(A/s) Mathematics Oct/Nov 2021 paper 2 variant 1
Question paper found on page 11 / 16 pages total, pdf
When a and b have these values, factorise f x − g x completely. [3] ....................................................................................................................
(A/s) Mathematics Oct/Nov 2021 paper 2 variant 3
Question paper found on page 11 / 16 pages total, pdf
When a and b have these values, factorise f x − g x completely. [3] ....................................................................................................................
(A/s) Mathematics Oct/Nov 2014 paper 2 variant 1
Question paper found on page 3 / 4 pages total, pdf
x + 2 and x + 3 are factors of 5 x 3 + ax 2 + b , find the values of the constants a and b . [4] (ii) When a and b have these values, factorise 5 x 3 + ax 2 + b completely, and hence solve the equation 5 3 y + 1 + a × 5 2 y + b = 0, giving any answers
(A/s) Mathematics Oct/Nov 2014 paper 2 variant 3
Question paper found on page 3 / 4 pages total, pdf
x + 2 and x + 3 are factors of 5 x 3 + ax 2 + b , find the values of the constants a and b . [4] (ii) When a and b have these values, factorise 5 x 3 + ax 2 + b completely, and hence solve the equation 5 3 y + 1 + a × 5 2 y + b = 0, giving any answers
(A/s) Mathematics May/June 2011 paper 2 variant 2
Question paper found on page 3 / 4 pages total, pdf
a and b are constants. It is given that ( x + 2 ) is a factor of p ( x ) and that, when p ( x ) is divided by ( x + 1 ) , the remainder is 24. (i) Find the values of a and b . [5] (ii) When a and b have these values, factorise p ( x ) completely. [3] 8
(A/s) Mathematics May/June 2011 paper 2 variant 3
Question paper found on page 3 / 4 pages total, pdf
a and b are constants. It is given that ( x + 2 ) is a factor of p ( x ) and that, when p ( x ) is divided by ( x + 1 ) , the remainder is 24. (i) Find the values of a and b . [5] (ii) When a and b have these values, factorise p ( x ) completely. [3] 8
(IGCSE) Mathematics Oct/Nov 2014 paper 4 variant 2
Question paper found on page 3 / 20 pages total, pdf
a) Solve the inequality. 7x – 5 > 3(2 – 5x) Answer(a) ................................................ [3] (b) (i) Factorise completely. pq – 2q – 8 + 4p Answer(b)(i) ..........................
(A/s) Mathematics May/June 2010 paper 2 variant 2
Question paper found on page 3 / 4 pages total, pdf
x − 3 ) the remainder is 30, and that when p ( x ) is divided by ( x + 1 ) the remainder is 18. (i) Find the values of a and b . [5] (ii) When a and b have these values, verify that ( x − 2 ) is a factor of p ( x ) and hence factorise p ( x ) completely. [4
(A/s) Mathematics May/June 2010 paper 2 variant 3
Question paper found on page 3 / 4 pages total, pdf
x − 3 ) the remainder is 30, and that when p ( x ) is divided by ( x + 1 ) the remainder is 18. (i) Find the values of a and b . [5] (ii) When a and b have these values, verify that ( x − 2 ) is a factor of p ( x ) and hence factorise p ( x ) completely. [4
(A/s) Mathematics Oct/Nov 2022 paper 2 variant 2
Question paper found on page 5 / 12 pages total, pdf
The polynomial p x is defined by p x = ax3 + 23x2 − ax − 8, where a is a constant. It is given that 2x + 1 is a factor of p x . (a) Find the value of a and hence factorise p x completely. [5] ........................................
(IGCSE) Mathematics - Additional Oct/Nov 2012 paper 1 variant 3
Question paper found on page 9 / 16 pages total, pdf
x 3 + 5x 2 + px + 8 ⬅ (x – 2)(ax 2 + bx + c), find the value of each of the integers a, b, c and p. [5] (ii) Using the values found in part (i), factorise completely 3x 3 + 5x 2 + px + 8. © UCLES 2012 0606/13/O/N/12 For Examiner’
(A/s) Mathematics Oct/Nov 2011 paper 2 variant 2
Question paper found on page 3 / 4 pages total, pdf
b , where a and b are constants, is denoted by p ( x ) . It is given that ( x + 2 ) is a factor of p ( x ) , and that when p ( x ) is divided by ( x + 1 ) the remainder is 12. (i) Find the values of a and b . [5] (ii) When a and b have these values
(A/s) Mathematics Oct/Nov 2009 paper 3 variant 2
Question paper found on page 2 / 4 pages total, pdf
x ) . The result of differentiating p ( x ) with respect to x is denoted by p ′ ( x ) . It is given that ( x + 2 ) is a factor of p ( x ) and of p ′ ( x ) . (i) Find the values of a and b . [5] (ii) When a and b have these values, factorise p ( x )
(A/s) Mathematics May/June 2013 paper 2 variant 1
Question paper found on page 2 / 4 pages total, pdf
x + 3 ) is a factor of p ( x ) , and that when p ( x ) is divided by ( x + 1 ) the remainder is 8. (i) Find the values of a and b . [5] (ii) When a and b have these values, factorise p ( x ) completely. [3] 5 The parametric equations of a curve are x = e 2 t
(IGCSE) Mathematics - Additional Oct/Nov 2016 paper 2 variant 3
Question paper found on page 5 / 16 pages total, pdf
x ) = x 3 + ax 2 + bx - 24 is divisible by x - 2 . When p ( x ) is divided by x - 1 the remainder is - 20 . (i) Form a pair of equations in a and b and solve them to find the value of a and of b. [4] (ii) Factorise p ( x ) completely and hence solve p (
(A/s) Mathematics May/June 2012 paper 2 variant 1
Question paper found on page 2 / 4 pages total, pdf
The variables x and y satisfy the equation y = A ( b x ) , where A and b are constants. The graph of ln y against x is a straight line passing through the points ( 0, 2.14 ) and ( 5, 4.49 ) , as shown in the diagram. Find the values of A and b , correct to 1 decimal place. [5] 3 The polynomial
(A/s) Mathematics May/June 2013 paper 2 variant 3
Question paper found on page 2 / 4 pages total, pdf
x + 3 ) is a factor of p ( x ) , and that when p ( x ) is divided by ( x + 1 ) the remainder is 8. (i) Find the values of a and b . [5] (ii) When a and b have these values, factorise p ( x ) completely. [3] 5 The parametric equations of a curve are x = e 2 t
(A/s) Mathematics May/June 2012 paper 2 variant 3
Question paper found on page 2 / 4 pages total, pdf
The variables x and y satisfy the equation y = A ( b x ) , where A and b are constants. The graph of ln y against x is a straight line passing through the points ( 0, 2.14 ) and ( 5, 4.49 ) , as shown in the diagram. Find the values of A and b , correct to 1 decimal place. [5] 3 The polynomial
(A/s) Mathematics May/June 2010 paper 3 variant 2
Question paper found on page 2 / 4 pages total, pdf
b , where a and b are constants, is denoted by p ( x ) . It is given that ( 2 x + 1 ) is a factor of p ( x ) and that when p ( x ) is divided by ( x + 2 ) the remainder is 9. (i) Find the values of a and b . [5] (ii) When a and b have these values,
(IGCSE) Mathematics - Additional For examination from 2013 paper 1
Specimen question paper found on page 5 / 16 pages total, pdf
ax 3 + bx 2 + 3x + 4. When f(x) is divided by x – 1, the remainder is 3. When f(x) is divided by 2x + 1, the remainder is 6. Find the value of a and of b. [5] 5 (i) Solve the equation 2t = 9 + 5 . t [3] 1 (ii) Hence, or otherwise, solve the equation
(IGCSE) Mathematics - Additional For examination from 2011 paper 1
Specimen question paper found on page 5 / 16 pages total, pdf
ax 3 + bx 2 + 3x + 4. When f(x) is divided by x – 1, the remainder is 3. When f(x) is divided by 2x + 1, the remainder is 6. Find the value of a and of b. [5] 5 (i) Solve the equation 2t = 9 + 5 . t [3] 1 (ii) Hence, or otherwise, solve the equation
(A/s) Mathematics Oct/Nov 2015 paper 2 variant 2
Question paper found on page 2 / 4 pages total, pdf
x = 6 x 3 + 11 x 2 + ax + a , where a is a constant. It is given that x + 2 is a factor of p x . (i) Use the factor theorem to show that a = − 4. [2] (ii) When a = − 4, (a) factorise p x completely, [3] (b) solve the equation 6 sec
(IGCSE) Mathematics - Additional Oct/Nov 2008 paper 1
Question paper found on page 3 / 8 pages total, pdf
Hence, or otherwise, solve the equation 2x 2 = 9 + 5x 2 . 7 [3] (i) Express 4x 2 – 12x + 3 in the form (ax + b) 2 + c, where a, b and c are constants and a > 0. [3] (ii) Hence, or otherwise, find the coordinates of the stationary point of the curve y = 4x 2 –
(A/s) Mathematics Oct/Nov 2015 paper 3 variant 1
Question paper found on page 2 / 4 pages total, pdf
a and b are constants, is denoted by p x . It is given that x + 1 is a factor of p x and that when p x is divided by 2 x + 1 the remainder is 1. (i) Find the values of a and b . [5] (ii) When a and b have these values, factorise p x completely. [3]
(A/s) Mathematics Oct/Nov 2015 paper 3 variant 2
Question paper found on page 2 / 4 pages total, pdf
a and b are constants, is denoted by p x . It is given that x + 1 is a factor of p x and that when p x is divided by 2 x + 1 the remainder is 1. (i) Find the values of a and b . [5] (ii) When a and b have these values, factorise p x completely. [3]
(A/s) Mathematics May/June 2013 paper 3 variant 2
Question paper found on page 2 / 4 pages total, pdf
x . (i) Find the value of a . [3] (ii) When a has this value, factorise p x completely. [3] 5 x y – a 3 a M The diagram shows the curve with equation x 3 + xy 2 + ay 2 − 3 ax 2 = 0, where a is a positive constant. The maximum point on the curve is M . Find the x
(A/s) Mathematics Oct/Nov 2009 paper 2 variant 1
Question paper found on page 2 / 4 pages total, pdf
a factor of p ( x ) . (i) Find the value of a . [2] (ii) When a has this value, factorise p ( x ) completely. [4] 4 (i) Show that the equation sin ( 60 ◦ − x )= 2 sin x can be written in the form tan x = k , where k is a constant. [4] (ii) Hence solve the
(A/s) Mathematics Oct/Nov 2013 paper 2 variant 2
Question paper found on page 2 / 4 pages total, pdf
The polynomial ax 3 + bx 2 − 25 x − 6, where a and b are constants, is denoted by p x . It is given that x − 3 and x + 2 are factors of p x . Find the values of a and b . [5] (ii) When a and b have these values, factorise p x completely. [2] 5 The
(IGCSE) Mathematics - Additional Oct/Nov 2010 paper 1 variant 1
Question paper found on page 3 / 8 pages total, pdf
Hence write down the number of solutions of the equation sin 2x – cos x = 0 for 0° x 180°. [1] 3 cos x cos x Show that 1 – sin x + 1 + sin x = 2 sec x. [4] 4 Factorise completely the expression 2x 3 – 11x 2 – 20x – 7. [5] 5 π π A curve has the equation
(IGCSE) Mathematics - Additional Oct/Nov 2010 paper 1 variant 2
Question paper found on page 3 / 8 pages total, pdf
Hence write down the number of solutions of the equation sin 2x – cos x = 0 for 0° x 180°. [1] 3 cos x cos x Show that 1 – sin x + 1 + sin x = 2 sec x. [4] 4 Factorise completely the expression 2x 3 – 11x 2 – 20x – 7. [5] 5 π π A curve has the equation
(A/s) Mathematics May/June 2023 paper 2 variant 1
Question paper found on page 5 / 12 pages total, pdf
The polynomial p x is defined by p x = 2x3 + 3x2 + kx − 30, where k is a constant. It is given that x − 3 is a factor of p x . (a) Find the value of k. [2] ....................................................
(IGCSE) Mathematics - Additional Feb/March 2016 paper 1 variant 2
Question paper found on page 9 / 16 pages total, pdf
The polynomial f ^ x h = ax 3 + 7 x 2 - 9 x + b is divisible by 2 x - 1 . The remainder when f ^ x h is divided by x - 2 is 5 times the remainder when f ^ x h is divided by x + 1 . (i) Show that a = 6 and find the value of b. (ii) Using the values from
(IGCSE) Mathematics May/June 2013 paper 1 variant 1
Question paper found on page 7 / 8 pages total, pdf
a) Which two of these have the same value? 2 5 5 –2 1 2 c m 2 2 2 c m 5 0.2 2 Answer(a) ........................ and ........................ [2] (b) Simplify. (i) a 6 × a 3 Answer(b)(i) .....
(A/s) Mathematics May/June 2005 paper 2
Question paper found on page 2 / 4 pages total, pdf
The polynomial x 3 − x 2 + ax + b is denoted by p ( x ) .Itisgiventhat ( x + 1 ) is a factor of p ( x ) and that when p ( x ) is divided by ( x − 2 ) the remainder is 12. (i) Find the values of a and b .[5] (ii) When a and b have these values, factorise p
(A/s) Mathematics Oct/Nov 2016 paper 2 variant 2
Question paper found on page 2 / 4 pages total, pdf
x = 4 x 3 + ax 2 + ax + 4, where a is a constant. (i) Use the factor theorem to show that x + 1 is a factor of p x for all values of a . [2] (ii) Given that the remainder is −42 when p x is divided by x − 2 , find the value of a . [2] (iii) When a
(A/s) Mathematics Oct/Nov 2008 paper 2
Question paper found on page 2 / 4 pages total, pdf
x ) . (i) Find the value of a .[2] (ii) When a hasthisvalue,factorisep ( x ) completely. [3] 3 x ln y (1.6, 0.9) (0, 1.3) O The variables x and y satisfy the equation y = A ( b − x ) ,where A and b are constants. The graph of ln y against x is a straight line passing
(A/s) Mathematics May/June 2015 paper 2 variant 2
Question paper found on page 2 / 4 pages total, pdf
Hence determine the number of integers n satisfying 20 − 5 < 2 n < 20 5 . 2 2 (i) Given that x + 2 is a factor of 4 x 3 + ax 2 − a + 1 x − 18, find the value of the constant a . [3] (ii) When a has this value, factorise 4 x 3 + ax 2 − a
(IGCSE) Mathematics Oct/Nov 2018 paper 3 variant 2
Question paper found on page 6 / 16 pages total, pdf
x 7 ................................................. [2] (b) Solve. 3x - 2 = 5x + 1 x = ................................................ [2] (c) Factorise completely. 3x
(A/s) Mathematics May/June 2015 paper 2 variant 3
Question paper found on page 2 / 4 pages total, pdf
Hence determine the number of integers n satisfying 20 − 5 < 2 n < 20 5 . 2 2 (i) Given that x + 2 is a factor of 4 x 3 + ax 2 − a + 1 x − 18, find the value of the constant a . [3] (ii) When a has this value, factorise 4 x 3 + ax 2 − a
(IGCSE) Mathematics May/June 2016 paper 4 variant 2
Question paper found on page 7 / 16 pages total, pdf
solve the equation f(x) + 2 = – 5x. x = ................... or x = ................... [4] (ii) f(x) + 2 = – 5x can be written as x 3 + ax 2 + bx – 1 = 0. Find the value of a and the value of b. a
(IGCSE) Mathematics - Additional Oct/Nov 2015 paper 2 variant 1
Question paper found on page 3 / 16 pages total, pdf
given that f ( x ) = 4 x 3 - 4 x 2 - 15 x + 18 . (i) Show that x + 2 is a factor of f ( x ) . [1] (ii) Hence factorise f ( x ) completely and solve the equation f ( x ) = 0 . [4] © UCLES 2015 0606/21/O/N/15 [Turn over
(IGCSE) Mathematics - Additional Oct/Nov 2015 paper 2 variant 2
Question paper found on page 3 / 16 pages total, pdf
given that f ( x ) = 4 x 3 - 4 x 2 - 15 x + 18 . (i) Show that x + 2 is a factor of f ( x ) . [1] (ii) Hence factorise f ( x ) completely and solve the equation f ( x ) = 0 . [4] © UCLES 2015 0606/22/O/N/15 [Turn over
(A/s) Mathematics May/June 2012 paper 2 variant 2
Question paper found on page 2 / 4 pages total, pdf
solve the equation 5 2 x + 5 x = 12, giving the value of x correct to 3 significant figures. [2] 3 (i) Find the quotient when the polynomial 8 x 3 − 4 x 2 − 18 x + 13 is divided by 4 x 2 + 4 x − 3, and show that the remainder is 4. [3] (ii) Hence, or otherwise, factorise the
(IGCSE) Mathematics - Additional May/June 2018 paper 2 variant 1
Question paper found on page 6 / 16 pages total, pdf
x + 4 is a factor of remainder is b. p ^ x h = 2 x 3 + 3 x 2 + ax - 12 . When p ^ x h is divided by x - 1 the (i) Show that a =- 23 and find the value of the constant b. [2] (ii) Factorise p ^ x h completely and hence state all the solutions of p ^
(A/s) Mathematics May/June 2006 paper 2
Question paper found on page 2 / 4 pages total, pdf
these stationary points. [7] 4 The cubic polynomial ax 3 + bx 2 − 3 x − 2, where a and b are constants, is denoted by p ( x ) .Itisgiven that ( x − 1 ) and ( x + 2 ) are factors of p ( x ) . (i) Find the values of a and b .[5] (ii) When a and b have these values
(IGCSE) Mathematics May/June 2014 paper 3 variant 1
Question paper found on page 14 / 16 pages total, pdf
a) Write down an expression for the total mass of c cricket balls, each weighing 160 grams, and f footballs, each weighing 400 grams. Answer(a) ...................................... grams [2] (b) Expand and simplify. 3(2x – 5y) – 4(x – 2y) Answer(b) ....
(A/s) Mathematics Feb/March 2022 paper 2 variant 2
Question paper found on page 9 / 12 pages total, pdf
Factorise p x + 6 completely and hence solve the equation for 0Å < 1 < 135Å. p cosec 21 + 6 = 0 [5] ............................................................................................
(IGCSE) Mathematics - Additional May/June 2013 paper 1 variant 2
Question paper found on page 9 / 20 pages total, pdf
x) = 6x 3 – 5x 2 + ax + b when divided by x – 1. (i) Show that b = 40 and find the value of a. (ii) Show that (iii) Hence solve f(x) = 0. © UCLES 2013 has a factor of x + 2 and leaves a remainder of 27 For Examiner’s Use [4] f(x) = (x
(IGCSE) Mathematics - Additional May/June 2018 paper 2 variant 3
Question paper found on page 6 / 16 pages total, pdf
x + 4 is a factor of remainder is b. p ^ x h = 2 x 3 + 3 x 2 + ax - 12 . When p ^ x h is divided by x - 1 the (i) Show that a =- 23 and find the value of the constant b. [2] (ii) Factorise p ^ x h completely and hence state all the solutions of p ^
(A/s) Mathematics Feb/March 2020 paper 2 variant 2
Question paper found on page 3 / 12 pages total, pdf
a) Find the quotient when 4x3 + 17x2 + 9x is divided by x2 + 5x + 6, and show that the remainder is 18. [3] ....................................................................................
(A/s) Mathematics Feb/March 2016 paper 3 variant 2
Question paper found on page 2 / 4 pages total, pdf
The polynomial 4 x 3 + ax + 2, where a is a constant, is denoted by p x . It is given that 2 x + 1 is a factor of p x . (i) Find the value of a . [2] (ii) When a has this value, (a) factorise p x , [2] (b) solve the inequality p x > 0
(A/s) Mathematics Oct/Nov 2016 paper 2 variant 3
Question paper found on page 2 / 4 pages total, pdf
x + 6 sin 3 x d x . [3] p x = ax 3 + 3 x 2 + 4 ax − 5, where a is a constant. It is given that 2 x − 1 is a factor of p x . (i) Use the factor theorem to find the value of a . [2] (ii) Factorise p x and hence show that the equation p x =
(IGCSE) Mathematics May/June 2016 paper 4 variant 3
Question paper found on page 3 / 16 pages total, pdf
a sale, the football club shop reduced the price of the football shirts to $23.80 . An error was made when working out this sale price. The price was reduced by 30% instead of 20%. Calculate the correct sale price for the football shirt. $ ...............................................
(A/s) Mathematics Oct/Nov 2016 paper 3 variant 3
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The polynomial 4 x 4 + ax 2 + 11 x + b , where a and b are constants, is denoted by p x . It is given that p x is divisible by x 2 − x + 2. (i) Find the values of a and b . [5] (ii) When a and b have these values, find the real roots of the equation p x = 0.
(IGCSE) Mathematics - Additional Feb/March 2019 paper 1 variant 2
Question paper found on page 6 / 16 pages total, pdf
x - 1 When p l ( x ) is divided by [2] is a factor of p (x). (ii) Find the value of a and of b. [4] (iii) Write p (x) in the form ( 2 x - 1 ) Q ( x ) , where Q (x) is a quadratic factor. [2] (iv) Hence factorise p (x) completely. [1]
(A/s) Mathematics Oct/Nov 2016 paper 2 variant 1
Question paper found on page 3 / 4 pages total, pdf
x + 3 is a factor of p x . It is also given that the remainder is 18 when p x is divided by x + 2 . (i) Find the values of a and b . [5] (ii) When a and b have these values, (a) show that the equation p x = 0 has exactly one real root, (b) solve the equation p sec y =
(A/s) Mathematics May/June 2012 paper 3 variant 1
Question paper found on page 2 / 4 pages total, pdf
x )= x 3 − 3 ax + 4 a , where a is a constant. (i) Given that ( x − 2 ) is a factor of p ( x ) , find the value of a . [2] (ii) When a has this value, (a) factorise p ( x ) completely, [3] (b) find all the roots of the equation p ( x 2 )=
(A/s) Mathematics May/June 2013 paper 3 variant 3
Question paper found on page 2 / 4 pages total, pdf
x − 1 the remainder is 1. (i) Find the values of a and b . [5] (ii) When a and b have these values, find the remainder when p x is divided by 2 x 2 − 1. [3] 6 x y O a The diagram shows the curves y = e 2 x − 3 and y = 2 ln x . When x = a the
(A/s) Mathematics May/June 2015 paper 2 variant 1
Question paper found on page 2 / 4 pages total, pdf
the values of a and b . [5] (ii) When a and b have these values, find the greatest possible value of g x − f x as x varies. [2] 5 (i) Given that Ó a 0 3e 1 2 x + 1 d x = 10, show that the positive constant a satisfies the equation a = 2 ln @ 16 − a
(A/s) Mathematics Oct/Nov 2011 paper 2 variant 3
Question paper found on page 2 / 4 pages total, pdf
The polynomial x 4 + ax 3 − x 2 + bx + 2, where a and b are constants, is denoted by p ( x ) . It is given that ( x − 1 ) and ( x + 2 ) are factors of p ( x ) . Find the values of a and b . [5] (ii) When a and b have these values, find the quotient when
(A/s) Mathematics May/June 2011 paper 3 variant 1
Question paper found on page 2 / 4 pages total, pdf
x ) in ascending powers of x up to and including the term in x 3 , simplifying the coefficients. [4] 2 Find d y d x in each of the following cases: (i) y = ln ( 1 + sin 2 x ) , [2] (ii) y = tan x x . [2] 3 Points A and B have coordinates (− 1, 2, 5 ) and (
(A/s) Mathematics Oct/Nov 2013 paper 2 variant 1
Question paper found on page 2 / 4 pages total, pdf
when p x is divided by x − 3 the remainder is 14, and that when p x is divided by x + 2 the remainder is 24. Find the values of a and b . [5] (ii) When a and b have these values, find the quotient when p x is divided by x 2 + 2 x − 8 and hence solve the equation
(A/s) Mathematics May/June 2016 paper 2 variant 1
Question paper found on page 2 / 4 pages total, pdf
x + 8e − x = 14, find the possible values of e x and hence solve the equation 3e x + 8e − x = 14 correct to 3 significant figures. [6] 4 The polynomial p x is defined by p x = 8 x 3 + 30 x 2 + 13 x − 25. (i) Find the quotient when p x is divided
(A/s) Mathematics May/June 2022 paper 3 variant 1
Question paper found on page 9 / 20 pages total, pdf
b) When a and b have these values, factorise p x completely. [3] .......................................................................................................................
(A/s) Mathematics Oct/Nov 2013 paper 2 variant 3
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when p x is divided by x − 3 the remainder is 14, and that when p x is divided by x + 2 the remainder is 24. Find the values of a and b . [5] (ii) When a and b have these values, find the quotient when p x is divided by x 2 + 2 x − 8 and hence solve the equation
(A/s) Mathematics Oct/Nov 2017 paper 2 variant 1
Question paper found on page 7 / 12 pages total, pdf
When a and b have these values, factorise p x completely. [3] ..........................................................................................................................
(A/s) Mathematics For examination from 2017 paper 3
Specimen question paper found on page 11 / 20 pages total, pdf
When a and b have these values, factorise p x completely. [3] ................................................... ................................................... ................
(A/s) Mathematics Oct/Nov 2017 paper 2 variant 3
Question paper found on page 7 / 12 pages total, pdf
When a and b have these values, factorise p x completely. [3] ..........................................................................................................................
(IGCSE) Mathematics May/June 2007 paper 3
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a) (ii) v = [2] (iii) Make m the subject of the formula. Answer(a) (iii) m = [2] (b) Factorise completely xy 2 – x 2 y . Answer(b) [2] (c) Solve the equation 3( x – 5) + 2(14 – 3 x ) = 7. Answer(c) x = [3] (d) Solve the simultaneous equations 4 x
(A/s) Mathematics Oct/Nov 2019 paper 2 variant 1
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The polynomial p x is defined by p x = ax3 + ax2 − 15x − 18, where a is a constant. It is given that x − 2 is a factor of p x . (i) Find the value of a. [2] ....................................................
(IGCSE) Mathematics May/June 2004 paper 2
Question paper found on page 9 / 12 pages total, pdf
x x and 12)(g xx . (a) Find the value of )9( gf . Answer(a) [1] (b) Find )( gf x , giving your answer in its simplest form. Answer(b) [2] (c) Solve the equation .1)(g 1 x Answer(c) [2] 20 (a) Factorise completely .312 22 yx Answer(a) [2] (b) (i)
(A/s) Mathematics Oct/Nov 2019 paper 2 variant 3
Question paper found on page 5 / 12 pages total, pdf
The polynomial p x is defined by p x = ax3 + ax2 − 15x − 18, where a is a constant. It is given that x − 2 is a factor of p x . (i) Find the value of a. [2] ....................................................
(A/s) Mathematics May/June 2011 paper 3 variant 3
Question paper found on page 2 / 4 pages total, pdf
a and b are constants, is denoted by p ( x ) . It is given that ( 2 x − 1 ) is a factor of p ( x ) and that when p ( x ) is divided by ( x − 2 ) the remainder is 12. (i) Find the values of a and b . [5] (ii) When a and b have these values, find the
(IGCSE) Mathematics - Additional Oct/Nov 2008 paper 2
Question paper found on page 3 / 8 pages total, pdf
the inverse matrix A –1 and hence solve the simultaneous equations 13x + 6y = 41, 7x + 4y = 24. [4] 2 Variables x and y are connected by the equation y = (2x – 9) 3 . Given that x is increasing at the rate of 4 units per second, find the rate of increase of y when x = 7. [4] 3 Find
(IGCSE) Mathematics May/June 2018 paper 2 variant 3
Question paper found on page 3 / 12 pages total, pdf
Solve. 1 - p = 4 3 p = ................................................ [2] 10 Factorise completely. 2 a + 4 b - ax - 2 bx .................................................
(IGCSE) Mathematics - Additional Oct/Nov 2016 paper 1 variant 2
Question paper found on page 12 / 16 pages total, pdf
The polynomial p(x) is ax 3 - 4 x 2 + bx + 18 . It is given that p(x) and p l ( x ) are both divisible by 2 x - 3 . (i) Show that a = 4 and find the value of b. [4] (ii) Using the values of a and b from part (i), factorise p(x) completely. [2] ©
(IGCSE) Mathematics - Additional Oct/Nov 2016 paper 1 variant 1
Question paper found on page 12 / 16 pages total, pdf
The polynomial p(x) is ax 3 - 4 x 2 + bx + 18 . It is given that p(x) and p l ( x ) are both divisible by 2 x - 3 . (i) Show that a = 4 and find the value of b. [4] (ii) Using the values of a and b from part (i), factorise p(x) completely. [2] ©
(IGCSE) Mathematics Oct/Nov 2017
Examiner report found on page 31 / 72 pages total, pdf
factorise the expression or that they did not see the request to factorise in the question. A very common error seen was the incorrect factorisation of (x + 4)(5x – 3). The answer of − Answer: 4, − 5 3 Question 15 The most common error was either calculating gf(x) as g(x) × f(x) or writing the first line of working as (5x –
(IGCSE) Mathematics May/June 2011 paper 3 variant 1
Question paper found on page 6 / 16 pages total, pdf
a) x = 3 m – k Find the value of (i) x when m = 2 and k = − 4, Answer(a) (i) [2] (ii) m when x = 19 and k = 5. Answer(a) (ii) [3] (b) Expand the brackets. g (7 f – g 2 ) Answer(b) [2] (c) Factorise completely. 18 h 2 –
(A/s) Mathematics May/June 2021 paper 2 variant 3
Mark scheme found on page 7 / 13 pages total, pdf
equation where signs of 5x and 2x are the sameM1 Solve 5 x = 5 − 2 x to obtain x = Obtain x = − 5 3 Substitute their values correctly May/June 2021 Guidance Allow AWRT 0.714 A1Allow AWRT –1.67 M1Substitution must be seen unless implied by a correct answer. Their values must come from consideration of 5 x = 5 − 2 x
(A/s) Mathematics May/June 2021 paper 2 variant 2
Mark scheme found on page 7 / 13 pages total, pdf
equation where signs of 5x and 2x are the sameM1 Solve 5 x = 5 − 2 x to obtain x = Obtain x = − 5 3 Substitute their values correctly May/June 2021 Guidance Allow AWRT 0.714 A1Allow AWRT –1.67 M1Substitution must be seen unless implied by a correct answer. Their values must come from consideration of 5 x = 5 − 2 x
(A/s) Mathematics May/June 2018 paper 2 variant 1
Question paper found on page 10 / 16 pages total, pdf
The cubic polynomial f x is defined by f x = x 3 + ax 2 + 14 x + a + 1, where a is a constant. It is given that x + 2 is a factor of f x . (i) Use the factor theorem to find the value of a and hence factorise f x completely. [5] ......................
(A/s) Mathematics Oct/Nov 2014 paper 3 variant 3
Question paper found on page 2 / 4 pages total, pdf
The polynomial 4 x 3 + ax 2 + bx − 2, where a and b are constants, is denoted by p x . It is given that x + 1 and x + 2 are factors of p x . (i) Find the values of a and b . [4] (ii) When a and b have these values, find the remainder when p x is
(IGCSE) Mathematics - Additional Oct/Nov 2009 paper 2
Question paper found on page 4 / 8 pages total, pdf
x for 0° x 360 °. [3] In order to solve the equation 1 + sin 2x = 2cos x another curve must be added to your diagram. (ii) Write down the equation of this curve and add this curve to your diagram. [3] (iii) State the number of values of x which satisfy the equation 1 + sin 2x = 2cos x for
(A/s) Mathematics Oct/Nov 2009 paper 2 variant 2
Question paper found on page 2 / 4 pages total, pdf
The polynomial ax 3 + bx 2 − 5 x + 2, where a and b are constants, is denoted by p ( x ) . It is given that ( x + 1 ) and ( x − 2 ) are factors of p ( x ) . (i) Find the values of a and b . [5] (ii) When a and b have these values, find the other linear
(IGCSE) Mathematics - Additional May/June 2019 paper 2 variant 2
Question paper found on page 4 / 16 pages total, pdf
x - 2 is a factor of ax 3 - 12 x 2 + 5 x + 6 , use the factor theorem to show that a = 4 . [2] (ii) Showing all your working, factorise 4 x 3 - 12 x 2 + 5 x + 6 and hence solve 4 x 3 - 12 x 2 + 5 x + 6 = 0 . [4] © UCLES
(A/s) Mathematics May/June 2019 paper 2 variant 3
Question paper found on page 3 / 12 pages total, pdf
Solve the equation 4 + 2x = 3 − 5x . [3] ..........................................................................................................................
(A/s) Mathematics Oct/Nov 2003 paper 2
Question paper found on page 2 / 4 pages total, pdf
x and y are related by the equation y = k ( a − x ) , where a and k are constants. Four pairs of values of x and y are measured experimentally. The result of plotting ln y against x is shown in the diagram. Use the diagram to estimate the values of a and k . [5] 3 The polynomial x 4 − 6 x 2 + x + a
(IGCSE) Mathematics May/June 2014 paper 1 variant 3
Question paper found on page 11 / 12 pages total, pdf
the brackets and simplify. 3(x – 2) – 4(2x – 3) Answer(c) ................................................ [2] (d) Solve the equation. 8x + 9 = 3(x + 8) Answer(d) x = ........................
(A/s) Mathematics May/June 2019 paper 2 variant 2
Question paper found on page 3 / 12 pages total, pdf
Solve the equation 4 + 2x = 3 − 5x . [3] ..........................................................................................................................
(A/s) Mathematics Oct/Nov 2004 paper 3
Question paper found on page 2 / 4 pages total, pdf
x 2 , simplifying the coefficients. [4] 2 Solve the equation ln ( 1 + x )= 1 + ln x , giving your answer correct to 2 significant figures. [4] 3 The polynomial 2 x 3 + ax 2 − 4 is denoted by p ( x ) .Itisgiventhat ( x − 2 ) isafactorofp ( x ) . (i) Find the value of a .[2] When a
(IGCSE) Mathematics May/June 2011 paper 4 variant 2
Question paper found on page 8 / 16 pages total, pdf
a) Solve 9 I 3 n + 6 Y 21 for integer values of n . Answer(a) [3] (b) Factorise completely. (i) 2 x 2 + 10 xy Answer(b) (i) [2] (ii) 3 a 2 O 12 b 2 Answer(b) (ii) [3] (c) NOT TO SCALE ( x + 17) cm x cm The area of this triangle
(IGCSE) Mathematics Oct/Nov 2010 paper 3 variant 1
Question paper found on page 10 / 16 pages total, pdf
2010 0580/31/O/N/10 For Examiner's Use 7 (a) Solve the equation. 4 x + 3 = 2 + 6 x Answer(a) x = [2] (b) Simplify. 7(3 x – 4 y ) – 3(5 x + 2 y ) Answer(b) [2] (c) Factorise completely. 6 g 2 – 3 g 3 Answer(c) [2]
(A/s) Mathematics Oct/Nov 2015 paper 2 variant 3
Question paper found on page 2 / 4 pages total, pdf
the equation of the tangent to the curve when t = 0, giving the answer in the form ax + by + c = 0 where a , b and c are integers. [6] 4 (i) Find the quotient when 3 x 3 + 5 x 2 − 2 x − 1 is divided by x − 2 , and show that the remainder is 39. [4] (ii)
(A/s) Mathematics Oct/Nov 2010 paper 2 variant 1
Question paper found on page 2 / 4 pages total, pdf
a and b are constants, is denoted by p ( x ) . It is given that ( x − 1 ) is a factor of p ( x ) , and that when p ( x ) is divided by ( x − 2 ) the remainder is 10. (i) Find the values of a and b . [5] (ii) When a and b have these values, solve the
(IGCSE) Mathematics - Additional Oct/Nov 2010 paper 1 variant 3
Question paper found on page 3 / 8 pages total, pdf
The remainder when the expression x 3 + kx 2 – 5x – 3 is divided by x – 2 is 5 times the remainder when the expression is divided by x + 1. Find the value of k. [4] 5 Solve the simultaneous equations log 3 a = 2 log 3 b, log 3 (2a – b) = 1. [5] 6 Solve the equation 3x 3 + 7
(A/s) Mathematics Oct/Nov 2010 paper 2 variant 2
Question paper found on page 2 / 4 pages total, pdf
a and b are constants, is denoted by p ( x ) . It is given that ( x − 1 ) is a factor of p ( x ) , and that when p ( x ) is divided by ( x − 2 ) the remainder is 10. (i) Find the values of a and b . [5] (ii) When a and b have these values, solve the