:Q 1. (+5) + (-9) = (a) -4 (b) -5 (c) 0 (d) +4 (e) -1 :RCA 1. (a) -4 Ans. +5 + -9 ---- -4 Ans. :RA :Q 2. (-3) + (-6) = (a) -3 (b) -9 (c) 1 (d) -6 (e) 0 :RCB 2. (b) -9 Ans. Note: When adding two numbers with like signs, add and keep the same sign. -3 + -6 ----- -9 Ans. :RA :Q 3. (+3) - (-7) = (a) 4 (b) -4 (c) 10 (d) 0 (e) 5 :RCC 3. (c) 10 Ans. +3 - -7 ---- +10 Ans. :RA :Q 4. (+12) - (-6) = (a) 15 (b) 18 (c) 6 (d) -18 (e) 4 :RCB 4. (b) 18 Ans. Note: Change the sign of the bottom number and follow the addition rule. +12 - - 6 ----- +18 Ans. :RA :Q 5. (-5)(-3) = (a) -8 (b) 5 (c) 0 (d) 15 (e) -15 :RCD 5. (d) 15 Ans. Note: Negative times negative equals a positive. -5 x -3 ---- 15 :RA :Q 6. (-7)(+1/3)(-9) = (a) 22 (b) 11 (c) -21 (d) 0 (e) 21 :RCE 6. (e) 21 Ans. Note: Multiply one at a time. (-7) x (+1/3) = (+7/3) (-7/3) x (-9) = 21 Ans. :RA :Q 7. (-8)(+5)/(-2) = (a) 20 (b) 10 (c) -4 (d) -20 (e) 0 :RCA 7. (a) 20 Ans. Note: Do multiplication first, then division. -8 x +5 ---- -40 -40/-2 = 20 Ans. :RA :Q 8. Solve for y: 4y + 3 = 9 (a) 2/3 (b) 2 (c) 3/2 (d) 1/2 (e) 1 :RCC 8. (c) 3/2 Ans. Note: Subtract 3 from both sides, then divide by 4. 4y 6 -- = - 4 4 y = 3/2 Ans. Note: Isolate the variable on one side by adding or subtracting, then divide the coefficient in front of the variable to both sides. :RA :Q K K 9. Solve for K: - + - = 1 5 6 (a) 30/11 (b) 3 (c) 20/11 (d) 0 (e) 24/11 :RCA 9. (a) 30/11 Ans. Note: Find the common denominator (30), then multiply both sides by that number. Next, solve for the variable. 30(K/5) + 30(K/6) = 30 6K + 5K = 30 11K = 30 K = 30/11 Ans. :RA :Q 10. Solve for y: ay = by + c (a) c/(b - a) (b) (a - b)/c (c) ab/c (d) ab (e) c/(a - b) :RCE 10. (e) c/(a - b) Ans. Note: Move all terms with y to one side, and solve for y. ay = by + c -by = -by ay - by = c y(a - b) c -------- = ----- (a - b) a - b c y = ----- Ans. a - b :RA :Q 11. If k + y = 8m and k - y = 6n then k is? (a) 4m + 3n (b) 7m + n (c) 2m + 3n (d) m + n (e) 4m + n :RCA 11. (a) 4m + 3n Ans. Note: Eliminate one unknown; solve for the other, then substitute. k + y = 8m k - y = 6n 2k + 0y = 8m+6n 2k 8m 6n -- = -- + -- 2 2 2 k = 4m + 3n Ans. :RA :Q 12. If 8y = 3y + 15 then, 4y + 5 = (a) 2 (b) 17 (c) 18 (d) 5 (e) 1 :RCB 12. (b) 17 Ans. 8y = 3y + 15 -3y = -3y 5y 15 -- = 0y + -- 5y 5y y = 3 Therefore: 4y + 5 = 4(3) + 5 = 12 + 5 = 17 Ans. :RA :Q 13. What is the value of A in: 2 y = x + Ax - 5 when y = 19 and x = 3 (a) -2 (b) -3 (c) 5 (d) 1 (e) 3 :RCC 13. (c) 5 Ans. 2 19 = (3) + A(3) -5 19 = 9 + 3A -5 19 = 4 + 3A -4 -4 15 3A -- = -- 3 3 5 = A Ans. Note: First substitute the numbers for the variables, then solve. :RA :Q 14. If .69y = 2.07 then y = (a) 1 (b) 2 (c) 6 (d) 3 (e) .03 :RCD 14. (d) 3 Ans. Multiply by 100 to get rid of the decimal, then solve for the unknown. 100(.69y) = 100(2.07) 69y 207 --- = --- 69 69 y = 3 Ans. :RA :Q 15. If 5ky + 8 = 9ky then ky = (a) 2 (b) 3 (c) 8 (d) 4 (e) 1 :RCA 15. (a) 2 Ans. 5ky + 8 = 9ky -5ky -5ky 8 4ky - = --- 4 4 2 = ky Ans. Note: Treat ky as one variable then solve for it. :RA :Q 16. Solve for y: 2 y + 18 = 9y (a) 2 or 6 (b) 1 or 6 (c) 6 (d) 6 or 3 (e) -9 :RCD 16. (d) 6 or 3 Ans. 2 y + 18 = 9y -9y -9y 2 y - 9y + 18 = 0 (y - 6)(y - 3) = 0 y = 6 or 3 Ans. Note: Move everything to one side to get the equation equal to zero, then treat it as a Quadratic Equation and factor. Be careful to arrange the variables in order of descending powers before factoring. :RA :Q 2 17. Solve for y: 5y = 80 (a) +/-2 (b) +/-4 (c) +/-8 (d) +/-12 (e) +/-6 :RCB 17. (b) +/-4 Ans. 2 5y - 80 = 0 2 5(y - 16) = 0 2 y - 16 = 0 (y + 4)(y - 4) = 0 y = +/-4 Ans. :RA :Q 2 18. Solve for y: 7y = 5y (a) 0 (b) 0 or 1/2 (c) 0 or 5/7 (d) 1 or 2 (e) -1 or -2 :RCC 18. (c) 0 or 5/7 Ans. 2 7y = 5y -5y -5y 2 7y - 5y = 0 y(7y - 5) = 0 y = 0 or 5/7 Ans. Note: Move everything to one side of the equation and factor out what is in common, then solve. :RA :Q 19. Solve for y: _____ / 2 \/ y + 8 - 2 = y (a) 2 (b) 4 (c) 0 (d) 10 (e) 1 :RCE 19. (e) 1 Ans. Note: Move everything that does not belong to the square root to the other side; square both sides, then treat it as a quadratic equation. :RA 19. _____ / 2 \/ y + 8 = y + 2 2 2 y + 8 = (y + 2) 2 2 y + 8 = y + 4y + 4 8 = 4y + 4 -4 - 4 4 = 4y y = 1 Ans. :RA :Q __ __ 20. Find the sum of \/80 and \/45. _ _ __ (a) 7\/5 (b) 7\/2 (c) 7\/10 (d) 0 (e) 5 :RCA _ 20. (a) 7\/5 Ans. __ __ _ _ \/80 = \/16\/5 = 4\/5 + __ _ _ _ \/45 = \/9\/5 = 3\/5 _ _ _ 4\/5 + 3\/5 = 7\/5 Ans. Note: Break the square roots down until fully simplified, then add. (Only add the coefficient and keep the square root the same.) :RA :Q 21. Find the difference between __ __ \/98 and \/32. _ _ _ (a) 3\/4 (b) 3\/2 (c) 3\/1 _ (d) 1 (e) 5\/3 :RCB _ 21. (b) 3\/2 Ans. __ __ _ _ \/98 = \/49\/2 = 7\/2 - __ __ _ _ \/32 = \/16\/2 = 4\/2 _ = 3\/2 Ans. Note: Follow the same format - as in the previous example, but subtract like roots. :RA :Q 22. Find the product of ___ __ \/32y and \/2y. (a) 64y (b) 4y (c) 1 (d) 8y (e) 2y :RCD 22. (d) 8y Ans. ____ ___ __ / 2 \/32y x \/2y = \/ 64y = 8y Ans. Note: Multiply what is in the square roots - then break it down. :RA :Q ___ 23. Solve: 1/y = \/.49 (a) 5/7 (b) 2/7 (c) 10/7 (d) 0 (e) 1 :RCC 23. (c) 10/7 Ans. Note: Take the square root and then solve for it. 1/y = .7 .7y = 1 10(.7y) = (1)10 7y = 10 y = 10/7 Ans. :RA :Q 3 24. If y = 2.86 find (2.86) to the nearest hundredth? (a) 23.39 (b) 26.39 (c) 23 (d) 3.39 (e) 1 :RCA 24. (a) 23.39 Ans. Note: Raise it to the third power, then round it off to the nearest hundredth. (2.86) (2.86)= 8.18 (8.18) (2.86)= 23.39 :RA :Q 25. Find the square root of 23409. (a) 15 (b) 5 (c) 93 (d) 90 (e) 153 :RCE 25. (e) 153 Ans. A quick way to identify the correct answer is to take the __square root of the last digit. The \/9 = 3, leaving choices (c) and (d) as possibilities. 93 squared = 8649; whereas 153 squared = 23409. :RA :Q 26. Find the square root of 15775.36? (a) 125.6 (b) 124.3 (c) 100 (d) 26.3 (e) 24.3 :RCA 26. (a) 125.6 Ans. The square root of the last two digits is .6. The only possible answer among the choices is (a) 125.6. :RA :Q __ __ 27. Divide 6\/80 by 3\/20. (a) 2 (b) 4 (c) 8 (d) 1 (e) 16 :RCB 27. (b) 4 Ans. Note: Simplify each root then divide. ______ _ 6\/16 x 5 6 x 4\/5 --------- = -------- _____ _ 3\/4 x 5 3 x 2\/5 _ 24\/5 ----- = 4 Ans. _ 6\/5 :RA :Q _______ / 2 2 / y + y 28. Find / -- - \/ 16 9 (a) 1/2y (b) 4y/12 (c) 5y/12 (d) 6y (e) 8y :RCC 28. (c) 5y/12 Ans. Note: Combine what is inside the square root, then take the square root of that. __________ ____ / 2 2 / 2 / 9y + 16y / 25y / ---------- = / ---- \/ 144 \/ 144 5y/12 Ans. :RA :Q 29. n/7 + 3n/2 = (a) 23n/14 (b) 24n/2 (c) 20 (d) 12n/7 (e) 0 :RCA 29. (a) 23n/14 Ans. Note: Find the common denominator, convert each fraction to that denominator, then add. 2n 21n 23n -- + --- = --- Ans. 14 14 14 :RA :Q 30. Combine into a single fraction: 1 + a/b (a) ba/b (b) ab/b (c) a/b (d) (b + a)/b (e) 1 :RCD 30. (d) (b + a)/b Ans. Note: b/b = 1 b/b + a/b = (b + a)/b Ans. :RA :Q k + y y + k 31. Divide ----- by ----- k - y y - k (a) 1 (b) 2 (c) -1 (d) 0 (e) -11 :RCC 31. (c) -1 Ans. Note: When dividing by a fraction you multiply by the reciprocal of the divisor. k + y y - k y - k ----- x ----- = ----- k - y y + k k - y -1(-y + k) = -------- (k - y) -1(k - y) = ------- (k - y) = -1 Ans. :RA :Q 1 - 1/y 32. Simplify: ------- a/y (a) (y - 1)/a (b) -1 (c) y-1 (d) (a - 1)/y (e) (1 - a)/y :RCA 32. (a) (y - 1)/a Ans. Note: To simplify a complex fraction multiply by the common denominator. 1 - 1/y y = ------- x - a/y y y - 1 = ----- Ans. a :RA :Q 2 3 33. (2k /y) = 6 5 8k 2k (a) --- (b) bk/y (c) --- 3 3 y y 2 5 (d) 6k /3y (e) 6k /y :RCA 6 8k 33. (a) --- Ans. 3 y Note: When a power is raised to another exponent, find the product of the exponents. a b ab Rule (x ) = x . :RA :Q 1 1 - - - k y 34. Simplify: ----- 4 (a) (y - k)/2ky (b) (y - k)/4ky (c) y - k (d) 2y - k (e) y - k :RCB 34. (b) (y - k)/4ky Ans. 1 1 = - - - k y (ky) ----- x ---- 4 (ky) y - k = ----- Ans. 4ky Note: To simplify a complex fraction, multiply by the common denominator. :RA :Q 2 35. If (k - y) = 49 and ky = 4 2 2 find k + y (a) 56 (b) 50 (c) 25 (d) 12 (e) 57 :RCE 35. (e) 57 Ans. 2 2 2 (k - y) = k - 2ky + y = 49 2 2 = k - 2(4) + y = 49 2 2 k - 8 + y = 49 2 2 k + y = 57 Ans. :ET :ET
