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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