MTH 101 CBT TEST EXAM MODE

1.

Determine the square of the remainder when 3x⁴ – 2x³ – 10x – 5 is divided by x – 4

2.

 The fourth term and the seventh term of an AP are in the ratio 5:8. Find the ratio of the 3^rd and 6^th term.

3. Find the 8th term and the sum of the first 8 terms of the GP sequence:1/2 , −1, 2, −4, … . . ?

4.

Simplify (216)^−1⁄3 × (0.16)^−1⁄2

5. Evaluate loga256= 4

6.

If R = {x: x² = 16, x > 5}, then R is equal to

7. The correct expression for the common difference in an A.P. is

8.

The sum of the first n terms of an AP whose difference is not zero equals half the sum of its subsequent  n members. Find the ratio of the sum of the first 3n terms and the sum of the first …terms .

9.

If U = (Integers < 20); D = {multiples of 4}; E = {multiples of 3}, the element of D^/ ∩ E are

10. Given the universal set U = {2,3,4,5,6,7,8,9} and subsets P = {2,4,6,8} and Q = {x:x^ 2< 50,x is odd }, find (P ∩Q )'

11.

In a certain class, 22 pupils take one or more of Chemistry, Economics and Government. 12 take Economics  €, 8 take Government (G) and 7 take Chemistry (C). Nobody takes Economics and Chemistry and 4 pupils  take Economics and Government. How many pupils take both Chemistry and Government?

12.

Determine the values of p & q if (x – 1) & (x + 2) are factors of 2x³ + px² – x + q 

13.

In a class, 220 students offer Mathematics or Chemistry or both. 125 offer Mathematics and 110 offer  Chemistry. How many offer Chemistry but not Mathematics?

14.

In a group of 40students, 22 study Maths, 18 study physics, 14 study statistics, 9 study both Maths and Physics,  7 study both Maths and Statistics, 5 study both Physics and Statistics and 2 study all the subjects. How many  study none of the subjects?

15. Find the roots of the equation: 3 + 5 2 − 2 − 24

16.

Find the 8^th term and the sum of the first 8 terms of the GP sequence: , −1, 2, −4, … . . ?

17. The universal set U has subsets M and N such that M ⊆ N . The set of M ∩ (M ∩ N )'
is

18.

The second term of an AP is four times the first term, the last term is 13 times the first term and the sum of  the series is 70. Find the first three terms of the progression

19.

What is the remainder when x³ + 3x² – 13x – 10 is divided by (x – 3)?

20.

A polygon has 25sides, the length of which starting from the smallest side are in AP. If the perimeter of the  polygon is 1100cm, and the length of the largest side is ten times that of the smallest, find the length of the  smallest side.

21.

Don Mike places a sum of money on a savings account in the bank. On each succeeding birthday, he deposits  two times more than on the previous birthday. His total sum of the first eleven deposits is N20,480. How  much was his first deposit?

22. The common difference in the series K, K+ 3,K + 6, … .. is

23. Given the following series: ln , ln 2 , ln 4 , ln 8, find the 21st term

24. If P = {prime factors of 84} and Q = {prime factors of 315}, the elements of P U Q & P ∩ Q are respectively

25. Find the range of x for which 12 +x − x^2< 0

26.

The union of the set A and B denoted by A U B denoted by A U B, is the set of elements which belong  to

27.

Given that -2 = A(x – 1)² + B(x – 1) (x – 2) + C(x – 2), find the value of C

28.

In the equation 5x⁴ + 9x³ – 12x² – 9x + 5 = 0, find the value of x –¹/x

29. The number of distinct elements found in a given set is called

30.

The 6^th and 13^th term of an A.P. are 0 and 14 respectively, find the 20^th term

31.

If A is a subset of a universal set U, the compliment of set A is given as:

32.

In a class of 100 students, 40 students study botany, 32 study microbiology while 44 study zoology. The  number of students that study botany and microbiology is 24, botany and zoology is 24, while 20 study  microbiology and zoology. If 20 students study all the three subjects, how many study none of the three  courses.

33.

The universal set U contains only elements of the sets A, B, C where A = {3,q,r}, B = {a,2,c} and  C = {1,3,4,b}. what are the elements in [(A - B) ∩ {C – (A ∩ C)’}]

34.

Find the value of the constant k if 4x³ + kx² + 7x – 23 has a remainder 7 when divided by 2x – 5

35.

The type of sequence in which the next term differs from the preceding term by a difference is termed

36. The set statement ( ∪ ) ∩ = ∪ ( ∩) is relevant to

37.

The word “Infinity” is

38. The universal set U contains only elements of the sets A, B, C where A = {3,q,r}, B = {a,2,c} and
C = {1,3,4,b}. what are the elements in [(A - B) ∩ {C – (A ∩ C)’}]

39.

The sum of the square of three positive numbers in arithmetic progression is 165. If the sum of the number  is 21, find the sum of cubes of each of the numbers?

40. If the first 3 terms of an A.P. are , 3 + 1, 7 − 4, find the 10th term of the sequence