University of Nizwa Maths Questions Cycle 1 PDF

University of Nizwa Foundation Institute Fall Semester 2024-2025 Created by : SAOUD ALSAADI Mathematics Basic/Pure (MATH-BP)/Applied (MATH-BA)...

University of Nizwa Foundation Institute Fall Semester 2024-2025 Created by : SAOUD ALSAADI Mathematics Basic/Pure (MATH-BP)/Applied (MATH-BA) Questions Cycle 1 Name Id Section Date Q1: What is the set of all real numbers between -2 and 5, excluding -2 and 5, written in interval notation? (-2, 5] [-2, 5) (-2, 5) [-2, 5] Q2: Which interval notation represents the set of all real numbers less than or equal to 4? (−∞,4] (−∞,4) (4, ∞) [4, ∞) 3) What is the intersection of the intervals [2, 8] and [5, 10]? [2, 10] [5, 8] [2, 5] [8, 10] 4) Which of the following sets is equivalent to the set {x | x ∈ R, x ≤ 5}? (-∞, 5] (-∞, 5) (5, ∞) [5, ∞ 5) What is the union of the intervals (-∞, -3) and (1, ∞)? (-∞, 1) (-3, ∞) (-∞, -3) U (1, ∞) (-∞, ∞) 6) Which interval notation represents the set of all real numbers greater than 2? (2,∞)(2,∞) [-2, ∞) (2, -∞) (-∞, 2] 7) What is the solution set for the inequality x ≥ −5 in interval notation? (−5,∞) [−5,∞) (−∞,−5] (−∞,−5)  8) Which of the following correctly represents the set of all real numbers greater than or equal to -5 and less than 3 in interval notation? (-5,3) [-5, 3) (-5, 3] [-5, 3] 9) Which of the following is a rational number? √2 π 1/3 √5 10) Which of the following is an irrational number? 0.3333... √9 2/5 √7 11) Which set represents the natural numbers? {..., -2, -1, 0, 1, 2,...} {0, 1, 2, 3,...} {1, 2, 3, 4,...} {-1, -2, -3,...} 12) What is the simplified form of the expression (x+2)2 ? 𝑥2 + 4 𝑥 2 + 2𝑥 + 4 𝑥 2 + 4𝑥 + 2 𝑥 2 + 4𝑥 + 4 13) What is the simplified form of the expression (x−3)(x+3) ? x2−9 x2+6x+9 x2−6x+9 x2+9 14) What is the factored form of the expression 𝑥2 − 4𝑥 + 4 ? (x−2)(x+2) (x+2)2 (x−2)2 (x−4)(x+1) 15) Simplify the expression: (x+2)(x−2). x2−4 x2+4 x2−2x+4 x2+2x+4 16) Simplify the expression: x3 ∗ x5. x15 x8 x2 x3/5 17) Simplify the expression: (x2)4. x6 x8 x2 x1/2 18) What is the value of 3−2? 9 -9 1/9 -1/9 19) Simplify the expression: x0. 0 1 x undefined 20) Which of the following is an example of the difference of squares identity? x2+2x+1 x2−4 x3+8 x2+6x+9 21) Which of the following is equivalent to (x+y)2? x2+y2 x2+2xy+y2 x2−2xy+y2 x2+xy+y2 22) What is the simplified form of (a−b)2? a2−b2 a2+b2 a2−2ab+b2 a2+2ab+b2 23) What is the factored form of the expression: x2+5x+6? (x+1) (x+6) (x+2) (x+3) (x+1) (x−6) (x−2) (x+3) 24) What is the factored form of the expression x2−10x+25? (x+5) (x+5) (x+5) (x−5) (x−5) (x−5) (x+10) (x−2.5)  𝑥 2 −4 25) Simplify the expression: 𝑥+2 x-2 x+2 x2 - 2 x2 + 2 𝑥 2 −5𝑥+6 26) Simplify the expression: : 𝑥−2 x-3 x+3 x2 - 2 x2 + 2 27) What is the solution to the equation 2𝑥 + 5 = 11? 𝑥 = 3 𝑥 = 8 𝑥 = −3 𝑥 = −8 28) Solve for x: 3𝑥 − 7 = 8. 𝑥 = 5 𝑥 = −5 𝑥 = 15/3 𝑥 = 1 29) What is the solution to the equation 4𝑥 + 3 = 15? 𝑥 = 3 𝑥 = 12 𝑥 = −3 𝑥 = −12 30) What is the solution to the equation 5𝑥– 2 = 3𝑥 + 8? 𝑥 = 5 𝑥 = −5 𝑥 = 3 𝑥 = −3 2𝑥 𝑥−1 31) Solve for x in the equation: + = 5. 3 2 𝑥 = 6 𝑥 = 3 𝑥 = 12 𝑥 = 9 𝑥+2 3𝑥 32) Solve for x in the equation: =. 𝑥−1 2𝑥+1 𝑥 = −1 𝑥 = 1/5 𝑥 = 2/5 𝑥 = 1  2𝑥+1 𝑥−3 33) Solve for x in the equation: + = 2. 𝑥−2 𝑥+1 𝑥 = −1 𝑥 = 1 𝑥 = −2 𝑥 = 2 34) What are the solutions to the quadratic equation x2−4x−5=0? 𝑥 = −1, 𝑥 = 5 𝑥 = 1, 𝑥 = −5 𝑥 = −1, 𝑥 = −5 𝑥 = 1, 𝑥 = 5 35) A rectangular garden has a length that is twice its width. The area of the garden is 162 square meters. What is the length of the garden? 9 meters 12 meters 18 meters 24 meters 36) A rectangular garden has a length that is twice its width. The area of the garden is 162 square meters. What is the width of the garden? 9 meters 12 meters 18 meters 24 meters 37) A rectangular garden has a length that is 5 meters longer than its width. The perimeter of the garden is 34 meters. What is the width of the garden? 6 meters 7 meters 8 meters 9 meters 38) A rectangular garden has a length that is 3 meters shorter than twice its width. The perimeter of the garden is 26 meters. What is the length of the garden? 7 meters 8 meters 9 meters 10 meters 39) Solve the following inequality and write your answer in interval notation: 3𝑥 − 5 < 10 40) Solve the following inequality and write your answer in interval notation: 2(3𝑥 − 1) + 5 > 4𝑥 − 7 41) Solve the following inequality and write your answer in interval notation: 2(𝑥 + 3) + 5 ≥ 7 − 3𝑥 42) Solve the following inequality and write your answer in interval notation: 4 − 2𝑥 < 5𝑥 + 11 43) Solve the following quadratic inequality and express your solution using interval notation: 𝑥 2 − 5𝑥 + 6 ≤ 0 44) Solve the following quadratic inequality and express your solution using interval notation: 𝑥 2 + 3𝑥 − 10 > 0 45) Solve the following quadratic inequality and express your solution using interval notation: −𝑥 2 + 4𝑥 − 3 ≥ 0 46) The midpoint of a line segment with endpoints at (2, 5) and (8, -3) is: (5, 1) (5, 4) (6, 1) (6, 4) 47) The distance between the points (1, 2) and (4, 6) is: 4 5 6 7 48) Find the midpoint of a line segment with endpoints at (0, -4) and (6, 2). (3, -1) (3, 1) (4, -1) (4, 1 49) The midpoint of a line segment is (3, 1). One endpoint of the segment is (1, -2). What are the coordinates of the other endpoint? Show all your work. 50) A line segment has endpoints at (-4, 3) and (2, -5). Find the distance between the endpoints and the coordinates of the midpoint. Show all your steps. 51) A line segment has endpoints at (-2, 5) and (4, -1). Find the midpoint of the segment and the length of the segment. Show all your work. 52) What is the slope of the line that passes through the points (2, 5) and (6, 11)? 1 2 3 4 53) What is the slope of the line represented by the equation 2x + 3y = 6? 2/3 -2/3 3/2 -3/2 54) What is the slope of the line that passes through the points (-2, 4) and (5, -1)? 1 -1 5/7 -5/7 55) Find the equation of the line that passes through the points (2, 3) and (-1, 5). Write your answer in slope-intercept form (y=mx+b). −2 56) A line has a slope of and passes through the point (6, -1). Find 3 the equation of this line in standard form (Ax+By=C). 57) Convert 120 degrees to radians. 2𝜋 3 3𝜋 3 𝜋 3 𝜋 6 5𝜋 58) Convert radians to degrees. 6 150 degrees 120 degrees 180 degrees 210 degrees 𝑥 2 −9𝑥+20 59) simplify. 𝑥 2 −2𝑥 −15 (𝑥+𝑦)2 33(𝑥−𝑦)2 60) perform and simplify (𝑥−𝑦)2 ∗. 44(𝑥+𝑦)7 61) In a right triangle, the length of the hypotenuse is 10 units and the length of one leg is 6 units. Find the sine, cosine, and tangent of the angle opposite the 6-unit leg. 62) A ladder leans against a wall, making an angle of 70 degrees with the ground. If the ladder is 12 feet long, how high up the wall does the ladder reach? 63) A right triangle has legs of length 5 and 12. Find the length of the hypotenuse. 64) A right triangle has a hypotenuse of length 15 and one leg of length 9. Find the length of the other leg. 3 65) In a right triangle, the sine of an angle is. What is the cosine of that 5 angle? 12 66) In a right triangle, the tangent of an angle is. What is the sine of 5 that angle? ****************