1ST-PERIODICAL-EXAM-MATH9-2023-2024.docx

**FIRST PERIODICAL TEST IN MATHEMATICS 9** ***Directions:** Read and analyze each question carefully. Shade the letter of the correct answer on your answer sheet.* 1.) Which of the following terms refers to second degree polynomial equation that can be written in the form\ *ax^2^ + bx + c = 0*, wh...

**FIRST PERIODICAL TEST IN MATHEMATICS 9** ***Directions:** Read and analyze each question carefully. Shade the letter of the correct answer on your answer sheet.* 1.) Which of the following terms refers to second degree polynomial equation that can be written in the form\ *ax^2^ + bx + c = 0*, where *a, b,* and *c* are real numbers and *a* ≠ 0? A. Linear Equation B. Linear Inequality C. Quadratic Equation D. Quadratic Inequality 2.) All the given equations are quadratic **EXCEPT ONE**, which is it? A. [9*m*^2^ − 25 = 0]{.math.inline} B. [8*r* − 3*r* = 0]{.math.inline} C. [*x*^2^ − 4*x* + 3 = 0]{.math.inline} D. [(3*x*+5)(*x*−1) = 0]{.math.inline} 3.) Given the quadratic equation [2*x*^2^ + *x* − 1 = 0]{.math.inline}, which is the linear term? A. [2*x*^2^]{.math.inline} B. [*x*]{.math.inline} C. [ − 1]{.math.inline} D. {.math.inline} 4.) In the quadratic equation [3*x*^2^ + 7*x* = 4]{.math.inline}, which is the constant term? A. [ − 7]{.math.inline} B. [ − 4]{.math.inline} C. {.math.inline} D. {.math.inline} **For numbers 5-7.** If the quadratic equation [2*x*^2^ − 17 =  − 5*x* ]{.math.inline}is to be written in standard form, answer the following questions. 5.) What is the value of [*a*]{.math.inline}? A. [ − 17]{.math.inline} B. [ − 5]{.math.inline} C. {.math.inline} D. {.math.inline} 6.) What is the value of [*b*]{.math.inline}? A. [ − 17]{.math.inline} B. [ − 5]{.math.inline} C. {.math.inline} D. {.math.inline} 7.) What is the value of [*c*]{.math.inline}? A. [ − 17]{.math.inline} B. [ − 5]{.math.inline} C. {.math.inline} D. {.math.inline} 8.) When [7 -- 5*x* = 3*x*^2^]{.math.inline} was written in standard form, Rose and Marie got the following answers:\ Rose: [3*x*^2^+ 5*x* -- 7 = 0]{.math.inline} while Marie: [ − 3*x*^2^ -- 5*x* + 7 = 0]{.math.inline}. Who got the correct answer? A. Rose got the correct answer. C. No one got the correct answer.\ B. Marie got the correct answer. D. Both Rose and Marie got the correct answer. 9.) Which of the following quadratic equations can be solved easily by extracting square roots?\ \ A. [4*t*^2^ -- 9 = 0]{.math.inline} B. [*v*^2^ + 7*v* + 12 = 0]{.math.inline} C. [2*w*^2^ + 7*w* -- 3 = 0]{.math.inline} D. [3*x*^2^ + 2*x* -- 8 = 0]{.math.inline} 10.) How many real number solutions does the equation [*x*^2^= *k*]{.math.inline}, where [*k* \> 0]{.math.inline}, have? A. one B. two C. three D. no real solutions 11.) What are the roots of the quadratic equation [*x*^2^ -- 64 = 0]{.math.inline}? A. [ ± 2]{.math.inline} B. [ ± 4]{.math.inline} C. [ ± 6]{.math.inline} D. [ ± 8]{.math.inline} 12.) Which of the following are the roots of [*a*^2^ − 6 = 10]{.math.inline}? A. [ ± 2]{.math.inline} B. [ ± 4]{.math.inline} C. [ ± 6]{.math.inline} D. [ ± 8]{.math.inline} 13.) Given [*x*^2^ + 225 = 0]{.math.inline}, what are the values of [*x*]{.math.inline}? A. [ − 15]{.math.inline} B. [ + 15]{.math.inline} C. [ ± 15]{.math.inline} D. [imaginary]{.math.inline} 14.) How do you describe the signs of the square root of a positive real number in quadratic equation? A. negative only C. positive and negative\ B. negative and negative D. positive and positive 15.) Marie has a piece of wood whose area is 40 square centimeters. What is the length of the side of the\ largest square that can be formed using the wood? A. [5 *centimeters*]{.math.inline} B. [6 *centimeters*]{.math.inline} C. [8 *centimeters*]{.math.inline} D. [10 *centimeters*]{.math.inline} 16.) What property is used to describe the statement "if [*xy* = 0]{.math.inline}, then [*x* = 0]{.math.inline} or [*y* = 0]{.math.inline}" where both [*x*]{.math.inline} and [*y*]{.math.inline} are\ real numbers? A. Addition Property C. Square Root Property\ B. Multiplication Property D. Zero Product Property 17.) What is the factored form of [*x*^2^ − 81 = 0]{.math.inline}? A. [(*x* + 3)(*x* + 3)]{.math.inline} B. [(*x*+3)(*x* − 3)]{.math.inline} C. [(*x* − 9)(*x* − 9)]{.math.inline} D. [(*x* + 9)(*x* − 9)]{.math.inline} 18.) Which of the following quadratic equations **CANNOT BE** factored out? A. [*x*^2^ + 2*x* − 1 = 0]{.math.inline} B. [*x*^2^ − 4*x* + 4 = 0]{.math.inline} C. [*x*^2^ + 3*x* + 2 = 0]{.math.inline} D. [*x*^2^ + 3*x* − 18 = 0]{.math.inline} 19.) What are the roots of [*x*^2^ + 5*x* + 4 = 0]{.math.inline}? A. [4, 1]{.math.inline} B. [ − 4, 1]{.math.inline} C. [4,  − 1]{.math.inline} D. [ − 4,  − 1]{.math.inline} 20.) Which of the following quadratic equations has the roots of [ − 5]{.math.inline} and {.math.inline}? A. x^2^ -- 8x + 15 = 0 B. x^2^ + 8x + 15 = 0 C. x^2^ + 2x -- 15 = 0 D. x^2^ -- 2x -- 15 = 0 21.) What mathematical expression will make the equation [*x*^2^ + *x* − 110 = (*x*+11)(\_\_\_\_\_\_\_) ]{.math.inline}true? A. [*x* + 8]{.math.inline} B. [*x* − 10]{.math.inline} C. [*x* + 20]{.math.inline} D. [*x* − 100]{.math.inline} 22.) The dimensions of a rectangle[ ]{.math.inline}are [(3*x* − 1)]{.math.inline} meters by [(*x*  + 4)]{.math.inline} meters. Which of the following quadratic\ equations in standard form represents the area of the rectangle [(3*x* − 1)(*x* + 4)]{.math.inline}? A. [3*x*^2^ + 11*x* − 4 = 0]{.math.inline} B. [ − 3*x*^2^ − 11*x* + 4 = 0]{.math.inline} C. [3*x*^2^ − 11*x* + 4 = 0]{.math.inline} D. [ − 3*x*^2^ + 11*x* − 4 = 0]{.math.inline} 23.) Which of the following is a perfect square trinomial? A. [*x*^2^ − 5*x* + 25 = 0]{.math.inline} B. [*x*^2^ + 5*x* − 25 = 0]{.math.inline} C. [*x*^2^ + 10*x* + 25 = 0]{.math.inline} D. [*x*^2^ − 10*x* − 25 = 0]{.math.inline} 24.) What is the missing term that will make the expression [*s*^2^ + \_\_\_\_\_\_ + 49]{.math.inline} a perfect square trinomial? A. [4*s*]{.math.inline} B. [9*s*]{.math.inline} C. [14*s*]{.math.inline} D. [16*s*]{.math.inline} 25.) What must be added to x^2^ -- 4x + \_\_\_\_\_\_ to make it a perfect square trinomial? A. 2 B. 4 C. 8 D. 16 26.) Which of the following expressions is the square of binomial of [*x*^2^ − 20*x* + 100]{.math.inline}? A. [(*x* + 5)^2^]{.math.inline} B. [(*x* − 10)^2^]{.math.inline} C. [(*x* + 15)^2^]{.math.inline} D. [(*x* − 20)^2^]{.math.inline} 27.) In solving the equation [*x*^2^ -- 8*x* =  − 1]{.math.inline} by completing the square, what must be added to both sides of the\ equation to make the left side a perfect square trinomial? A. 1 B. 2 C. 4 D. 16 28.) Which of the following are the roots of the quadratic equation [*b*^2^− 6*b* + 5 = 0]{.math.inline} by completing the square? A. [1, 5]{.math.inline} B. [ − 1, 5]{.math.inline} C. [2, 5]{.math.inline} D. [ − 2, 5]{.math.inline} 29.) Using the completing the square, what are the roots of the quadratic equation [*x*^2^ − 8*x* − 9 = 0]{.math.inline}? A. [ − 1, 9]{.math.inline} B. [1,  − 9 ]{.math.inline} C. [ − 2, 7]{.math.inline} D. [2,  − 7]{.math.inline} 30.) What are the solutions of the quadratic equation [ax^2^ + *bx* + *c* = 0]{.math.inline} when it is solved by using quadratic\ formula? A. [\$x = \\frac{b \\pm \\sqrt{b\^{2} - 4ac}}{2a}\$]{.math.inline} B. [\$x = \\frac{b \\pm \\sqrt{b\^{2} + 4ac}}{2a}\$]{.math.inline} C. [\$x = \\frac{- b \\pm \\sqrt{b\^{2} - 4ac}}{2a}\$]{.math.inline} D. [\$x = \\frac{- b \\pm \\sqrt{b\^{2} + 4ac}}{2a}\$]{.math.inline} 31.) Which is the correct substitution of the values of [*a*, *b*,]{.math.inline} and [*c*]{.math.inline} in the quadratic formula of the equation\ [2*x*^2^ + 3*x* -- 27 = 0]{.math.inline}? A. [\$x = \\ \\frac{- 3\\ \\pm \\ \\sqrt{3\^{2} - 4(2)( - 27)}}{2(2)}\$]{.math.inline} C. [\$x = \\frac{3\\ \\pm \\ \\sqrt{({3)}\^{2} - 4(2)( - 27)}}{2(2)}\$]{.math.inline} B. [\$x = \\frac{- 3\\ \\pm \\ \\sqrt{{( - 3)}\^{2} - 4(2)(27)}}{2(2)}\$]{.math.inline} D. [\$x = \\frac{3\\ \\pm \\ \\sqrt{({- 3)}\^{2} - 4(2)(27)}}{2(2)}\$]{.math.inline} 32.) If the roots of 2x^2^ -- 3x -- 2 = 0 is solved by using the quadratic formula, what is the first thing to consider? A. Solve the values of [*x*]{.math.inline}.\ B. Identify the values of [*a*, *b*,]{.math.inline} and [*c*]{.math.inline}.\ C. Divide both sides by a common factor\ D. Substitute the values of [*a*, *b*,]{.math.inline} and [*c*]{.math.inline} in the quadratic formula. 33.) What are the roots of the quadratic equation [*x*^2^ + 5*x* − 14= 0]{.math.inline}? A. [2 *and* 7]{.math.inline} B. [ − 2 *and* − 7]{.math.inline} C. [2 *and* − 7]{.math.inline} D. [ − 2 *and* 7]{.math.inline} 34.) One of the roots of the equation [5*x*^2^ − 3*x* − 2= 0]{.math.inline} is {.math.inline}, what is the other root? A. [\$- \\frac{5}{2}\$]{.math.inline} B. [\$\\ - \\frac{2}{5}\$]{.math.inline} C. [\$\\frac{2}{5}\$]{.math.inline} D. [\$\\frac{5}{2}\$]{.math.inline} 35.) What is the positive real root of the equation [3*x*^2^ + 5*x* − 2= 0]{.math.inline}? A. [\$\\frac{1}{5}\$]{.math.inline} B. [\$\\text{\\ \\ }\\frac{1}{4}\$]{.math.inline} C. [\$\\frac{1}{3}\$]{.math.inline} D. [\$\\frac{1}{2}\$]{.math.inline} 36.) How many real roots does the quadratic equation [*x*^2^ + 5*x* + 7= 0]{.math.inline} have? A. {.math.inline} B. {.math.inline} C. {.math.inline} D. {.math.inline} 37.) In the quadratic formula [\$x\\ = \\ \\frac{- b \\pm \\sqrt{b\^{2} - 4ac}}{2a},\\ \$]{.math.inline}which of the following terms refers to expression [*b*^2^ − 4*ac*]{.math.inline}? A. determinant B. discriminant C. dividend D. domain 38.) Which expression shows the substitution in getting the discriminant of the quadratic equation [*x*^2^ − 121 = 0]{.math.inline}? A. [0^2^ − 4(1)(121)]{.math.inline} B. [0^2^ − 4(1)( − 121)]{.math.inline} C. [0^2^ − 4( − 1)(121)]{.math.inline} D. [0^2^ − 4( − 1)( − 121)]{.math.inline} 39.) Given the quadratic equation [*x*^2^ + 6*x* + 9 = 0]{.math.inline}, what is the value of discriminant? A. {.math.inline} B. {.math.inline} C. {.math.inline} D. {.math.inline} 40.) If the value of the discriminant is equal to 49, what is the nature of roots of the quadratic equation? A. no real roots C. real, rational but not equal\ B. real, rational, and equal D. real, irrational but not equal 41.) Given the equation [2*x*^2^ + 5*x* − 8 = 0]{.math.inline}, what is the nature of its roots? A. The roots are imaginary and unequal. C. The roots are real, rational but not equal.\ B. The roots are real, rational, and equal. D. The roots are real, irrational but not equal. 42.) The roots of the quadratic equation are imaginary. Which of the following statements is true about the\ discriminant of equation? A. The discriminant is negative. C. The discriminant is positive and a perfect square.\ B. The discriminant is equal to zero. D. The discriminant is positive and not perfect square. 43.) What is the value of [*k*]{.math.inline} in the quadratic equation [*x*^2^ − 10*x* + *k* = 0]{.math.inline} whose roots are equal, rational and\ real? A. [ − 25]{.math.inline} B. [ − 10]{.math.inline} C. {.math.inline} D. {.math.inline} 44.) Given the quadratic equation [ax^2^ + *bx* + *c* = 0]{.math.inline}, where [*a*, *b*]{.math.inline}, and [*c*]{.math.inline} are real numbers and [*a* ≠ 0]{.math.inline}, which of the following represents the sum and product of the roots? A. [\$Sum:\\ \\frac{- b}{a}\\ \\ \\ ;\\ \\ \\ Product:\\ \\frac{c}{a}\$]{.math.inline} C. [\$Sum:\\ \\frac{- c}{a}\\ \\ \\ ;\\ \\ \\ Product:\\ \\frac{b}{a}\$]{.math.inline}\ B. [\$Sum:\\ \\frac{b}{a}\\ \\ \\ ;\\ \\ \\ Product:\\ \\frac{- c}{a}\$]{.math.inline} D. [\$Sum:\\ \\frac{c}{a}\\ \\ \\ ;\\ \\ \\ Product:\\ \\frac{- b}{a}\$]{.math.inline}\ \ 45.) In the quadratic equation [*x*^2^ + 5*x* − 7 = 0]{.math.inline}, what is the sum of the roots? A. [ − 7]{.math.inline} B. [ − 5]{.math.inline} C. {.math.inline} D. {.math.inline} 46.) What is the product of the roots in the quadratic equation [*x*^2^ − 7*x* − 12 = 0]{.math.inline}? A. [ − 12]{.math.inline} B. [ − 7]{.math.inline} C. {.math.inline} D. {.math.inline} 47.) If the sum and product of the roots is 17 and 60, respectively, what are the roots of the quadratic equation? A. [15 *and* 2]{.math.inline} B. [12 *and* 5]{.math.inline} C. [11 *and* 6]{.math.inline} D. [10 *and* 7]{.math.inline} 48.) The sum of the roots is [ − 8]{.math.inline} and the product of the roots is {.math.inline}. What is the quadratic equation? A. [*x*^2^ + 8*x* + 12 = 0]{.math.inline} B. [*x*^2^ + 8*x* − 12 = 0]{.math.inline} C. [*x*^2^ − 8*x* + 12 = 0]{.math.inline} D. [*x*^2^ − 8*x* − 12 = 0]{.math.inline} 49.) The sum of the roots of a quadratic equation is 5. If one of the roots is 1, which of the following is the\ quadratic equation? A. [*x*^2^ + 5*x* + 4 = 0]{.math.inline} B. [*x*^2^ + 5*x* − 4 = 0]{.math.inline} C. [*x*^2^ − 5*x* + 4 = 0]{.math.inline} D. [*x*^2^ − 5*x* − 4 = 0]{.math.inline} 50.) The sum and product of two consecutive numbers are 31 and 240, respectively. What is the larger number? A. {.math.inline} B. {.math.inline} C. {.math.inline} D. {.math.inline} "The only way to **LEARN** mathematics is to **DO** mathematics." -- PAUL HALMOS\ Good luck & God Bless You! RNAMiñas\ SJDNomo\ DMMBaloncio