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New Syllabus Mathematics Book 1 7th Edition Teh Keng Seng, Loh Cheng Yee, Joseph Yeo, Ivy Chow - Solutions
(i) Find a formula for the sum S of any three consecutive even numbers.(ii) Hence, calculate the value of S when the smallest even number is 14.
If t = 3 v = 2 1/2 and u = 1 1/3 2. Ifr, find the value of a when
1. If (2x + y - 3z)/(y + 3x) = x/(2y) find the value of when x = 1 and y = 4.
If (3x - 5y)/(7x - 4y) = 3/4 find the value of x/y
If 4x + y = 3x + 5y find the value of (3x)/(16y)
By showing your working clearly, verify if is the solution of the equation x = 19/20 2x - 3/4 = 1/3 * x + 5/6
Solve each of the following equations. (a) 10x- 4.x 5.x +4 =7 (b) = 3 (c) 1-x+3=-1 (d) 1-y5-3(y-1) (e) 6(x-2)-12=2(x-7) 7 3 (1)-2-(2-y)=1
Solve each of the following equations. 12 11 (a) =2 (b) x+3 2x-1 32 (c) 2r-5 (e) (g) 1+5 -6 56 5 = 3 3+6 (d)= (f) 3y-5 (h) 73 3 9y-5
Solve each of the following equations. (a) 5x+1 =7 (b) 2x-3=1=3 3.r (e) (d) (5y+4)=(2x-1) 2y-1 y+3=0 (6) 2x+3+x-5=0 6
Solve each of the following equations. (a) -3(2-x)=6r (b) 5-3x=-6(x+2) (c) -3(9y+2)=2(-4y-7) (d)-3(4y-5)=-7(-5-2y) (e) 3(5-h)-2(-2)=-1
Solve each of the following equations. N/K (a) 45 " (b) 12 Film =
Solve each of the following equations. (a) x=12- w/. 2-1-2-3 5500 (b) x=x+ () 35 53 34 2y+ 12
Solve each of the following equations. (a) 2(x+3)=8 (c) 7(-2x+4)=-4.x (e) 2(2x-2.2) 4.6 (g) 3(2y+3)=4y+3 (b) 5(x-7)=-15 (d) 3(2-0.4x) 18 (f) 4(3y+4.1) = 7.6 (h) 3(y+1) 4y-21 (i) 3(v+2) = 2(y+4)) 5(5y-6)=4(-7) (k) 2(36-4)=5(b+6) (0) 3(2c+5)=4(c-3) (m) 9(2d+7)=11(d+14) (n) 5(7f-3)=28(-1)
Solve each of the following equations. (a) 2(x+3)=8 (c) 7(-2x+4)=-4x (e) 2(2x-2.2) 4.6 (g) 3(2y+3)=4y+3 (i) 3(v+2) = 2(y+4) (k) 2(36-4)=5(b+6) (b) 5(x-7)=-15 (d) 3(2-0.4x)= 18 (f) 4(3y+4.1)=7.6 (h) 3(v+1) 4y-21 ( 5(5y-6)=4y - 7) (0) 3(2c+5)=4(c-3) (m) 9(2+7)=11(d+14) (n) 5(7f-3)=28(-1)
Solve each of the following equations. (a) 3x-7=4-8r (c) 30+ 7y=-2y-6 (b) 4x-10=5x+7 (d) 2y-7-7y-27
Solve each of the following equations. (a) 4x=-28 (c) 3x-4=11 (e) 12-7x=5 (g) 4y-1.9 6.3 (i) 7y-2= (b)-24x=-144 (d) 9x+4=31 (f) 3-7y=-18 (h)-3y-7.8=-9.6 (i) 1-2y= 4
Solve each of the following equations. (a) x+8=15 (c) x-5=17 (e) y+0.4 1.6 (g) -2.7+a-6.4 (b)x+9=-5 (d) y-7=-3 (f) y-2.4-3.6
Solve each of the following equations. (a) 2x-3 =4 (b) y-3 y+4 32
Solve each of the following equations. 2/5 9 (a) =3 2x-5 (b) y+4 2y-3
Solve each of the following equations. (a)+9=5 (b) 2+2=1+31 (c)
Solve each of the following equations. (a) 3x-8=6 (b) 12 +31 = +5 3:+2 (c) 3 5
Solve each of the following equations. (a)x+0.7 2.7 (b) 2y-1.3-2.8
Solve each of the following equations. (b) 3x-2=4 (c) 7x+2=2x-13 (a)x+9=4 (d) 3(3y+4)=2(2y+1) (e) 2(y-1)+3(y-1)=4-2y
Solve each of the following equations. (a) 2r+3=9 (c) 2(2y-3)=5(y-1) (b) 5r-9 3r+3 (d) 2(3y+5)-7(x-4)=13
Subtract the sum ofand 5x + 7 from the sum of - 8x + 9 and 15-4x. - 7x + 4
Devi would like to buy a rectangular carpet for her living room. The carpet measures 4 m by 2 29 m. 10 10(i) Write down a calculation you could do mentally to estimate the area of the carpet.(ii) Given that each square metre of the carpet costs $89.75, write down a calculation you could do mentally
Kate has two boxes of buttons. After she transfers 15 buttons from Box A to Box B, the number of buttons in Box B becomes of the number of buttons in Box A. If there are 35 buttons in Box B originally, find the initial number of buttons in Box A.
(a) Without using a calculator, find the value of(b) Use a calculator to evaluate each of the following, giving your answer correct to 3 decimal places. 2113 5.
At midnight, the temperature erature of a town in the northern hemisphere is -6 °C. At 8 a.m., the temperature has risen by 8 °C. By 6 p.m., the temperature has dropped by 4 °C. Find(i) the temperature of the town at 6 p.m.,(ii) the overall change in the temperature from midnight to 6 p.m.,
Given that the HCF and the LCM of 1764 and a number p are 36 and 8820 respectively, find the value of p.
By using prime factorisation, find the value of each of the following. (a) -9216 (b) 2/8000
(a) Find the HCF of 54, 126 and 342.(b) Find the LCM of 16, 28, 44 and 68.
An apple costs a cents while a pear costs & cents more than an apple. Find the total cost of 10 apples and one dozen pears, giving your answer in dollars.
Given that 1. h = 2 c = 0 and d = - 3 evaluate each of the following expressions without the use of a calculator. (a) (b) a bd 3ac-d bc + d be a + b (c) a+b + d 2 (d) .P- -be-d'
Lixin takes 6.8 minutes to walk from her home to the shopping mall 628 m away. Write down a calculation you could do mentally to estimate the average speed for her journey in m/s.
Estimate each of the following without using a calculator. (a) 101 x 80.7 (b) 26 x 502 +49 (c) 65 x 63 + 17
The numbers-2, 1, 1, 2, 3, 4, 5 and 6 are written on eight separate cards, with one number on each card. List(i) the pairs of cards that have a sum of 4,(ii) the pairs of cards that have a product of 2,(iii) the groups of three cards that have a sum of 10.
Mr Lee has agreed to sponsor 105 bags of crisps and 126 packets of fruit juice for a class gathering. Each item is to be equally distributed among the students. Find(i) the greatest number of students that the refreshment can cater to,(ii) the number of bags of crisps each student will
The numbers 405 and 1960, written as the products of their prime factors, are 405 = 3 ^ 1 * 5 and 1960 = 2 ^ 1 * 5 * 7 ^ 2 Hence, find(i) the greatest whole number which is a factor of both 405 and 1960,(ii) the smallest whole number that is divisible by both 405 and 1960.
(a) Find the HCF of 42, 66 and 78(b) Find the LCM of 7, 13 and 14.
Suppose we wish to multiply a 2-digit number with another 2-digit number. If the digits in the tens place are the same and their ones digits add up to ten, there is a shortcut to it! For example, multiply the digit in the tens place with its next integer te. 7 x 8 = 16Try this method to find 58 x
If x, y and z are positive integers such that x
A teacher is showing a magic trick to his students. He places 12 coins on a table, 5 of which are heads up and 7 are tails up. He then places a blindfald over his eyes and shuffles the coins, keeping the faces up. Next, he separates the coins into two piles of 5 and 7 respectively. He flips over
An examination consists of 3 papers. The minimum total score required to pass the examination is (10p + 5q) marks. Michael scores (p - 3q + 13) marks and (3p + 5q - 4) marks in the first two papers.(i) Find Michael's total score in the first two papers.(ii) Given that Michael obtained the minimum
Shirley and Kate worked during their school holidays. Shirley was paid Sx per hour and Kate was paid Sy per hour. Their overtime rates were 1.5 times their hourly rates. Shirley worked 25 hours, of which 5 were overtime hours, while Kate worked 18 hours, of which 4 were overtime hours.(1) Find the
(a) Find the difference between 3y minutes and 25y seconds, giving your answer in seconds.(b) Find the sum of 50(322) minutes and 4(z + 1) hours, giving your answer in seconds.
Farhan cycles x km in 3 hours. If he maintains the same average speed, how far can he cycle in y minutes?
A collection of coins contains only 10-cent and 5-cent coins. There arex 5-cent coins in the collection. Find(a) the total value of the 5-cent coins,(b) the total value of the 10-cent coins if there are three times as many 10-cent as 5-cent coins,(c) the total value of the coins if there are seven
Factorise each of the following expressions completely.(a) 21pq+14q-28qr(b) 4x-8(y-2)
Express each of the following as a fraction in its simplest form. 5-x (a) +++* y (b) - 3x-2y 12 (c) (20- 4(2a-b) 2(3a+b) 3 5 h+f f+k 4h-k (d) +k+ 3 2 5 (e) 3q-4p-3q q-+p 5 6 04x-5)_5(r-2)7xv]
Expand and/or simplify each of the following expressions. (a) 3ab-5xy+4ab+2yx (b) 4(3p-5q)+6(2q-5p) (c) 2a+3a-(b-a)]+7(2b-a) (d) -213x-(4x-5y)-2(3x-4y)] (e) 4{h-3-6f-h)]} (f) 5(x+5y) (2x-[3x-3(x-2y) + y]}
Find the value ofy = - 4 and z = 2 3x-51-2.xyz when x=3,
Given that a = - 2 and b = 7 evaluate each of the following expressions.(a) 4a + 5b(b) 2a ^ 2(c) (2a) ^ 2(d) a(b - a)(e) b - a ^ 2(f) (b -a) ^ 2
Express each of the following as a fraction in its simplest form. (a) 24 5(p-q) 2q-P 2(p+q) 14 7 (b) 2a +b 3(a-3b) 4(a+2b) 2 5 (c) 31 3f-h) 7(h+k) 5(k-f) + 5(k- 6 (d) 43(y+4) 5(x+32) 4 8
Factorise each of the following expressions completely. (a) 5x+10x(b+c) (b) 3xy-6x(y-2 (c) 2x(7+ y)-14x(y+2) (d)-3a(2+b)+18a(b-1) (e)-4y(x-2)-12y(3-x)
Express each of the following as a fraction in its simplest form. 7(x-3) 5(2x-5) (a) 2 3x-4 3 3(x-1) (b) 5 2 3(-2) 4(2-3) (c) (-2)+(2- (d) 2(p-4q) 3(2p+ 3 2b 3(a-2b) (e) - 2b 36 5 2(x+3) 1 3x-4 (f) (g) +14-3 a-3 Sa-2 + (h) x+1x+3 x+35x-1 6 2(a-b) 2a+3b a+b (i) a+b 7 14 35(3x+4) +1 6
Expand and simplify each of the following expressions. (a) y-(9x-3y) (b) - {6(p+q)-3p-2(p- 3g)}}
Factorise each of the following expressions completely. (a) 12r-9 (c) 27b-36by (e) 4m-6my-18: (b)-25y-35 (d) 8ax+12a-40%
Express each of the following as a fraction in its simplest form. (a)+ (c) 2/1 + (e) 4x+1+3x-1 (g) a-2 a+7 (b) (d) 3x x+2 8 (6) 3y-1-2y- (h) 3p-2q 4p-5q 3
Expand and simplify each of the following expressions. (a) 5a-4b-3c-2a -120-: (b) (2x+2(x-3)] (c) 112p-(5+2p)| (d) 18x+10-6(1-4) 3
Simplify each of the following expressions. (a) I 10 (b) a-b+2u-b (c) + 3 7 4 9 28 (d) 25
Factorise each of the following expressions completely.(a) 6x - 12(b) 4ay-24a
Express each of the following as a fraction in its simplest form. (a) + 2x-3 x-42x-5 (b) 2x+ 4 3
Express each of the following as a fraction in its simplest form. (a) x-3+2x-5 (b) 2 2x-7 x-2 2x 22 3
The average monthly salary of m male employees and / female employees of a company is $2000. If the average monthly salary of the male employees is \$ (b + 200) , find the average monthly salary of the female employees.
Expand and simplify each of the following expressions.(a) - 2\{3a - 4|a - (2 + a)|\}(b) 5\{3c - |d - 2(c + d)|\}
Subtract(a)-6-3 from 2x-5,(b) 6x-y+5: from 10x-2y+(c) 8p+9q-5rs from-4p-49+15sr,(d) 8a-3b5c-4d from 10a-b-4c-8d. 6. Expand and simplify each of the following expressions. (a) 4u-3(2u-5v) (b)-2a-3(a-b) (c) 7m-2n-2(3-2) (d) 5(2x+4)-3(-6-x) (e)-4(a-3b)-5(a-3b) (f) 5(3p-2q)-2(3p+2q) (g)x+y-2(3x-4y+3)
Expand and simplify each of the following expressions. (a) 4u-3(2u-5v) (b)-2-3(a-by (c) 7m-2-2(3-2) (d) 5(2x+4)-3(-6-x) (e)-4(a-3b)-5(a-3b) (f) 5(3p-2q)-2(3p+2q) (g)x+y-2(3x-4y+3) (h) 3(p-2)-4(2p-3q-5) (i) 9(2a+4h-7c)-4(b-c)-7(-c-4h) (j) -415(2x+3y)-4(x+2y)]
Devi bought 7 skirts at Sx each, a skirts at $12 each, (2n + 1) skirts at $15 each and 4 skirts at $3x each. Find the total cost of the skirts she bought.
A pear costs ir cents. An orange costs y cents less than a pear. Find the cost of 4 pears and half a dozen of oranges.
Khairul is x years old. Khairul's uncle is four times as old as Khairul will be in 5 years. Find the present age of Khairul's uncle.
Expand and simplify each of the following expressions. (b) 7(p+ 10g)+2(6p+7q) (a) 5(a+2b)-3b (c) a+3b-(5a-4b) (d) r+3(2x-3y+2)+7:1
Expand each of the following expressions. (a)-(x+5) (c) 2(3y+7) (e) 8(3a-4b) (g) -4(d-6) (b)-(4-x) (d) 8(2y-5) (f) -3(c+6) (h) 2a(x-y)
Michael is 5 years older than Rui Feng and Vishal is thrice as old as Michael.If Rui Feng is p years old, find(i) Michael's present age,(ii) Vishal's present age,(iii) the sum of their ages in 6 years' time,(iv) the sum of their ages 3 years ago.
Expand and simplify each of the following expressions.(a) 6(4x + y) + 2(x - y)(b) x - [y - 3(2x - y)](c) 7x - 2|3(x - 2) - 2(x - 5)|
At a famous roti prata shop, for every two people who order egg prata, there are five people who order plain prata.(a) If a people order egg prata, how many people order plain prata?(b) If b people order plain prata, how many people order egg prata?(c) If there are a total of a people in the shop,
Huixian bought 8 books at $w each and 7 pens at $m each. She had S(3w + 5m) left. Find the amount of money she had at first.
Raj is 12m years old. His son was born when he was 9m years old.(i) Find Raj's age 5 years later.(ii) Find the sum of their ages in 5 years' time.
(i) Simplify the expression 3p + (- q) - 7r - (- 8p) - q + 2r(ii) Find the value of the expression when p = 2 r = - 5 q = - 1 1/2
Simplify each of the following expressions. (a) *** (c) + a (b) (d)
Simplify each of the following expressions.(a) 15x + (- 7y) + (- 18x) + 4y(b) - 3x + (- 5y) - (- 10y) - 7x(c) 9x - (2y) - 8r - (- 12y)(d) - 7x - (- 15y) - (- 2x) + (- 6v)
Given that a = 3 b = - 4 and c = - 2 evaluate each of the following expressions. (a) 3a-b 3a-C + 2c c-b (b) 2c-a 5a+4c 30+b (c) a+b+2c 5c b-c bc ac (d) + 3c-a-b4b 3c+4b a b
Write down an algebraic expression for each of the following statements.(a) Subtract the cube root of the product ofx and 3y from the square of the sum of a and b.(b) The total value of x 20-cent coins and y 5-dollar notes in cents.
Find the sum of each of the following expressions.(a) 2x+4y, -5y(b)-b-4a, 76-ба(c) 6d-4c, -7c+bxl(d) 3pq-6hk, -3qp+14kh
Simplify each of the following expressions.(a) 5x + 22 - 6x - 23(b) x + 3y + 6x + 4y(c) 6xy + 13x - 2yx - 5x(d) 6x - 20y + 7z - 8x + 25y - 11z
Given that a = 3 b = - 5 and c = 6 evaluate each of the following expressions. (a) a(3c-b) (c) - (d) (b) ab-ac b+c a+c b+c a + b
Given that.x x = 6 and y = - 4 evaluate each of the following expressions. 5.x (a) 4x-7y (c) 2-y (b) 35 +3 (d) 3x+
Write down an algebraic expression for each of the following statements.(a) Add 5y to the product of a and b.(b) Subtract 3 from the cube of J.(c) Multiply k by 64.(d) Divide 2w by 3.xy.(e) Subtract 4 times the positive square root of from thrice of ..(f) Twice the variable p divided by the product
Which of the following is likely to be the mass of an ordinary car?(a) 20 kg(b) 200 kg(c) 2000 kg(d) 20 000 kg
Without using a calculator, determine whether 987 x 123 is greater or less than 988 x 122.
Without using a calculator, decide which of the options is better value for money. Option A Option B 250 ml Hand Lotion $15.20 250 ml + 50 m/ Hand Lotion $17.45
Store A sells a 500 GB hard disk for $85.05 with a 20% discount while Store B sells the same hard disk for $76.05 with a 10% discount. Write down a calculation you could do mentally to help you decide which store to buy the hard disk from.
A battery-operated device needs to function for 28.2 hours. It functions for an average of 4.03 hours on one battery. Write down a calculation you could do mentally to estimate the number of batteries required.
The masses of 1 packet of sugar, 1 bottle of cooking oil and 1 box of baking powder are 109 g, 148 g and 84 g respectively. Write down a calculation you could do mentally to estimate the total mass of 3 packets of sugar, 2 bottles of cooking oil and 5 boxes of baking powder.
A toy costs 35 000 Indonesian rupiah (Rp). The conversion rate is Rp 1000 = S * 0.5 * 0.145 * 598 Without using a calculator, estimate the price of the toy in SS.
The mass of a chocolate truffle is 0.025 kg, correct to 2 significant figures. What is the smallest possible mass of the chocolate truffle?
(i) Express 4.793 and 39.51 correct to 2 significant figures.(ii) Use your answers in part (i) to estimate 4.793/39.51
Round off 6479.952 to the nearest(a) 100,(b) 1000,(c) tenth.
A handbag costs 26 700 Korea won (KRW). The conversion rate is S$1 KRW 876.333. Without using a calculator, estimate the price of the handbag in SS.
Shop A sells a dress for $79.50 with a 20% discount while Shop B sells the same dress for $69.50 with a 10% discount. Write down a calculation you could do mentally to help you decide which shop to buy the dress from.
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