# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#2

Question Given , find the value of   when x=8, writing your answer in the form  where a is a rational number. Solution We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve  with respect to  is: Therefore; Rule for differentiation is of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#3

Question a.   Simplify Giving your answer in the form  , where a is an integer. b.    Hence, or otherwise, simplify Giving your answer in the form , where b and c is are integers and . Solution a.   We are given; Since ; Since ; b.     We are given; We have found in (a) that; Therefore; If we need a […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#1

Question Simplify a.   b.    giving your answer in the form a + √b , where a and b are integers. Solution a.   We are given; b.     We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#5

Question Solve the equation Give your answer in the form  where a and b are integers. Solution a.   We are given;

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#6

Question a)   Write  in the form , where c is a positive constant. A rectangle R has a length of  cm and an area of  cm2. b)  Calculate the width of R in cm. Express your answer in the form , where p and q are integers to be found. Solution a.     Since ; b.   […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#1

Question Fully simplify a.   b.   Solution a.   We are given; b.     We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is of the form  then multiply both numerator and denominator by . ü If the denominator is of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#2

Question Express in the form  , where k is an integer. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is of the form  then multiply both numerator and denominator by .  ü If the denominator is of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#1

Question Simplify giving your answer in the form  , where a and b are integers. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If the denominator is of the form  then multiply both numerator and denominator by .  […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | January | Q#3

Question      i.       Express   in the form  , where a and b are integers.      ii.        Express in the form , where c is an integer. Solution i.   We are given; Since ; Since ;    ii.   We are given; Since ;

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#3

Question Show that  can be written in the form , where a and b are integers. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is of the form  then multiply both numerator and denominator by .  […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#2

Question a.   Simplify giving your answer in the form  , where  is an integer.   b.   Simplify  giving your answer in the form  , where b and c are integers. Solution a.   We are given; Since ; Since ; b.   As demonstrated in (a) we can write the numerator as; If we need a rational number in the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#6

Question Given that  can be written in the form , a.   Write down the value of p and the value of q. Given that  , and that y=90 when x=4; b.   find  in terms of x, simplifying the coefficient of each term. Solution a.   We are given; b.   We are required to find y […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#9

Question The line L1 has equation 2y − 3x − k = 0, where k is a constant. Given that the point A (1, 4) lies on L1, find a.   the value of k, b.   the gradient of L1. The line L2 passes through A and is perpendicular to L1. c.   Find an equation of L2 giving […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#3

Question Simplfy Giving your answer in the form , where p and q are rational numbers. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is of the form  then multiply both numerator and denominator by .  […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | June | Q#10

Question a.   On the axes below sketch the graphs of                                     i.       y = x (4 – x)                                    ii.       y = x2 (7 – x) showing clearly the coordinates of the points where the curves cross the coordinate axes. b.   Show that the x-coordinates of the points of intersection of y = x (4 – x) and y = […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | June | Q#1

Question Write in the form , where k and x are integers. Solution We are given; Since ; Since;

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | January | Q#2

Question a.  Expand and simplify   b.  Express  in the form , where a and b are integers. Solution a.     We are given; Since ; b.     We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | June | Q#9

Question  , x>0 a)   Show that , where A and B are constants to be found. b)  Find c)   Evaluate . Solution a)     We are given; Utilizing algebraic identity; b)   We are given; We are required to find . We can write the given equation/function as; Gradient (slope) of the curve is the derivative of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | June | Q#1

Question Simply a. b. Solution a.     We are given; 63 b.     We are given; Since ;

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#3

Question Expand and simplify . Solution We are given; We have algebraic formula;