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
1(a)Expand and simplify 3(3x+9). Answer (a)[1]
(b)Expand and simplify 3(4x+6)+2(2x−5). Answer (b)[1]
2(a)Write down an algebraic expression for n divided by 5, then increased by 1. Answer (a)[1]
(b)Mei Ling has $x. She buys 3 cups of bubble tea at $5 each. Write down an expression, in terms of x, for the amount of money, in dollars, she has left. Answer (b)[1]
3(a)Simplify 4x−5y−6x−4y. Answer (a)[1]
(b)Simplify −7x−y+8+x+8y−7. Answer (b)[1]
4(a)Factorise 2x2+7x completely. Answer (a)[2]
(b)Factorise 2x2+6xy−12x completely. Answer (b)[2]
Section B
5(a)(i)Expand and simplify 6(5x−4)+5(5x+4). Answer (a)(i)[1]
(a)(ii)Expand and simplify 4(2x−5y)+4(x+6y). Answer (a)(ii)[1]
(b)(i)Factorise 4x2+7x completely. Answer (b)(i)[2]
(b)(ii)Expand and simplify 3x+3(5x−3y+6). Then factorise your answer completely. Answer (b)(ii)[2]
6(a)Given that x=−6 and y=−6, find the value of 2xy−5. Answer (a)[2]
(b)Express 24x−1−3x−3 as a single fraction in its simplest form. Answer (b)[2]
(c)(i)Write down the coefficient of xy in the expression 2+3y−9y2−xy. Answer (c)(i)[1]
(c)(ii)Write down the coefficient of y in the expression 5+3y2−4xy−6x+5y. Answer (c)(ii)[1]
7(a)Given that x=−3 and y=−1, find the value of 2y3x−y. Answer (a)[2]
(b)(i)Write down an algebraic expression for subtract 5 from t. Answer (b)(i)[1]
(b)(ii)A taxi charges a flag-down fare of $5 and $2 for every kilometre travelled. Write down an expression, in terms of k, for the fare, in dollars, for a trip of k km. Answer (b)(ii)[1]
(c)(i)Factorise 15x+35 completely. Answer (c)(i)[2]
(c)(ii)Factorise 6xy+7y completely. Answer (c)(ii)[2]
END OF PAPER
Question 1
(a)Answer: 3(3x+9)=9x+27[1] 3(3x+9)=9x+27 (b)Answer: =16x+8[1] 3(4x+6)+2(2x−5)=12x+18+4x−10=16x+8 Question 2
(a)Answer: 5n+1[1] 5n5n+1 (b)Answer: x−15[1] (3×5= 15x−15 Question 3
(a)Answer: =−2x−9y[1] =4x−6x−5y−4y=−2x−9y (b)Answer: =−6x+7y+1[1] =−7x+x−y+8y+8−7=−6x+7y+1 Question 4
(a)Answer: x(2x+7)=2x2+7x ✓[2] HCF of 2 and 7= 1Every term has an x, so x is a common factor too.2x2+7x=x(2x+7)x(2x+7)=2x2+7x ✓ (b)Answer: 2x(x+3y−6)=2x2+6xy−12x ✓[2] HCF of 2,6 and 12= 2Every term has an x, so x is a common factor too.2x2+6xy−12x=2x(x+3y−6)2x(x+3y−6)=2x2+6xy−12x ✓ Question 5
(a)(i)Answer: =55x−4[1] 6(5x−4)+5(5x+4)=30x−24+25x+20=55x−4 (a)(ii)Answer: =12x+4y[1] 4(2x−5y)+4(x+6y)=8x−20y+4x+24y=12x+4y (b)(i)Answer: x(4x+7)=4x2+7x ✓[2] HCF of 4 and 7= 1Every term has an x, so x is a common factor too.4x2+7x=x(4x+7)x(4x+7)=4x2+7x ✓ (b)(ii)Answer: 9(2x−y+2)=18x−9y+18 ✓[2] 3x+3(5x−3y+6)=3x+15x−9y+18=18x−9y+18HCF= 9=9(2x−y+2)9(2x−y+2)=18x−9y+18 ✓ Question 6
2xy−5=2(−6)(−6)−5=72−5=67 (b)Answer: =610x+3[2] LCM of 2 and 3= 624x−1−3x−3=63(4x−1)−2(x−3)=612x−3−2x+6=610x+3 (c)(i)Answer: coefficient= −1[1] The term in xy is −xy.coefficient= −1 (c)(ii)Answer: coefficient= 5[1] The term in y is 5y.coefficient= 5 Question 7
2y3x−y=2(−1)3(−3)−(−1)=−2−8=4 (b)(i)Answer: t−5[1] “Subtract 5 from t” means start with t and take away 5.t−5 (b)(ii)Answer: 2k+5[1] (c)(i)Answer: 5(3x+7)=15x+35 ✓[2] HCF of 15 and 35= 5No letter is in every term.15x+35=5(3x+7)5(3x+7)=15x+35 ✓ (c)(ii)Answer: y(6x+7)=6xy+7y ✓[2] HCF of 6 and 7= 1Every term has a y, so y is a common factor too.6xy+7y=y(6x+7)y(6x+7)=6xy+7y ✓