T-Leng Tuition · mugcornersg.com
Total: 30 marksSuggested time: 45 minutes
Name: ______________________________Class: ____________ Date: ____________
Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
Section A
1Given that x+y=−5 and xy=4, find the value of x2+y2. Answer[2]
2(a)Factorise x2−5x−14. Answer (a)[1]
(b)Factorise 9x2−22x−15. Answer (b)[1]
3(a)Expand and simplify (x+5)(x+8). Answer (a)[1]
(b)Expand and simplify (x−3)(x+8). Answer (b)[1]
4(a)Given that 2x2−5x−25=(2x+5)(x−5), factorise 2(y+1)2−5(y+1)−25 completely. Answer (a)[1]
(b)Given that 2x2−7x+6=(2x−3)(x−2), factorise 2(3y−2)2−7(3y−2)+6 completely. Answer (b)[1]
5(a)Factorise 64x3−196x completely. Answer (a)[1]
(b)Factorise 2x2+5xy−3y2 completely. Answer (b)[2]
Section B
6(a)(i)Factorise x2−18x+81. Answer (a)(i)[1]
(a)(ii)Factorise x2−15x+56. Answer (a)(ii)[1]
(b)(i)Expand (x+2)2. Answer (b)(i)[1]
(b)(ii)Expand (3x+5)2. Answer (b)(ii)[1]
7(a)(i)Factorise 4ax−7bx+20ay−35by completely. Answer (a)(i)[1]
(a)(ii)Factorise 81p2−64q2 completely. Answer (a)(ii)[1]
(b)(i)Factorise x2+13x+42. Answer (b)(i)[1]
(b)(ii)Factorise 7x2−51x+14. Answer (b)(ii)[1]
(c)(i)Expand and simplify (x+4)(3x2−2x−4). Answer (c)(i)[1]
(c)(ii)Use (a+b)(a−b)=a2−b2 to evaluate 84×76 without using a calculator. Answer (c)(ii)[2]
8(a)(i)Factorise 5mx2−40mx+80m completely. Answer (a)(i)[1]
(a)(ii)Factorise 5kx2−50kx+125k completely. Answer (a)(ii)[1]
(b)(i)Factorise 7x2+32x+16. Answer (b)(i)[1]
(b)(ii)Factorise 6x2−17x+5. Answer (b)(ii)[1]
(c)(i)Expand and simplify (3x+6)(2x+2). Answer (c)(i)[1]
(c)(ii)Expand (x−8)2. Answer (c)(ii)[1]
(d)Given that x−y=2 and xy=24, find the value of x2+y2. Answer (d)[2]
END OF PAPER
Question 1
x2+y2=(x+y)2−2xy=(−5)2−2(4)=17 Question 2
(a)Answer: (x−7)(x+2)[1] (x−7)(x+2) (b)Answer: (9x+5)(x−3)[1] (9x+5)(x−3) Question 3
(a)Answer: x2+13x+40[1] x2+13x+40 (b)Answer: x2+5x−24[1] x2+5x−24 Question 4
(a)Answer: =(2y+7)(y−4)[1] 2(y+1)2−5(y+1)−25=[2(y+1)+5][(y+1)−5]=(2y+7)(y−4) (b)Answer: =(6y−7)(3y−4)[1] 2(3y−2)2−7(3y−2)+6=[2(3y−2)−3][(3y−2)−2]=(6y−7)(3y−4) Question 5
(a)Answer: =4x(4x+7)(4x−7)[1] 64x3−196x=4x(16x2−49)=4x(4x+7)(4x−7) (b)Answer: =(x+3y)(2x−y)[2] −1×6=−6 and −1+6=52x2+5xy−3y2=2x2−xy+6xy−3y2=x(2x−y)+3y(2x−y)=(x+3y)(2x−y) Question 6
(a)(i)Answer: (x−9)(x−9)[1] (x−9)(x−9) (a)(ii)Answer: (x−8)(x−7)[1] (x−8)(x−7) (b)(i)Answer: x2+4x+4[1] (b)(ii)Answer: 9x2+30x+25[1] 9x2+30x+25 Question 7
(a)(i)Answer: =(4a−7b)(x+5y)[1] 4ax−7bx+20ay−35by=x(4a−7b)+5y(4a−7b)=(4a−7b)(x+5y) (a)(ii)Answer: =(9p+8q)(9p−8q)[1] 81p2−64q2=(9p)2−(8q)2=(9p+8q)(9p−8q) (b)(i)Answer: (x+6)(x+7)[1] (x+6)(x+7) (b)(ii)Answer: (7x−2)(x−7)[1] (7x−2)(x−7) (c)(i)Answer: =3x3+10x2−12x−16[1] (x+4)(3x2−2x−4)=3x3−2x2−4x+12x2−8x−16=3x3+10x2−12x−16 (c)(ii)Answer: =6384[2] 84×76=(80+4)(80−4)=802−42=6400−16=6384 Question 8
(a)(i)Answer: =5m(x−4)2[1] 5mx2−40mx+80m=5m(x2−8x+16)=5m(x−4)2 (a)(ii)Answer: =5k(x−5)2[1] 5kx2−50kx+125k=5k(x2−10x+25)=5k(x−5)2 (b)(i)Answer: (7x+4)(x+4)[1] (7x+4)(x+4) (b)(ii)Answer: (3x−1)(2x−5)[1] (3x−1)(2x−5) (c)(i)Answer: 6x2+18x+12[1] 6x2+18x+12 (c)(ii)Answer: x2−16x+64[1] x2−16x+64 x2+y2=(x−y)2+2xy=(2)2+2(24)=52