SCHOOL OF BASIC AND REMEDIAL STUDIES (SBRS, AFIT)
MATHEMATICS CAT
INSTRUCTION: ANSWER ALL QUESTIONS
TIME: 1HOUR
1) The binary operation * is defined on the set of integers p and q by p*q = pq + p
+ q. Find 2 * (3 * 4).
A. 59
B. 19
C. 67
D. 38
2) If -2 is the solution of the equation 2x + 1 - 3c = 2c + 3x - 7, find the value of c.
A. 4
B. 3
C. 2
D. 1
3) Given that 𝐼3 is the identity matrix, find |𝐼3 |
A.1 B.2 C.3 D.0
3
4
0
2
2
26
26
−2
4) (−2 6 −3) × ( 5 ) gives? A. ( 5 ) B. (29) C. ( 29 ) D. ( 5 )
7 −4 1
−1
−1
7
−7
1
5)Simplify2134 x 234 A. 103114 B. 103214 C. 122314 D. 132114
6)In a class of 40 students, 32 offer mathematics, 24 offer Physics, and 4 offer
neither Mathematics nor Physics. How many offer both Mathematics and
Physics? A. 20 B. 16 C. 8 D. 4
7) If the operation * on the set of integers is defined by P * Q = √𝑃𝑄, find the
value of 4 * ( 8 * 32). A. 8 B. 3 C. 16 D. 4
8) x varies directly as the product of u and v and inversely as their sum. If x = 3
when u = 3 and v = 1, what is the value of x if u = 3 and v = 3? A. 3 B. 4 C. 6 D. 9
−1
1
−1
−1
9)Simplify(25) 2 × (27)3 + (121) 2 × (625) 4
A. 34/55 B. 9/11 C. 14/5 D. 3/275
3
2
10) Find the remainder when 3x + 5x - 11x + 4 is divided by x + 3.
A. -4 B. 4 C. 1 D. -1
11) W ∝ L2 &W = 6 when L = 4. If L = √17 find W A. 67/8 B. 65/8 C. 63/8 D.61/8
12) If x10 = 12145 find x A. 124
B. 121 C. 184 D. 180
13) If m * n = n - (m+2) for any real number m and n find the value of 3*(-5)
A. -6 B. -8 C. -10 D. -12
14) If 6logx2 - 3logx3 = 3log50.2, find x. A. 8/3 B. 4/3 C. ¾ D. 3/8
15) If 3214 is divided by 234 and leaves a remainder r, what is the value of r?
A. 0 B. 1 C. 2 D. 3
16) Find P, if 4516 - P7 = 3056 A. 627 B. 1167 C. 6117 D. 1427
17) Find the value of m if 13m + 24m = 41m A. 8 B. 6
C. 5
18) If Log102 = 0.3010 and Log103 = 0.4771, evaluate Log104.5
A. 0.9542 B. 0.6532 C. 0.4771 D. 0.3010
D. 2
19) A binary operation ⊕ defined on the set of real number is such that x⊕y =
xy/6 for all x, y ∈ R. Find the inverse of 20 under this operation when the identity
element is 6 A. 1/12 B. 10/3 C. 1/20 D. 9/5
2
20) Factorize 2t + t – 15
A. (2t - 3)(t + 5) B. (t + 3)(2t - 5) C. (t + 3)(t - 5) D. (2t + 3)(t - 5)
21) Find y, if √12 − √147 + 𝑦√3 = 0 A. 5 B. 1 C. 7 D. 3
22)A binary operation * is defined on the set of positive integers is such x*y = 2x3y+2 for all positive integers x and y. The binary operation is
A. commutative and close 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 cummutative but closed on the set of positive integers
23) Simplify(√6 + 2)2 −(√6 − 2)2
A. 2√6 B. 4√6 C. 8√6 D. 16√6
24)A polynomial in x whose zeros are -2, -1 and 3 is
A. x3 - 7x + 6 B. x3 + 7x – 6 C. x3 + 7x + 6 D. x3 - 7x – 6
−1
1 2
2 3
25) Given that 𝐴 = (
) and 𝐵 = (
) calculate AB
3 6
3 4
1
2
−1 −2
−1 2
1 0
A. (
) B. (
) C. (
) D. (
)
15 30
9 18
5 15
0 1
26) If n(P) = 20 and n(Q) = 30 and n(PuQ) = 40, find the value n(PnQ)
A. 10 B. 30 C. 15 D. 40
1
0 1
−1 1
2
27)If𝑋 = ( 2 −1 0) 𝑎𝑛𝑑 𝑌 = ( 0 −1 −1), Find 2X-Y
−1 0 1
2 −1 1
3 −1 0
3 −1 0
3 −1 0
3 −1 0
A. ( 4 −3 −1) B. ( 4 −1 1) C. ( 4 −3 1) D. ( 4
1 1)
−4 1
1
−4 1 1
−4 1 1
−4 −1 1
3
5 −4
28)Given matrix 𝑁 = ( 6 −3 −5), find |N|.A.65 B.23 C.91 D.17
−2 2
1
2 −3
−1
29) If 𝑃 = (
), what is 𝑃 .
1 1
1
3
1 3
1 3
1
3
−
−
−
5
A.( 51
B. (51 52)
C. ( 51 52) D. ( 5 1 52)
2)
−
−
−
−
5
5
5 5
5 5
5 5
𝑥 3
30)If |
| = 15, find the value of x A.4 B.5 C.2 D.3
2 7