26/03/2020 Algebra(Study by Topics Senior Class Test) 26/03/2020 0Comments by Gate Academy Please, fill out the information below to continue. Note: This is a sample test, and you can only take it for a limited period, after which you will be required to subscribe to a plan NAME EMAIL PHONE NUMBER 1. If y = (2/3)x + 1 andz = (2/3) y + 1, then the value of z when x = 66 is 31 21 31/2 61 2. Evaluate: 27.63² - 22.37² 263.0 27.7 189.0 241.3 3. Solve the equation: 6z² - 7z - 5 = 0 z = 5/3 or -1/2 z = 1/3 or 5/2 z = 1/2 or -5/2 z = -5/3 or 1/2 4. The 2nd and 9th terms of an A.P are 391 and 328 respectively. The 7th term is 373 355 346 400 5. Solve the equation:6(y - 4) + 3(y + 7) = 6 0 1 2/3 3/2 6. Solve the equation 3x + 10 = x² 5 or 2 -5 or 2 -5 or -2 5 or -2 7. The sum of the first five terms of the G.P 3, -6, 12, is 33 93 -33 31 8. Given that A varies inversely as B, and B varies directly as the square of C, and A = 1 when C = 3, find the value of A when C = 1/3 27 1/9 1/27 81 9. The length of a rectangle exceeds its width by 2cm. If the area of the rectangle is 80cm², the length of the rectangle is 10 cm 16 cm 8 cm 5 cm 10. If z ∝ 1/y² and z = 4 when y = 3, find the value of z when y = 2 9 3 1 18 11. A motorist drove a distance of 90km at constant speed for the first 40km and then drove 20km/hr faster for the rest of the journey. If the whole journey took him one hour, his average speed for the first 40km was 70 km/hr 40 km/hr 60 km/hr 80 km/hr 12. Given that the quadratic expression 3m² - 7m + K is a perfect square, the value of K is 49/4 49/24 49/12 49/36 13. Solve the equation:(log3a) – 6log3a + 9 = 0 9 18 81 27 14. For what range of values of y is y - 1 > 4(y + 2)? -3 < y < -2 2 < y < 3 y > -3 y < -3 15. The sum of the digits in a 2-digit number is 13. With the digits interchanged, the new number exceeds the original number by 27. The original number is 76 67 49 58 16. The 23rd term of the sequence 4, 7, 10, ... is 92 67 73 70 17. If 4x - 2 = 3x -5, the value of 7x is 7 -21 -3 -49 18. One of the roots of the equation: 6y² = 5 - 7y is -1/3 1/2 -1/2 5/3 19. Simplify : 8a - 3(2a - 3b) 2a + 9b 2a + 3b 2a - 9b 5a - 9b 20. If a and b are two positive numbers such that a > 2b, then the following are true except -a < -2b -b < 2a -a > -2b 21. If 2x - y = 6 and 2x + 4y = 1, the value of 4x + 3y is 1 5 3 7 22. Solve the inequality 12y² < y + 1 -1/4 < y < 1/3 1/4 < y < 1/3 - 1/4 < y < -1/3 -1/3 < y < 1/4 23. Given that a+b = 3/2 and a-b = 5/2, the value of 2b + a is 2/3 1 1/2 -2 24. What is the common factor to the binomial expressions 4x²-9y², 8x³+27y³ and (4x+6y)² ? 2x-3y 4x+6y 4x-6y 2x+3y 25. Five years ago, a father was four times as old as his son. In five years time the father will be twice as old as the son. If x and y are the present ages of the father and the son respectively, the equations relating x and y are: x - 4y = 15; y - 2x = 5 4y - x = 0; x- 2y = 0 4y - x = 25; x - 2y = 5 4y - x = 15; x - 2y = 5 1 out of 25 Time is Up! Time's up