nor intelligent"?

y⟺ ~x v z

y⟺ ~x v ~z

y⟺ ~x ^ ~z Ìdáhùn tó tọ́

y⟺ ~x ^ z

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Logical Reasoning (WAEC)

Logical Reasoning

Wo Idahun

Ibeere 21 Ìròyìn

A committee consists of 6 boys and 4 girls. In how many ways can a sub-committee consisting of 3 boys and 2 girls be formed if one particular boy and one particular girl must be on the sub-committee?

120 Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Permutation And Combinations (WAEC)

Permutation And Combinations

Wo Idahun

Ibeere 22 Ìròyìn

The gradient ofy= 3x\(^2\) + 11x + 7 at P(x.y) is -1. Find the coordinates of P.

(-3, -2)

(-2,-3) Ìdáhùn tó tọ́

(-2,3)

Awọn alaye Idahun

Wo Idahun

Ibeere 23 Ìròyìn

A binary operation * is defined on the set of real numbers, R, by

P * q = \(\frac{q^2 - p^2}{2pq}\). Find 3 * 2

\(\frac{13}{12}\)

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

\(\frac{-5}{12}\) Ìdáhùn tó tọ́

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

Awọn alaye Idahun

The binary operation * is defined as: P * q = (q^2 - p^2) / (2pq). To find 3 * 2, we need to substitute the values of p and q in the equation: 3 * 2 = (2^2 - 3^2) / (2 * 3 * 2) = (-5) / (12) = -5/12 So, the answer is -5/12.

Ka ìwé ẹ̀kọ́ nípa Binary Operations (WAEC)

Binary Operations

Wo Idahun

Ibeere 24 Ìròyìn

If 2i +pj and 4i -2j are perpendicular, find the value of p.

4 Ìdáhùn tó tọ́

Awọn alaye Idahun

To find the value of p, we need to use the concept of perpendicular vectors. Two vectors are perpendicular if and only if the dot product of the two vectors is equal to zero. The dot product of two vectors can be calculated as the product of the magnitudes of the two vectors and the cosine of the angle between them. If the angle between the two vectors is 90 degrees, the cosine of the angle is zero and the dot product is also zero. Therefore, to find the value of p, we need to calculate the dot product of the two vectors, 2i + pj and 4i - 2j, and set it equal to zero. The dot product of two vectors (a, b) and (c, d) is given by: (a, b) * (c, d) = ac + bd So, the dot product of 2i + pj and 4i - 2j is: (2i + pj) * (4i - 2j) = (2 * 4) + (p * -2) = 8 - 2p = 0 Therefore, 2p = 8 and p = 4. So, the value of p is 4.

Ka ìwé ẹ̀kọ́ nípa Surds (WAEC)

Surds

Wo Idahun

Ibeere 25 Ìròyìn

If \(\frac{15 - 2x}{(x+4)(x-3)}\) = \(\frac{R}{(x+4)}\) \(\frac{9}{7(x-3)}\), find the value of R

\(\frac{-32}{7}\)

\(\frac{-23}{7}\)

\(\frac{23}{7}\) Ìdáhùn tó tọ́

\(\frac{32}{7}\)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Polynomial Functions (WAEC)

Polynomial Functions

Wo Idahun

Ibeere 26 Ìròyìn

If sin x = \(\frac{12}{13}\) and sin y = \(\frac{4}{5}\), where x and y are acute angles, find cos (x + y)

\(\frac{48}{65}\)

\(\frac{13}{15}\)

\(\frac{-33}{65}\) Ìdáhùn tó tọ́

\(\frac{-48}{65}\)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Trigonometry (WAEC)

Trigonometry

Wo Idahun

Ibeere 27 Ìròyìn

If 2y\(^2\) + 7 = 3y - xy, find \(\frac{dy}{dx}\)

\(\frac{-y}{4x+y-3}\)

\(\frac{y}{4x+y-3}\)

\(\frac{-y}{4x+x-3}\)

\(\frac{y}{4x+x-3}\) Ìdáhùn tó tọ́

Awọn alaye Idahun

Wo Idahun

Ibeere 28 Ìròyìn

A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t + \(\frac{5}{2t^2}\) - t\(^3\).

Calculate the maximum height reached.

418.5m

56.0m

31.5m Ìdáhùn tó tọ́

30.0m

Awọn alaye Idahun

Wo Idahun

Ibeere 29 Ìròyìn

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

\(\frac{-1}{33}\)(6 + √3)

\(\frac{-1}{33}\)(6 - √3)

\(\frac{1}{33}\)(6 + √3) Ìdáhùn tó tọ́

\(\frac{1}{33}\)(6 - √3)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Surds (WAEC)

Surds

Wo Idahun

Ibeere 30 Ìròyìn

Given that f: x --> x\(^2\) - x + 1 is defined on the Set Q = { x : 0 ≤ x < 20, x is a multiple of 5}. find the set of range of F.

{21, 91, 221} Ìdáhùn tó tọ́

{21, 91, 221, 381}

{1,21, 91, 221}

{1,21, 91, 221,381}

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Sets (WAEC)

Sets

Wo Idahun

Ibeere 31 Ìròyìn

A fair die is tossed 60 times and the results are recorded in the table

Number of die	1	2	3	4	5	6
Frequency	15	10	14	2	8	11

Find the probability of obtaining a prime number.

\(\frac{7}{30}\)

\(\frac{1}{6}\)

\(\frac{7}{15}\)

\(\frac{8}{15}\) Ìdáhùn tó tọ́

Awọn alaye Idahun

A prime number is a number greater than 1 that is only divisible by 1 and itself. The prime numbers on a die are 2, 3, and 5. We know that the die is fair, which means that each number has an equal probability of being rolled. There are a total of 60 rolls, so we can use the frequency table to count the number of times each prime number appears on the die. The frequency of the number 2 is 10, the frequency of the number 3 is 14, and the frequency of the number 5 is 8. Therefore, the total number of times a prime number was rolled is: 10 + 14 + 8 = 32 The probability of rolling a prime number on a fair die is the total number of times a prime number was rolled divided by the total number of rolls: 32/60 = 8/15 Therefore, the answer is option D, 8/15.

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Probability

Wo Idahun

Ibeere 32 Ìròyìn

Given that F\(^1\)(x) = x\(^3\) √x, find f(x)

\(\frac{2x^{9/2}}{9}\) + c Ìdáhùn tó tọ́