Algebra Quiz 29:52 Congratulations - you have completed Algebra Quiz. You scored 0 out of 30. Your performance has been rated as Need more practice! Your answers are highlighted below. Question 1 WRONG What is the remainder if x3−3x2+x+4 is divided to x−2? A 3 B 2 C 4 D 1 Question 1 Explanation: Using the remainder theorem, we get R=f(c) where x−c=x−2 c=2 f(2)=(2)3−3(2)2+2+4 f(2)=8−12+2+4 f(2)=2 R=2 Question 2 WRONG A train covers the distance d between two cities in h hours arriving 2 hours late. What speed would permit the train to arrive on schedule? A dh-2 B [d/h]-2 C h-2 D d/[h-2] Question 2 Explanation: d/h is the speed arriving 2 hrs late. Where d is the distance and h is time ( hrs.). To arrive in schedule, the train has to travel distance d in h – 2 hours. Rate = distance/time = d/[h-2] Question 3 WRONG Pipe A can fill a specific container in 8 minutes, while Pipe B can fill the same container in just 6 minutes. Pipe C on the other hand can empty the container in 4 minutes. If all pipes are open, how long does it take to fill the container? PIPE Rate Time Work A 18 x x8 B 16 x x6 C 14 x x4 A 24 minutes B 36 minutes C 12 minutes D 1 hour Question 3 Explanation: Take note that Work = Rate x Time Tabulating the work done by all 3 pipes: (done above) Adding the work done by all three pipes (Pipe C’s work done is negative since it is emptying the container) x8+x6−x4=1 Multiplying both sides by the LCD = 24 and combining like terms: (x8+x6−x4=1)24 3x+4x−6x=24 x=24 Question 4 WRONG Which of the following equations will produce an inconsistent system if pair with 6x+8=2y A y=3x+4 B None of the above C x+y=4 D 2y−6x=2 Question 4 Explanation: A pair of linear equation is said to be inconsistent if they have the same slopes by different y-intercepts. Manipulating the given equation to y=mx+b y=3x+4 with slope 3. Question 5 WRONG A number is 3 more than thrice another number. What are the numbers if their difference is 15? A 2 and 17 B 12 and 27 C 6 and 21 D 7 and 22 Question 5 Explanation: Let x = the 1st number 3x+3=the 2nd number The difference of the two numbers can be represented by: (3x+3)−x=15 By combining similar terms2x+3=15 egin{align} [latex]2x=15-3 2x=12 end{align}[/latex] Dividing both sides by two x=6 Substituting x to 3x+3 3(6)+3=21 Question 6 WRONG Teza deposited PHP 5,000.00 at 5% per annum interest. How much money will she have at the end of the year if the money is compounded semi-annually? A PHP 5,000.53 B PHP 5,153.13 C PHP 5,253.13 D PHP 5200.37 Question 6 Explanation: Solution: Using the formula: A=P(1+rn)nt Where: P is the principal r is the interest rate n is the number of times that the amount is compounded A is the amount after t years t is the number of years A=5000(1+0.052)(2)(1)A=5000(1.025)2 A=5000(1.050625) A=PHP5,253.13 Question 7 WRONG A given radioactive substance has a half-life of 60 years. What percent of the said substance will remain after 240 years? A 10.5% B 12.5% C 2.25% D 6.25% Question 7 Explanation: Solution: Using the formula N=Nkt Since the half life of the substance is 60 years the formula should be N=Nkt60 where k=0.5 N240=N(0.5)24060 N240=N(0.5)24060 N240=N(0.5)4 N240=0.0625N Question 8 WRONG Find the number if the sum one-fourth and three-eighth of the said is 15. A 25 B 20 C 24 D 22 Question 8 Explanation: Solution: Working equation x4+3x8=15 Getting the LCD 2x+3x8=15 Cross multiplying 2x+3x=120 5x=120 x=24 Question 9 WRONG Find x in the expression 62x+3=216x−2 A 6 B 9 C 7 D 8 Question 9 Explanation: Solution: 62x+3=216x−2 62x+3=(63)x−2 62x+3=63x−6 2x+3=3x−6x=9 Question 10 WRONG On what quadrant of the Cartesian plane is the ordered pair (6,-18) located? A II B I C IV D III Question 10 Explanation: Quadrant I contains (x,y), II contains (-x,y), III contains (-x,-y), and IV contains (x,-y) Question 11 WRONG A rectangular lot is 108 sqm. in area. If the length of the lot is three more than its width, find its dimensions. A 9 B 18 C 15 D 12 Question 11 Explanation: Let: ð x be the width ð y be the length Working equations xy=108 y−x=3Representing y in terms of x in the second equation y−x=3→y=x+3x(x+3)=108 x2+3x=108 x2+3x−108=0 Solving for the roots by factoring x2+3x−108=0 (x+12)(x−9)=0 x=−12 x=9 The width would be 9 m since the measure cannot be negative. Question 12 WRONG Look at the table below. Which variation formula represents the relationship between x and y? x 2 4 6 8 y 3 6 9 12 A y=xk where k=1.33 B y=kx where x=2╱3 C y=xk where x=3╱2 D y=kx where x=3╱2 Question 12 Explanation: Solution: Using the variation formula we get the value of k by substituting the value of x and y y=kx k=32=64=96.... Question 13 WRONG What is the equation of the line that passing through (1,1) and parallel to line y = 2x– 5? A y = 2x B y = -(1/2)x + 1 C y = 2x - 1 D y = 2x + 1 Question 13 Explanation: line parallel to: y = 2x – 5 Passing through pt. (1, 1) Since y = mx + b; m = 2 y = 2x + b; then substitute the coordinates of pt. (1, 1) 1 = 2(1) + b; b = 1 – 2 b = -1 y = 2x - 1 Question 14 WRONG Simplify the following expression : 1a+2√+3a√a+2√ A 1+3a√a+2 B (1+3a√)(a+2√)a+2 C 1+3a√a+2√ D 3a√a+2√ Question 14 Explanation: 1a+3√+3a√a+2√=1+3a√a+2√, then we multiply by a+2√a+2√, = (1+3a√)(a+2√)a+2 Question 15 WRONG Jack is now 14 years older than Jill. If in 10 years Jack will be twice as old as Jill, how many years old will Jack be in 5 years? A 21 B 23 C 9 D 19 Question 15 Explanation: let x = Jill’s age x + 14 = Jack’s age age 10 years from now: jill: x+10 jack: x+24, x + 24 = 2( x + 10 ), x + 24 = 2x + 20, 2x – x = 24 – 20, x = 4 , Jack’s present age: x + 14 = 4 + 14 = 18, 5 years from now: 18 + 5 = 23 Question 16 WRONG One number is 17 less than another. Their sum is 125. What is the smaller number? A 108 B 71 C 54 D 60 Question 16 Explanation: let x – smaller number, then x + 17 is the bigger number, the sum of the two numbers is 125, x + x + 17 = 125, 2x = 108, x = 54 --- smaller number, Question 17 WRONG Grace can finish cleaning their room in 45 minutes. When her sister Abby helps her, it takes them 18 minutes to clean the room completely. How many minutes would it take Abby to clean their room alone? A 20 B 35 C 30 D 25 Question 17 Explanation: Grace: Rate: 1/45. Time: 18, Work: 18/45, Abby: Rate: 1/x, Time: 18, Work: 18/x, 18/45 + 18/x = 1 ; multiply both sides by 45x, 18x + 18( 45 ) = 45x, 45x – 18x = 810, 27x = 810, x = 30 min Question 18 WRONG N=N15t represents the rate of population growth of a certain bacteria culture where t is time in hours. If you started with 3000 bacteria in a dish how many bacteria will you have after 2 hours. A 15000 B 675000 C 150000 D 67500 Question 18 Explanation: Solution: N2=(3000)(152) N2=(3000)(225) N2=675000 Question 19 WRONG The area of a certain square lot was increases by 176 sqm by increasing each of its side by 4 meters. Find the area of the original square. A 250 sqm B 200 sqm C 300 sqm D 400 sqm Question 19 Explanation: Let x be the original side of the square x2 - original area (x+4)2 - new area Working equation: (x+4)2=x2+176 x2+8x+16=x2+176 x2−x2+8x=176−16 8x=1608 x=20 2=400 Question 20 WRONG A nutritionist would like to produce a milk brand that has 2% butterfat. She is planning to add 50 liters of 1% butterfat milk to her regular milk solution that has 4% butterfat. How many liters of regular milk does she need to add to come up with her new milk brand? A 10000 Liters B 100 Liters C 10 Liters D 1000 Liters Question 20 Explanation: Let x=# of liters of the new milk brand. To come up with the working equation we must understand that the resulting butterfat for the mixture is 0.02(50+x)Therefore (0.04)50L+(0.01)x=10L+0.02x Multiplying both sides by 100 to remove the decimals we get 4(50L)+x=2(50+x) 200L+x=100+2xCombining similar terms 2x−x=200L−100L x=100L Question 21 WRONG Carol is driving from Manila to Tagaytay with an average speed of 55kph. After an hour, her boyfriend, Charles followed her driving at an average of 70 kph. How long does it take Charles to overtake Carol assuming that Charles is using the same route as Carol? Rate Time Distance Carol 55 kph x+1 55(x+1) Charles 70 kph x 70x A None of the above B 1.67 hours C 3.67 hours D 4.67 hours Question 21 Explanation: Tabulating the distance travelled by Carol and Charles where Distance = Rate x Time (done above) The distance traveled by both Carol and Charles should be equal the moment Charles overtakes Carol. Therefore: 55(x+1)=70xMultiplying and combining like terms 55x+55=70x 15x=5515 x=323hrs Question 22 WRONG Find the equation of a line that passes through point (3,-5) with a slope of -4. A y=−4x−2 B y=−4x C y=4x+2 D y=2x−1 Question 22 Explanation: Using the slope-intercept form of the line equation m=y−y1x−x1 Substituting yields −4=y+5x−3 Cross-multiplying yields −4x+3=y+5 Transposing y to the left and combining integers will produce y=−4x−2 Question 23 WRONG Which of the following best describes the relationship of the graph between 2x+3y=8and x+y=3? A Consistent B Dependent C Complicated D Inconsistent Question 23 Explanation: A system is consistent if the slopes of the two equations are different. It is Dependent of the slopes and y-intercepts are equal. It is Inconsistent of their slopes are equal but their y-intercepts are different. Manipulating the equations in the form y=mx+b (1) y=−23x+83 (2) y=−x+3 Therefore the equations are Consistent Question 24 WRONG Which of the following ordered pairs represents a function? A {(1,4),(2,5),(3,6),(4,7)} B {(0,3),(0,6),(2,10),(4,9)} C None of the above D {(−2,4),(−1,5),(0,8),(−1,9)} Question 24 Explanation: Only {(1,4),(2,5),(3,6),(4,7)} shows a relation wherein no distinct ordered pairs has the same first element which coincides with the definition of a function. Question 25 WRONG Subtract the sum of 3x2−4y2 and 2x2+5y2 from the difference of 5x2−10y2 and 2x2−y2. A −6x2−10y2 B −2x2−10y3 C −2x2−10y2 D −2x5−10y2 Question 25 Explanation: [(5x2−10y2)−(2x2−y2)]−[(3x2−4y2)+(2x2+5y2)] Grouping similar terms ð (5x2−10y2−2x2+y2)−(3x2−4y2+2x2+5x2) ð(5x2−10y2−2x2+y2)−(3x2−4y2+2x2+5y2) ð −2x2−10y2 Question 26 WRONG Using the table below find the value of 163.2 20.1=1.072 20.4=1.320 20.7=1.625 20.2=1.149 20.5=1.414 20.8=1.741 20.3=1.231 20.6=1.516 20.9=1.866 A 7131.136 B 7231.125 C 3456.123 D 1317.261 Question 26 Explanation: Solution: 163.2 163⋅160.2 (24)3⋅(24)0.2 212⋅20.8 642⋅(1.741) 4096⋅(1.741)7131.136 Question 27 WRONG Alin sa mga sumusunod na ekspresyon ang perfect square trinomial? A x2+10x+36 B 9x2−12x−4 C 4x2+10x+25 D 4x2−20x+25 Question 27 Explanation: perfect square trinomial: a2x2±2abx+b2=(ax±b)2:4x2−20x+25=(2x−5)2 Question 28 WRONG Find x in the equation 3x=9x−1 A 1 B 4 C 3 D 2 Question 28 Explanation: Solution: 3x=9x−1 3x=(3x−1)2 3x=32x−2 x=2x−2 x=2 Question 29 WRONG Ang eksponensyal na ekspresyong 32/n sa pormang radical ay _______. A n√3 B 9√n C 3n−−√ D n√9 Question 29 Explanation: 32/n=32−−√n=9√n Question 30 WRONG Which of the following statements is NOT true about the graph of y=x2−6x−16 A The graph is a parabola with vertex (3,-25). B The graph is a parabola opening upward. C The graph is a parabola intersecting the x-axis n points at (-2,0) and (8,0) D The graph is a parabola with axis of symmetry x=1 Question 30 Explanation: Solution: Manipulating the equation to the form y=a(x−h)2+k by completing the squares y=x2−6x−16 y=(x2−6x)−16 y=(x2−6x+9)−16−9 y=(x−3)2−25 ð a>0 there the graph is opening upwards ð Vertex is at (3,-25) ð Axis of symmetry is at x=3 and NOTx=1 ð The roots of the equation are 12 and 8 thus it intersects the x axis at points (-2,0) and (8,0)
Posted on: Wed, 10 Jul 2013 07:43:12 +0000
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