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201-013 Final Exam — December 2011
(Marks)
Algebra Page 1
(8) 1. Evaluate the following expressions ( simplify all fractions): a) 16 ÷ 2 [8 − 3 (7 − 5)] + 2 b) 7 12
c) (−4)^2 + 5^0 − |− 10 | d)
(7 − 5)^2
6 ÷^
(8) 2. Factor completely: a) 2 x^2 − 5 x − 3 b) 9 x^3 − 30 x^2 + 24x
c) x^3 y − xy^3 d) 3 ab − 2 b + 9a − 6
(6) 3. Solve the following linear equations: a) 4 (6x + 1) = 43 + 3 (4x + 3) b)
4 −^
5 x^ =
c) 4 (3x − 1) − (3 − 5 x) = 17 (x − 2) + 27
- Use long division to evaluate: x
(^3) − 6 x (^2) + 5 x + 2
(3)
(15) 5. Perform the indicated operations and simplify your answer.
a) 9 x^2 + 5xy + 3 − 2 x(4x + 3y − 5) b)
6 x^2 + 13x + 6 4 x^2 − 9 ÷^
6 x^2 + x − 2 2 x − 1 c) (3x − 4)^2 + (2x + 5)(2x − 5) d) 2 x x^2 − x − 6
x + 2 e) 2 x
(^2) + 4x x^2 + x − 6
· (x^ + 3)
2 x^2 − 4
(9) 6. Simplify the following expressions:
a)
3 x^3 y^2
4 xy^3
3 x^5 y^7
b)
8 a−^2 b^4 12 a^7 b−^3
c)
x
x^2 1 − 25 x^2
(4) 7. Simplify the following:
a)
32 x^2 y^7 z^10 b)
√^18 x^9 y^5 2 x^3 y
(6) 8. Perform the indicated operations and simplify your answers: a)
48 b) y^2
x^5 y + x
x^3 y^5 c)
x + 3√y
x − 3 √y
201-013 Final Exam — December 2011
(Marks)
Algebra Page 2
(6) 9. Solve the following equations by factoring: a) x^2 − 5 x − 6 = 0 b) x^3 − 3 x^2 − x + 3 = 0 c) x (x − 2) = 4x + 16
(12) 10. Solve the following equations or show that there is no solution: a) 2 2 x + 3
4 x − 5
b) x 2 x^2 − x − 1
x^2 − 1
2 x + 1
c)
6 x − 5 − 2 = 3 d)
x + 3 −
x = 1 (3) 11. Solve 2 x^2 + 5x − 1 = 0 by using the quadratic formula. (3) 12. Solve x^2 = 6x − 4 by completing the square. (2) 13. Solve (x − 3)^2 = 5 (3) 14. Given the formula A = P + P rt solve for P.
- Rationalize the denominator and simplify:
√^12
(2)
(6) 16. a) The sum of two numbers is fourteen. The difference between two times the smaller and the larger is one. Find the two numbers.
b) If I borrow $ 3500 for 2 years at a simple interest rate of 5%, how much will I need to pay back?
c) The sum of three consecutive odd integers is fifty-one. Find the three integers.
(4) 17. a) A pair of jeans costing $40 sold for $62. Find the markup rate.
b) A telescope is on sale for $165 after a markdown of 40% off the regular price. Find the regular price. Answers
1.a) 18 b)−
36 c) 7^ d)
2.a) (2x + 1)(x − 3) b) 3x(3x − 4)(x − 2) c) xy(x + y)(x − y) d) (3a − 2)(b + 3)
3.a) x = 4 b) x = −
3 c)^ x^ is any real number^ 4)^ x
(^2) − 8 x + 16 − 27 x + 2
5.a) x^2 − xy + 10x + 3 b) (^2) x 1 − 3 c) 13x^2 − 24 x − 9 d) (^) (x −− 3)(x^ + 9x + 2) e)^2 (xx( x−^ + 3) 2) 2
6.a)
4 x^2 y^12 b)
9 a^18 4 b^4 c)^
x + 3 x + 5 7.a) 4xy
(^3) z 5 √ 2 y b) 3x (^3) y 2
8.a) − 16
3 b) 2x^2 y^2 √xy c) 4x − 9 y 9.a) x = 6, − 1 b) x = 3, − 1 , 1 c) x = 8, − 2 10.a) x =
2 b)^ x^ = 0,^ −^
2 c)^ x^ = 5^ d)^ x^ = 1^ 11)^ x^ =^
4 12)^ x^ = 3^ ±
- x = 3 ±
5 14) P =
A
1 + rt 15) 3(
16.a) 5 and 9 b) $3850 c) 15, 17 , 19 17.a) 55% b) $
