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OXFORD New Syllabus Mathematics Book 2 7th Edition Teh Keng Seng, Loh Cheng Yee, Joseph Yeo, Ivy Chow - Solutions

Simplify each of the following. (a) ab 4c x 6ab (b) pr 24 4x-16 8 . h (h-1) (c) (d) x x+y 5x+5y h-2h+1 2/1+1
Simplify each of the following. (a) 3v2-9v 1--9 (b) p -7pq+12q x-3xv+2.xz-6yz (c) 5p -20pq ay-2x-3y+6yz
Simplify each of the following. 2m-4m (a) (b) m - 4 r-3xy-4y 3x-12.xy a-ac + ab-bc (c) 2ab+ac-2bc-c
Simplify each of the following. h+7hk 15p 4z (a) (b) (c) 5hk 10p -5p 42-16
(i) If a and ẞ are the solutions of the quadratic equation a * x ^ 2 + bx + c = 0 b show that a + B = - and aẞ =(ii) Hence, if p and q are the solutions of the equation 2x ^ 2 + 10x + 7 = 0 where p> q, find the value of pq.
Given that the difference between the solutions of the equation 2r ^ 2 - 6x - k = 0 is 5, find the value of k.
A golfer strikes a golf ball into the air from the ground. The height, / metres, of the ball can be modelled by h = 32t - 4t ^ 2 where is the time in seconds after it leaves the ground.(i) On a sheet of graph paper, using a scale of 2 cm to represent I unit on the 1-axis and I em to represent 5
The variables x and y are connected by the equation y = x ^ 2 + 3x - 4 Some values of.x and the corresponding values of y are given in the table. 4 -3 x -5 y P To 0 -4 26 -1 0 -6-6-4 (a) Find the value of p. 0 26 (b) On a sheet of graph paper, using a scale of 2 cm to represent I unit on the x-axis
In the figure, the curve y = (1 - x)(x + 5) cuts the x-axis at two points A and B, and the y-axis at the point C. Find the coordinates of A, B and C. A 0 B y= (1-x)(x+5) x
The height, y metres, of an object projected directly upwards from the ground can be modelled by y = 20r - 5t ^ 2 where is the time in seconds after it leaves the ground.(Find the height of the object 2 seconds after it leaves the ground.(ii) When will the object be 15 m above the ground?
If each student in a class sends a New Year greeting card to each of his classmates, a total of 870 cards will be sent. Find the number of students in the class.
The length and the breadth of a rectangle are (2x + 5) cm and (2-1) cm respectively. The area of the rectangle is three times the area of a square of sides (x + 1) cm.(i) Form an equation in x and show that it reduces to x ^ 2 + 2x - 8 = 0(ii) Solve the equation.² x ^ 2 + 2x - 8 = 0(iii) Find the
Ethan's father is years old while Ethan is.x years old. In 4.x years' time, Ethan's father will be twice as old as him.(i) Form an equation in .x and show that it reduces to x ^ 2 - 6x = 0(ii) Solve the equation x ^ 2 - 6x = 0(iii) Find the age of Ethan's father when Ethan was born.
The difference between two numbers is 3. If the square of the smaller number is equal to four times the larger number, find the two numbers.
(i) x = 3 is a solution of the equation 2v ^ 2 - 5x + k = 0 find the value of k.(ii) Hence, find the other solution of the equation.
(i) Solve the equation 2x ^ 3 - 11x - 21 = 0(ii) Hence, solve the equation 2 * (y + 2) ^ 2 - 11(y + 2) - 21 = 0
Solve each of the following equations.(a) 6k ^ 2 + 11k - 10 = 0(b) 3m(8 - 3m) = 16(c) (3n - 1) ^ 2 = 12n + 8(d) (5p + 1)(p + 4) = 2(7p + 5)
1. Solve each of the following equations.(a) - 6a(- 5 - 2a) = 0(b) (4b + 11)(3b - 7) = 0(c) 4c ^ 2 = 7c(d) 9 + 6d + d ^ 2 = 0(e) 49f ^ 2 - 140f + 100 = 0(f) 147 - 3h ^ 2 = 0
The value of an asset can he modelled by v = 2v ^ 2 - 4v + 7 where y is the value of the asset in thousands of dollars and is the time in years.(i) On a sheet of graph paper, using a scale of 1 em to represent 1 year on the x-axis and I em to represent $1000 on the y-axis, draw the graph of y = 2x
The variables and y are connected by the equation V = x ^ 2 - 2x Some values of x and the corresponding values of y are given in the table. x -2 -I 0 1 2 3. 4 y 8 3 0 -1 0 3 8 (a) On a sheet of graph paper, using a scale of 2 cm to represent I unit on each axis, draw the graph of y=x-2x for -2x=4.
The length of a side and the corresponding height of a triangle are (x+2) cm and (7-x) cm respectively.(i) Write down a formula for the area, A, of the triangle in terms of x, and show that 5 1(ii) On a sheet of graph paper, using a scale of I cm to represent I cm on the x-axis and I cm to
If a store prices each book at Sr, (64-8t) books will be sold.(i) The total amount of money earned from the sale of the books is $y. Express y in terms of x.(ii) On a sheet of graph paper, using a scale of 2 cm to represent $1 on the x-axis and I em to represent $10 on the y-axis, draw the graph of
The variables and y are connected by the equation y=10-x-. Some values of and the corresponding values of y are given in the table. -4-3 x y -2 4 -2 -I 0 2 3 8 10 10 8 + -2 (a) On a sheet of graph paper, using a scale of 2 cm to represent I unit on the x-axis and I cm to represent I unit on the
The figure shows the curve y = - t ^ 2 - x + 20(i) The curve cuts the x-axis at two points A and B, and the y-axis at the point C. Find the coordinates of A, B and C.(ii) The point D(3, h) lies on the curve. Find the value of h. A O D y=-xx+20 B
The variables.r and y are connected by the equation y = 2 - 3x - 2x ^ 2 Some values of v and the corresponding values of y are given in the table. -4-3 -3-2 -1 y -18 P 0 3 0 12 - 2 4-12 (a) Find the value of p and of q. (b) On a sheet of graph paper, using a scale of 2 cm to represent I unit on the
The variables x and y are connected by the equation y = x ^ 2 + 2x - 8 Some values of x and the corresponding values of y are given in the table. x 5 4 -4-3-2 -I I 2 7 a -5 -8 -9 b 0 7 37 (a) Find the value of a and of b. (b) On a sheet of graph paper, using a scale of 2 cm to represent I unit on
An object slides down from the top of a slope. Its distance travelled, s metres, can be modelled by x = 4r + r ^ 2 where is the time in seconds after it leaves the top of the slope.(a) On a sheet of graph paper, using a scale of 2 cm to represent I second on the 1-axis and 2 cm to represent 5 m on
A stone is thrown vertically upwards from the top of a cliff. Its height, h metres, above level ground, can be modelled by h = 28 + 42t - 12t ^ 2 where is the time in seconds after the stone has been thrown.(a) How high is the cliff?(b) On a sheet of graph paper, using a scale of 2 cm to represent
The height, I metres, of a ball projected directly upwards from the ground can be modelled by where is the time in seconds after it leaves the ground. h = 56t - 7r ^ 2(i) Find the height of the ball 3.5 seconds atter it leaves the ground.(ii) At what time will the ball strike the ground again?(iii)
1The height, y metres, of an object projected directly upwards from the ground can be modelled by 171-5, where is the time in seconds after it leaves the ground.(i) Find the height of the object 2.5 seconds after it leaves the ground.(ii) At what time will the object strike the ground again?(iii)
13. When (x + 1) is divided by 2, the quotient is 16 and the remainder is 3. Find the values of x.
1A hawk drops its prey from a certain height above the ground. The height, I metres, of the prey can he modelled by h = 4 + 11r - 3r ^ 2 where is the time in seconds after it is dropped by the hawk.(i) At what height above the ground does the hawk drop its prey?(ii) At what time will the prey fall
11. Amirah walks at an average speed of (x + 1) km/h tor a hours and cycles at an average speed of (2x+5) km/h for (x-1) hours. She covers a total distance of 90 km.(i) Form an equation in x and show that it reduces to 3x ^ 2 + 4x - 95 = 0(ii) Solve the equation 3x ^ 2 + 4x - 95 = 0(iii) Find the
The figure shows an ancient coin which was once used in China. The coin is in the shape of a circle of radius 3 em with a square of sides x cm removed from its centre. The area of each face of the coin is 7 cm².(1)Form an equation in v and show that it reduces to 2pi - x ^ 2 = 0(ii) Solve the
A piece of wire 44 cm long is cut into two parts. Each part is bent to form a square. Given that the total area of the two squares is 65 cm³, find the perimeter of each square.
The length of a side and the corresponding height of a triangle are (x + 3) cm and (2v-5) cm respectively. Given that the area of the triangle is 20 cm³, find the value of x.
The difference between two numbers is 9 and the product of the numbers is 162. Find the two numbers.
The difference between two positive numbers is 7 and the square of their sum is 289. Find the two numbers.
Two consecutive positive numbers are such that the sum of their squares is 113. Find the two numbers.
If four times a whole number is subtracted from three times the square of the number, the result 15 is obtained. Find the number.
The sum of a whole number and twice the square of the number is 10. Find the number.
A ball is thrown vertically upwards from the top of a school building. Its height. 4 metres, above the ground, can be modelled by h = 18 + 6H - 4r ^ 2 where is the time in seconds after it leaves the top of the building.(i) How tall is the school building?(ii) At what time will the hall strike the
1. The height, y metres, of a model rocket launched directly upwards from the ground can be modelled by y = 96t - 4r ^ 2 where is the time in seconds after it leaves the ground.(i) Find the height of the rocket 12 seconds after it leaves the ground.(ii) At what time will the rocket strike the
The height, y metres, of an object projected directly upwards from the ground can be modelled by y = 45t - 5t ^ 2 where is the time in seconds after it leaves the ground.(i) Calculate the height of the object 5 seconds after it leaves the ground.(ii) At what time will the object strike the ground
(i) If r = 5 is a solution of the equation X ^ 2 - qY + 10 = 0 find the value of q.(ii) Hence, find the other solution of the equation.
Solve the equation x - (2x - 3) ^ 2 = - 6(x ^ 2 + x - 2)
Solve the equation 9xy * 2y * 2 - 12xy + 4 = 0 expressing v in terms of x.
Solve each of the following equations. (a)+= =0 (b) 2-3.5-9.75y=0
(i) Solve the equation 6x ^ 2 - x - 15 = 0(ii) Hence, solve the equation 6 * (y - 3) ^ 2 - (y - 3) - 15 = 0
Solve each of the following equations.(a) k(2k + 5) = 3(b) 2m(m - 5) = 5m - 18(c) (n - 2)(n + 4) = 27(d) (p - 1)(p - 6) = 126(e) (2q - 3)(q - 4) = 18(1) 3r ^ 2 - 5(r + 1) = 7r + 58(g) (3s + 1)(s - 4) = - 5(s - 1)(h) (t + 2)(t - 3) = t + 2
Solve each of the following equations.(a) 7f + f deg = 60(b) 15 = 8h - 2h
Solve each of the following equations. (a) 121-=0) (c) -=0 (b) 128-26-0 4 d (d) () = 925
Solve the equation 7x ^ 3 + 21x ^ 2 = 0
Solve each of the following equations. (c) (a) +10x+21=0 +6-27=0 (e) 3 +49 + 60 = 0 (g) 3y+7x-6=0 (b) 161+63=0 (d)-5-24 0 (f) 6-29x+20=0 (h) 2-3-14=0
Solve each of the following equations. (a) k12k +36=0 -16=0 (C) (e) 4q-12g+9=0 (b) m 16m+64 = 0 (d) 25p+ 70p+ 49 = 0) (f) 42 100=0)
Solve each of the following equations. (a) a + 9 = 0) (c) 5c+25=() (e) 3-81-0 (b) b-7b=0 (d) 3d-4d=0) (f)-4-16h= 0)
Solve each of the following equations. (a) (k-4)(k-9)=0 (c) (n+4)(-11)=0 (e) (7-6)(4q-5)=() (g) (5x+3)(2-3)=() (b) (m-3)(m+5)=0 (d) (p+1)(p+2)=0 (f) (3r-5)(2r+1)=0 (h) (-21-5)(81-5)= 0)
Solve each of the following equations. (a) a(a-9)=() (c) 5c(c + 1) = 0) (e)-(3-7)=0 (b) (b+7)= 0) (d) 2d(d-6)=() (0)-h(2h+3)=0
Solve each of the following equations.(a) x(x+1)=6(b) 9y(1-y)=2
Solve each of the following equations.(a) x(x + 6) = - 5(b) 2y(8y + 3) = 1
(6) x = - 2 is a solution of the equation x ^ 2 + px + 8 = 0 find the value of p.(ii) Hence, find the other solution of the equation.
(i) Solve the equation 3x ^ 2 - 10x + 8 = 0(ii) Hence, solve the equation 3 * (y + 1) ^ z - 10(v + 1) + 8 = 0
Solve each of the following equations.(a) 3x ^ 2 - 15x = 0(c) x ^ 2 + 5x + 4 = 0(b) x ^ 2 + 8x + 16 = 0(d) 3x ^ 2 - 17x + 10 = 0
Solve each of the following equations.(a) 2v ^ 2 + 6v = 0(b) 9x ^ 2 - 4 = 0(c) x ^ 2 - 3v - 28 = 0(d) 2x ^ 7 + 5x - 12 = 0
Solve each of the following equations.(a) x(x + 2) = 0(b) 3x(x - 1) = 0(c) (x + 5)(x - 7) = 0(d) (3x + 2)(4x - 5) = 0
Solve each of the following equations.(a) x(x - 1) = 0(b) 2x(x + 1) = 0(c) (x - 2)(x + 3) = 0(d) (2x - 3)(3x + 5) = 0
Without using a calculator, evaluate each of the following.(a) 805(b) 903-97-
Factorise each of the following expressions completely.(a) 2f+5cd-12(b) 25l * r ^ 2 * k ^ 2 + 10hk + 1(c) 16 - 4 * (m + 2) ^ 2(d) 3prps+6yr-2qs
Expand and simplify each of the following expressions. (a) (a-7a+6)(3a-2)-a(2a-7) (b)
There are chickens and y rabbits on a farm. Given that the animals have a total of 70 heads and 196 legs, formulate a pair of simultaneous equations involving x and y. By solving the simultaneous equations, find the number of chickens and rabbits on the farm.
The coordinates of the point of intersection of the lines px + y = 3 x + 2x = q are (2,3). Find the value of p and of 4.
If y is inversely proportional to 2x ^ 2 + 5 and 7 when x = 2(6) find an equation connecting .r and y,() find the value of y when x = 8(iii) calculate the values of x when v = 5.2
The energy stored in a spring is directly proportional to the square of its extension, When a spring is stretched by dem, the energy stored in it is E joules (U). If the extension of the spring is decreased by 25%, find the percentage decrease in the energy stored.
The figure shows a trapezium ABCD where AB = 3x cm and DC = (5x + 6) cm. Given that the perpendicular distance between AB and DC, AH = (4x - 3) cm, show that the area of the trapezium can be expressed as (16x ^ 2 - 9) * c * m ^ 2 A 3.x cm B D H (4x-3) cm (5x+6) cm C
6. Factorise each of the following expressions completely.(a) 4f ^ 2 - 10f + 6(b) 1 - 12hk + 36h ^ 2 * k ^ 7(c) 5m ^ 2 * n - 15m * n ^ 2 - 25mn(d) 2px + 3qy - 2py - 3qx
Expand and simplify each of the following expressions. (a) (2a+5b)-(a+3b)(a-6b) (b) (4c+d4c-d)- (4c+dx4c-d)-(2-d)
Two iron atoms and three oxygen atoms contain 76 protons. One iron atom and one oxygen atom contain 34 protons. How many protons are there in each atom?
Solve the simultaneous equations 8x + 3y = 14 2r + y = 4
The resistance, R ohms (2) of a copper wire of fixed length is inversely proportional to the square of its diameter, d mm. Given that the resistance of a wire 2.5 mm in diameter is 20 2, find the diameter of a wire with a resistance of 31.25 2.
The variables x and y are connected by the equation v = k * sqrt(x - 3) where k is a constant. Some values of x and the corresponding values of y are given in the table. x 39 67 4 y P 2 2.75 Find the values of k, p and q.
(i) Expand and simplify the expression (+3.(ii) Hence, expand and simplify the expression |(2h + k) + 3| ^ 2
2 * (x - y) ^ 2 = 116 and v = 24 find the value of x ^ 2 + y ^ 2
Without using a calculator, evaluate each of the following.(a) 899(b) 659 ^ 2 - 341 ^ 2
Factorise the expression x ^ 2 + x ^ 2 - 4x - 4 completely.
Factorise each of the following expressions completely. (a)-14xy-212 (c) (2x-3y)(a+b)+(xy)(b+a) (e) + 3y+2x+6y (g) 4cx-6cy-8dx + 12dy (b) 9xy-36cy (d) 5(x-2)-(x-2) (f) 3x-2+3x-2 (h) 5xy-10x-12x+6
5. Factorise each of the following expressions completely. (1 (a) 1-121 (b) +6y+91- (c) 25-100xy + 100y (d) 36y-49(x+
Expand each of the following expressions. (a) (-x+51) (c) (b) (+)(y) (d) 3 (e) y5x (f) IV+ XV
Factorise each of the following expressions completely. (a) + 2xy-6.3 (c) 6-51-4 (b) 2+5x+3y (d) 32-80yz +4
Expand and simplify each of the following expressions. (a) 2p(3p-5q)-q(2q-3p) (c) (St-u)(+91)-(2-71) (b) -4s(3x+4r)-2r(2r-5s) (d) (2+3x)(-5x)-(3w+7x)(w-7x)
Expand each of the following expressions.(a) - 2a(a - 5h + 7)(b) (2c + 3d)(3c + 4d)(c) (k + 3h)(5h - 4k)(d) (2m + 1)(m ^ 2 + 3m - 1)
(i) Factorise the expression x ^ 3 + 3x - x ^ 2 - 3 completely.(ii) Hence, express (r ^ 2 - 3) ^ 2 - (2 - r ^ 2) ^ 2 + 3(r ^ 2 - 3) in the form (x ^ 2 + A * x ^ 2 + B)(x ^ 2 + C) where A, B and C are integers.
(i) Factorise the expression ppr completely.(ii) Hence, by substituting suitable values of p, q and r. find the value of 1/3 * 1.2 ^ 2 * 36 + 4/3 * 1.2 ^ 2 * 16
Factorise each of the following expressions completely.(a) 144p(v - 5x ^ 2) - 12q(10x ^ 2 - 2v)(b) 2(5x + 10v) * (2v - x) ^ 2 - 4(6v + 3x)(x - 2v)
Factorise each of the following expressions completely. (a) (b) 3ax+28by+4ay + 21bx 12cy+20c-15-9y (c) dy+fy-f-d (d) 3x+6xy-4-8y (e) 2xy-8x+12-3y (f) 5xy-25x+50x-10y (g) -5-5xy + xy (h) ky+hy-hx-ky
Factorise each of the following expressions completely. (a) (x+ya+b)-(+)(a+b). (b) (+2d)-(c + 2d)(3c-7d) (c) x(2h-k)+3y(k-2h) (d) 6x(4m-n)-2(n-4m)
Factorise each of the following expressions completely. (a) ax-5a+4x-20 (c)x+x+2y+2 (b) ax + bx+ay + by (d) -3x+2xy-6y
Factorise each of the following expressions completely. (a) batx-2y)+5(x-2y). (b) 2b(x+3y)-c(3y+x) (c) 3d(5v) - 4/51-1) (d) 5h(x+3y) + 10k(x + 3y)
Factorise each of the following expressions completely. (a) 45x-81xy (c) ay-y (b) 39xy-15 (d) -15xxy 10xx
Factorise each of the following expressions completely.(a) xy + 4y + 3y + 12(b) 3by + 4ax + 12ay + bx(c) x ^ 1 - x ^ 2 - 1 + x(d) 6xy - 4x - 2z + 3yz
Factorise each of the following expressions completely.(a) ax-hbx+2ax2by(b) bax + 12x + 9x + Sav(c) x²+xy-31-3(d) 6x1.5y+100-45

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