MATHEMATICS - ALGEBRA

PROBLEM SET # 1
INSTRUCTION: Encircle the letter that corresponds to the correct answer of your choice.

1. Which number has four significant figures?

A. 0.0025 B. 0.02525 C. 0.0252 D. 2.4250

2. What is the solution of the equation 25x2 + 2(x – 4)2 = -3, where x is a real-valued variable?
A. -6.12 and -3.88 B. -0.52 and 0.700 C. 7.55 D. no solution

4 1
3. What is the determinant of the following 2 x 2 matrix? ! &
2 6
A. 18 B. 20 C. 22 D. 24

1 3 6
4. What is the determinant of the following matrix? '2 −1 1 *
1 2 −1
A. 30 B. 34 C. 38 D. 42

5. Solve the following set of simultaneous linear equations for A, B, and C.

2A + 3B – C = -10 -A + 4B + 2C = -4 2A – 2B + 5C = 30
A. 8.38, -4.81, 4.32 C. 6.38, -9.81, 4.32
B. 1.38, -5.81, 4.32 D. 1.38, -2.81, 4.32

6. What is the value of A satisfying the expression A-5/4 = 0.001?

A. 211.19 B. 231.19 C. 251.19 D. 271.19

7. Refer to the following systems of equations.

4x + 3y + 10z = 5 8x – 2y + 9z = 5 8x + y – 10z = 5
What is the classical adjoint of the coefficient matrix?
é 10 42 47 ù é 11 40 57 ù
A. ê152 - 120 44 ú
ú C. ê152 - 120 44 ú
ú
ê ê
êë 24 20 - 32úû êë 64 20 - 32úû
é11 450 47 ù é 11 40 47 ù
B. ê12 - 120 44 ú
ú D. ê152 - 120 44 ú
ú
ê ê
êë24 20 - 32úû êë 24 20 - 32úû

8. Refer to the following systems of equations.

4x + 3y + 10z = 5 8x – 2y + 9z = 5 8x + y – 10z = 5
What is the inverse of the coefficient matrix?
é0.0648 0.054 0.535 ù é0.0148 0.454 0.0635 ù
A. êê0.2054 - 0.162 0.0594 úú C. êê0.6054 - 0.162 0.0594 úú
êë0.0324 0.027 - 0.043úû êë0.0324 0.027 - 0.043úû
é0.0148 0.054 0.0635 ù é0.5148 0.054 0.2635 ù
B. êê0.2054 - 0.162 0.0594 úú D. êê0.2054 - 0.462 0.0594 úú
êë0.0324 0.027 - 0.043úû êë0.0324 0.027 - 0.043úû

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9. What is the matrix difference A – B of matrices A and B?
é3 4 1 ù é5 2 -6 ù
A = ê ú B = ê ú
ë5 2 - 2û ë- 5 4 7û
A. éê
7ù
C. éê
-2 5 -2 0 7ù
8 - 2 - 9 ú 1 - 2 - 9 ú
ë û ë û
é
B. ê
-2 1 7ù é
D. ê
-2 2 7ù
ú ú
ë10 - 2 - 6û ë10 - 2 - 9û

é1 - 3 2ù
10. The determinant of matrix A is -7. What is the missing value a? ê ú
A = ê0 1 2ú
êë3 - 1 aúû
A. 11 B. 45 C. 75 D. 15

11. How many significant digits do the 20,540.00 have?

A. 7 B. 5 C. 6 D. 4

12. Which of the following is not true of the given equations below?
n
A. xm/n = xm B. mx = my, then x = y C. a2 + b2 = a + b D. (x/y)a = xa y-a

2 2
13. Solve for x: x = (b - 4 b + 16)(b - 16)
3
b + 64
b2 - 4
A. b + 4 B. b - 4 C. D. b – 4
b + 4 b + 4

14. Factor the expression as completely as possible 3x3 - 3x2 - 18x.

A. 3x(x+2)(x+3) B. 3x(x-2)(x-3) C. 2x(x+2)(x-3) D. 3x(x+2)(x-3)

15. Factor the expression as completely as possible x4 - y4.

A. (x2-y2)(x+y)(x-y) B. (x2+y2)(x-y)(x-y) C. (x2+y2)(x+y)(x+y) D. (x2+y2)(x+y)(x-y)

16. Factor the expression as completely as possible x2 + 8x + 16.

A. (x+6)2 B. (x+4)2 C. (x-4)2 D. (x+4)3

¥ - 4000
= ?
17. ¥
A. 0 B. 1 C. infinity D. indeterminate

18. i23 is equal to

A. i B. 1 C. -1 D. -i

19. Factor the expression as completely as possible ay + ax –xb – by.

A. (x+y)(a-b) B. (x+y)(a+b) C. (xy)(ab) D. (x+y)(ab)

20. Solve the equation simultaneously 4x + 2y = 5 and 5x - 3y = -2

A. 1, 2 B. ½ , 3/2 C. 2, 3 D. ½, ¾

21. Solve for x: x – 3y = 10 and 2x + y = 6

A. 1 B. 2 C. 3 D. 4

22. Three bars of iron weigh 3 2/5, 5 1/2, and 7 3/10 kilograms. Find their average weight.
A. 4.4 kg B. 5.4 kg C. 6.4 kg D. 7.4 kg

23. A number minus 4 is 9. Find the number.

A. 10 B. 11 C. 12 D. 13

24. What are the solutions to the following equation? x2 – x – 20 = 0

A. x1 = 3; x2 = -4 B. x1 = 5; x2 = -4 C. x1 = 7; x2 = -4 D. x1 = 9; x2 = -4

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25. Determine the SUM of the positive-valued solutions to the simultaneously equations:
xy = 24 yz = 32 xz = 48
A. 18 B. 16 C. 15 D. 17

26. Solve for x: 3x + 9x = 27x.

A. 0.438 B. 0.460 C. 0.415 D. 0.482

é2 - 1ù
27. Determine the product of the following matrices: ê1 0 ú x é1 - 2 - 5ù
ê ú ê3 4 0 ú
êë3 4 úû ë û

é- 1 - 8 - 10ù é- 1 - 8 - 10ù
A. ê 1 - 2 - 5 úú B. ê- 1 - 2 5 úú
ê ê
êë15 10 - 15úû êë 9 22 15 úû
é0 0 - 10ù é0 0 - 10ù
C. ê 1 - 2 - 5 úú D. ê1 - 2 - 5 ú
ê ê ú
êë0 21 15 úû êë0 21 - 15úû

2 3 1
28. If A = - 1 2 4 . What is the cofactor with the second row, third column element?
0 5 7
1 3 2 3
A. B. -
0 5 0 5
1 7 3 1
C. - D.
2 0 0 7

29. A student had an average of 72 so far in her 4 quizzes. How much should he get in her fifth quiz to raise his
average to 75?
A. 83 B. 85 C. 87 D. 89

30. The average of six scores is 83. If the highest score is removed, the average of the remaining scores is 81.2.
Find the highest score.
A. 91 B. 92 C. 93 D. 94

31. Jody’s English quiz scores are 56, 93, 72, 89 and 87. What is the median of her scores?
A. 87 B. 85 C. 72 D. 56

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