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"Algebra" question number distribution across years
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JAMB questions for "Mathematics :: Algebra"
Q1

If y varies directly as the square root of x and y when x = 16. Calculate when x = 64

A

3

B

5

C

6

D

12

E

Answer: C

Algebra
Q2

Factorize completely: x3 + 3x2 - 10x/2x2 - 8

A

x(x - 5)/2(x - 2)

B

x2 + 5/2x + 4

C

x(x - 5)/2(x +2)

D

x(x + 5)/2(x + 2)

E

Answer: D

Algebra
Q3
Make Q the subject of the formula if P = M(x + Q) + 1/5
A
5P + MX - 5/M
B
5P + MX - 5/ M
C
5P - MX + 5/ M
D
5P - MX - 5/ M
E

Answer: D

Algebra
Q4

Solve for x and y if x - y = 2 and x2 - y2 = 8

A

(-3, 1) 

B

(1, 3)

C

(-1, 3)

D

(3, 1)

E

Answer: D

Algebra
Q5

If 9x2 + 6xy + 4y2 is a factor of 27x3 - 8y3

A

3x + 2y 

B

3x - 2y 

C

2y + 3x 

D

2y -3x

E

Answer: B

Algebra
Q6

If x is inversely proportional to y and x = 21/2 when y = 2, find x if y = 4

A

11/4

B

21/4

C

4

D

5

E

Answer: A

Algebra
Q7

For what range of values of x is 1/2 x + 1/4 >1/3x + 1/2?

A

x < -3/2

B

x > -3/2

C

x < 3/2

D

x > 3/2

E

Answer: D

Algebra
Q8

Solve the inequalities -6 ≤ 4 - 2x < 5 -x.

A

-1 ≤ x ≤ 6

B

-1 ≤ x < 6

C

-1 < x  < 5 

D

-1 < x ≤ 5

E

Answer: D

Algebra
Q9

Find the sum to infinity of the following series. 0.5 + 0.05 + 0.005 + 0.0005 + ......

A

5/11

B

5/9

C

5/8

D

5/7

E

Answer: B

Algebra
Q10

The 3rd term of an arithmetic progression is -9 and the 7th term is -29. Find the 10th term of the progression.

A

165

B

44

C

-44

D

-165

E

Answer: C

Algebra
Q11

If x * y = x + y2, find the value of (2 * 3) * 5

A

55

B

36

C

25

D

11

E

Answer: B

Algebra
Q12

If p and q are two non-zero numbers and 18 (p + q) = (18 + p)q, which of the following must be true?

A

q < 1

B

q = 18 

C

p < 1

D

p = 18 

E

Answer: B

Algebra
Q13

Evaluate 

A

-102 

B

-42 

C

18

D

102

E

Answer: A

Algebra
Q14

if P =  what is p-1 = ?

A
B
C
D
E

Answer: D

Algebra
Q15

Find the distance between the point (1/2 , 1/2) and (-1/2, -1/2).

A

√3

B

√2

C

1

D

0

E

Answer: B

Algebra
Q16

Find the gradient of the line passing through the points  P (1 , 1) and Q (2 , 5).

A

5

B

4

C

3

D

2

E

Answer: B

Algebra
Q17

Find the equation of the line parallel to y = 4x + 2 passing through (2 , 3).

A

y + 4x - 11 = 0 

B

y - 4x + 11 = 0

C

y + 4x + 11 = 0

D

y - 4x - 11 = 0

E

Answer: A

Algebra
Q18

At what value of x does the function y = -3 -2x + x2  attain a minimum value ?

A

4

B

1

C

-1

D

-4

E

Answer: B

Algebra
Q19

If cot θ = 8/15 , where θ is acute, find sin θ.

A

16/17

B

13/15

C

8/17

D

15/17

E

Answer: D

Algebra
Q20

If m* n = n - (m + 2) for any real numbers m and n, find the value of 3 * (-5)

A

-6

B

-8

C

-10

D

-12

E

Answer: C

Algebra
Q21

Find to infinity, the sum of the sequence 1, 9/10, (9/10)², (9/10)³, ................

A

10

B

9

C

10/9

D

9/10

E

Answer: A

Algebra
Q22

The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35, ..................... is

A

n(3n - 0.5)

B

 

n(3n + 2)

 

C

 

n(3n + 2.5)

 

D

 

n(3n + 5)

 

E

Answer: B

Algebra
Q23

Determine the value of x for which (x² - 1) > 0

A

x < -1 or > 1

B

-1 < x < 1

C

x > 0

D

x < -1

E

Answer: B

Algebra
Q24

W is directly proportional to U. If W = 5 when U = 3, find U when W = 2/7

A

6/35

B

10/21

C

21/10

D

35/6

E

Answer: A

Algebra
Q25

Which of the following equations represents the graph above?

A

y = 2 + 7x + 4x²

B

 

y = 2 - 7x + 4x²

 

C

 

y = 2 + 7x - 4x²

 

D

 

y = 2 - 7x - 4x²

 

E

Answer: D

Algebra
Q26

A polynomial in x whose roots are 4/3 and -3/5 is 

A

15x² - 11x - 12

B

 

15x² + 11x - 12

 

C

 

12x² - 11x - 12

 

D

 

12x² + 11x - 12

 

E

Answer: A

Algebra
Q27

Find the range of values of x for which 3x -7 ≤ 0 and x + 5 > 0

A

- 5 < x < 7/3

B

- 5 ≤ x ≤ 7/3

C

- 5 < x ≤ 7/3

D

- 5 ≤ x < 7/3

E

Answer: C

Algebra
Q28

In the diagram, PQ//RS. The size of the angle marked x is

A

100°

B

80°

C

50°

D

30°

E

Answer: B

Algebra
Q29

A binary operation on the set of real numbers excluding -1 is such that for all m, n ε R, m Δ n = m + n + mn. Find the identity element of the operation.

A

1

B

0

C

-1/2

D

-1

E

Answer: B

Algebra
Q30

A binary operation * defined on the set of positive integers is such that x * y = 2x - 3y + 2 for all positive integers x and y. The binary operation is 

A

commutative and closed on the set of positive integers

B

neither commutative nor closed on the set of positive integers

C

commutative but not closed on the set of positive integers

D

not commutative but closed on the set of positive integers

E

Answer: B

Algebra
Q31

The fifth term of an A.P is 24 and the eleventh term is 96. Find the first term.

A

12

B

4

C

-12

D

-24

E

Answer: D

Algebra
Q32

Solve the quadratic inequality x² - 5x + 6 ≥ 0

A

x ≤ 2, x ≥ 3

B

x ≤ 3, x ≥ 2

C

 

x ≤ -2, x ≥ -3

 

D

 

x ≤ -3, x ≥ 2

 

E

Answer: A

Algebra
Q33

Find the range of values of x which satisfy the inequalities 4x - 7  ≤ 3x and 3x - 4 ≤  4x

A

-4 ≤  x ≤  7

B

 -7 ≤  x ≤  4

C

x ≥ -7

D

-7 ≤  x ≤  6

E

Answer: A

Algebra
Q34

If p varies inversely as the square of q and p = 8 when q = 4, find q when p = 32

A

±16

B

±8

C

±4

D

±2

E

Answer: D

Algebra
Q35

If x - 3 is directly proportional to the square of y and x = 5 when y = 2, find x when y = 6

A

30

B

21

C

16

D

12

E

Answer: B

Algebra
Q36

Factorize completely (4x + 3y)² - (3x - 2y)²

A

(x + 5y)(7x + y)

B

(x + 5y)(7x - y)

C

(x - 5y)(7x + y)

D

(x - 5y)(7x - y)

E

Answer: A

Algebra
Q37

Find the dervaitive of y = (x7 - x6)/ x4

A

x(x² - 1)

B

3x(x² - 1)

C

3x² - 1

D

7x6 - 5x4

E

Answer: C

Algebra
Q38

If 2x² - kx - 12 is divisible by x - 4, find the value of k

A

4

B

5

C

6

D

7

E

Answer: B

Algebra
Q39

Make Q the subject of the formula when L = 4/3M√PQ

A

9L²/16M²P

B

3L/4M√P

C

√3L/4MP

D

 

3L²/16M²P

 

E

Answer: A

Algebra
Q40

If X = {n² + 1 : n = 0, 2, 3} and Y = {n + 1 : n = 2, 3, 5}, find X ∩ Y

A

{1,3}

B

{5,10}

C

Ø

D

{4,6}

E

Answer: C

Algebra
Q41

If (1 + √2) / (1 - √2) is expressed in the form x + y√2, find the value of x and y.

A

(-3, -2)

B

(-2, 3)

C

(3, 2)

D

(2, -3)

E

Answer: A

Algebra
Q42

If y = x cos x, find dy/dx

A

sin x - x cos x

B

sin x + cos x

C

cos x + x sin x

D

cos x - x sin x

E

Answer: D

Algebra
Q43

The graph above is represented by

A

y = x³ - 3x - 2

B

y = x³ + 2x² - x - 2

C

y = x³ - 4x² + 5x - 2

D

y = x³ - 4x - 2

E

Answer: B

Algebra
Q44

Factorize 2t² + t - 15

A

(2t - 3)(t + 5)

B

(t + 3)(2t - 5)

C

(t + 3)(t - 5)

D

(2t + 3)(t - 5)

E

Answer: B

Algebra
Q45

Solve the inequality -3(x - 2) < -2(x + 3)

A

x > 12

B

x < 12

C

x > -12

D

x < -12

E

Answer: A

Algebra
Q46

A binary operation Δ is defined by a Δ b = a + b + 1 for any real numbers a and b. Find the inverse of the real number 7 under the operation Δ, if the identity element is -1

A

-7

B

-9

C

5

D

9

E

Answer: B

Algebra
Q47

The nth term of the sequence 3/2, 3, 7, 16, 35, 74, ... is

A

5.2n-2 - n

B

 

5.2n-2 - n+1/2

 

C

 

35.2n-2 

 

D

3/2n

E

Answer: A

Algebra
Q48

If y = (1 + x)², find dy/dx

A

2x - 1

B

x - 1

C

2 + 2x

D

1 + 2x

E

Answer: C

Algebra
Q49

The solution of the quadratic inequality (x² + x - 12) ≥ 0 is

A

x ≥ -3 or x ≤ 4

B

x ≥ 3 or x ≥ -4

C

x ≤ 3 or x≤ -4

D

x ≥ 3 or x ≤ -4

E

Answer: D

Algebra
Q50

W α L² and W = 6 when L = 4. if L = √17. Find W.

A

67/8

B

65/8

C

63/8

D

61/8

E

Answer: C

Algebra
Q51

Find the sum to infinity of the series 2 + 3/2 + 9/8 + 27/32 + ...

A

1

B

2

C

8

D

4

E

Answer: C

Algebra
Q52

Find y, if √12 - √147 + y√3 = 0

A

5

B

1

C

7

D

3

E

Answer: A

Algebra
Q53

If x10 = 12145, find x

A

124

B

121

C

184

D

180

E

Answer: C

Algebra
Q54

Evaluate (0.5625)² - (0.4375)² / 0.04 correct to 3 significant figures

A

3.11

B

3.13

C

0.313

D

3.12

E

Answer: B

Algebra
Q55

If the lines 3y = 4x - 1 and qy = x + 3 are parallel to each other, the value of q is

A

-4/3

B

-3/4

C

4/3

D

3/4

E

Answer: D

Algebra
Q56

Differentiate (x2 - 1/x)2 with respect to x.

A

4x3 - 2 -2/x3

B

4x3 - 2 + 2/x3

C

4x3 - 3x + 2/x

D

4x3 - 4x - 2/x

E

Answer: A

Algebra
Q57

PQ and RS are two parallel lines. If the coordinates of P, Q, R, S are (1,q), (3, 4), (5,2q) respectively, find the value of q.

A

4

B

1

C

2

D

3

E

Answer: C

Algebra
Q58

For what value of n is n + 1C3 = 4(nC3) ?

A

4

B

6

C

3

D

5

E

Answer: C

Algebra
Q59

Find the variance of 2x, 2x - 1 and 2x + 1.

A

√2/3

B

2

C

1

D

2/3

E

Answer: D

Algebra
Q60

How many terms of the series 3, -6, +12, -24, +...... are needed to make a total of 1 - 28?

A

9

B

12

C

8

D

10

E

Answer: C

Algebra