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King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 162 Recitation (R1, R2) Question 1: How many rational and irrational numbers are possible between 0 and 1? (a) 1 (b) Finite (c) 0 (d) Infinite (e) 2 Question 2: Á will contain how many elements from the original set A (a) 1 (b) Infinite (c) 0 (d) All elements in A (e) More elements than U Question 3: Given the sets U= {y|y is an even number with −8 < 𝑦 < 10} A= {−6, −4, −2, 0} B={y|y is an even prime number only} C= {y|y is a composite number < 9} Then 𝐴́ ∩ (𝐵 ∪ 𝐶)́ = (a) 𝐴́ (b) 𝐵 ∪ 𝐶 (c) 𝐴 (d) 𝑈 Question 4: Which one of the following statements is TRUE? (a) Every rational number has a multiplicative inverse (b) Every irrational number is not real number (c) Every even integer has an additive inverse (d) 𝜋 = 22 7 (e) The set { −1, 0 } is closed under addition (e) ∅ Question 5: Which one of the following statements is TRUE? (a) The set of irrational numbers is closed with respect to multiplication. (b) The set {−1, 0, 1} is closed with respect to multiplication. (c) If 𝑥 is any integer and 𝑦 is any irrational number, then 𝑥⁄𝑦 is irrational. (d) The distributive law states that 𝑎 ÷ (𝑏 + 𝑐) = (𝑎 ÷ 𝑏) + (𝑎 ÷ 𝑐) (e) Any irrational number has a terminating or repeating decimal expansion. Question 6: Given 1 3 2 2 1 3 3 4 ≤ 𝑥 < , the expression |𝑥 − | − | − 𝑥| can be written without the absolute value symbols as: (a) − 11 12 (b) 2𝑥 − 11 (c) 12 11 12 − 2𝑥 (d) − 5 (e) 12 5 12 Question 7: Which one of the following sets has the closure property with respect to multiplication? (a) {−1} (b) {−2, 1} (c) {1, 2} (d) {−1, 1} (e) {−1, 0} Question 8: The expression [−2 + to: (a) − (b) 4 7 3 (c) − (d) 79 97 49 12 (e) − 4 5 12 11 5 11 1 1 −32 + (− )] ÷ ( − ) − ( 5 3 4 4 ) + 2 simplifies King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 162 Recitation (R.3) Question 1: If 3x 4 12 x 2 6 x 15 R( x) Q( x) 2 2 x 1 x 1 (a) 𝑅(𝑥) = (b) 𝑄(𝑥) = , then (c) The leading coefficient of 𝑄(𝑥) = 2 1 7 Question 2: If the coefficient of 𝑥 3 in the product 𝑥 2 (𝑘𝑥 − ) (5𝑥 + ) is − , 𝑘 𝑘 3 then 𝑘 is equal to (a) −3 (b) − 30 4 (c) 3 (d) √ 6 7 Question 3: Which one of the following is a polynomial of degree 2? 2 (a) 𝑥 2 + + 𝑥 + 1 𝑥 (b) 𝑥 2 + 𝑥 3⁄2 + √2 (c) (3𝑥 + 2)3 + √2𝑥 2 − 27𝑥 3 (d) 𝑥 𝑥 3 −1 (e) 𝑥 2 + 𝑥 + 1 + √𝑥 Question 4: If 𝑋 = (𝑎 − 2𝑏)3 and 𝑌 = (2𝑎 + 𝑏)3 , then 𝑋 − 𝑌 = (e) −√ 6 7 King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 162 Recitation (R.4) Question 1: Factor each polynomial. (a) 6𝑝4 + 7𝑝2 − 3 (b) 𝑎3 − 𝑏 3 − 1 + 𝑎3 𝑏 3 (c) 9(𝑎 − 4)2 + 30(𝑎 − 4) + 25 (d) 5𝑥 6 − 40𝑦 3 Question 2: One of the factors of 4𝑦 4 − 13𝑦 2 + 9 is (a) 𝑦 2 + 1 (b) 4𝑦 2 + 9 (c) 𝑦 + 3 (d) 2𝑦 + 3 (e) 1 − 2𝑦 Question 3: The possible value(s) of 𝑘 that make(s) the trinomial 36𝑥 2 + 𝑘𝑥𝑦 + 49𝑦 2 a perfect square is (are) (a) 84 (b) -84 (c) ± 84 (d) ± 42 Question 4: One of the factors of 4𝑥 2 − 8𝑥𝑦 − 5𝑦 2 − 4𝑥 + 10𝑦 (a) 2𝑥 + 𝑦 − 2 (b) 4𝑥 − 4𝑦 − 2 (c) 2𝑥 + 𝑦 (d) 2𝑥 − 𝑦 + 2 (e) 5𝑥 − 2𝑦 (e) -42 King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 162 Recitation (R.5) Question 1: Simplify the following rational expressions (a) (𝑏) 2 + 4+𝑥 4 2−𝑥 + 16 + 𝑥 2 −16 5 𝑥 2 +2𝑥+4 6 4−𝑥 ÷ 𝑥 2 −4𝑥+4 𝑥 3 −8 Question 2: Simplify the following expressions 1 (a) 𝑥+𝑥+2 1 𝑥−𝑥+2 (𝑏) 1 + 1 1 1 + 1+𝑥 Question 3: The expression (𝑎) 𝑥+1 𝑥−2 (b) 2𝑥2 −3𝑥−2 𝑥2 −1 2 2𝑥 +5𝑥+2 𝑥2 +𝑥−2 𝑥−2 (c) 𝑥+1 simplifies to: 2𝑥+1 𝑥+2 (d) 𝑥+2 2𝑥+1 (e) Question 4: The least common denominator (LCD) of the expression 1 𝑥 3 −1 + 3 14(𝑥−1)3 − 5 24(𝑥 3 +𝑥 2 +𝑥) is (a) 2𝑥(𝑥 − 1)3 (𝑥 2 + 𝑥 + 1) (b) 168𝑥(𝑥 − 1)3 (𝑥 2 + 𝑥 + 1) (c) 2(𝑥 − 1)3 (𝑥 + 1)3 (d) 168(𝑥 − 1)3 (𝑥 + 1)3 (e) 2(𝑥 + 1)3 (𝑥 3 − 1) 𝑥+2 𝑥−1 King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 162 Recitation (R.6) −2 Question 1: The expression 5 9 (𝑎) − (b) −27 3 ( 8 ) 41 9 1 6 1 6 − (2) (−32 ) + 3(−2)0 simplifies to: (c) 31 9 (d) 23 9 (e) 49 9 Question 2: Simplify the expression below: 𝑥 1⁄2 𝑦 2 4 4𝑥 −2 𝑦 −4 ( 2𝑦1⁄4 ) ( 𝑦2 1⁄2 ) , where 𝑥 > 0 𝑎𝑛𝑑 𝑦 > 0 Question 3: Simplify the expression: 𝑥 −2 − 𝑦 −2 𝑥 −1 + 𝑦 −1 Question 4: Simplify the expression: 1 3 (7 − 3𝑥)1⁄2 + 𝑥(7 − 3𝑥)−2 2 7 − 3𝑥 Question 5: If 𝑥 = 1, 𝑦 = 4, and 𝑧 = 32 , then the value of the expression 𝑥 −2⁄3 𝑥 −2 1⁄6 ( 𝑦1⁄2 ) (𝑦−3) (a) −1 (b) −3 (c) 5 (d) −5 (e) 3 + 𝑧 2/5 is King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 162 Recitation (R.7) Question 1: Simplify the following expressions: (a) 𝟐 𝟑 √𝟖𝟏 +𝟑 𝟒 √𝟐𝟒 𝟏 −𝟑 3 √𝟑 21𝑥 3 (b) 5𝑥 √24𝑥 4 + 3 √−9𝑥 2 Question 2: If 𝑴 = 𝟒 −𝟒 𝟏 + 𝟐√𝟐𝟎 − √𝟒𝟓 and 𝑵 = √𝟐𝟒𝟑 √√𝟑 , then 𝑴 + 𝑵 = (a) −2 − √2 (b) 2 − √2 (c) 4 − √5 (d) 4 − 2√5 (e) −4 − √5 Question 4: If 𝑥 < −3 , then simplify and write the expression 𝟑 √(−𝟕)𝟐 − √49 + 42𝑥 + 9𝑥 2 + √(−7)𝟑 without absolute value symbols. Question 5: By rationalizing the denominator, the expression to: (a) √𝑥 − √𝑦 (b) 2√𝑥 (c) 2√𝑦 (d) 2(√𝑥 + √𝑦) (e) 2 2𝑥−2𝑦 √𝑥−√𝑦 simplifies