Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#11

Question Given that f(x) = 2×2 + 8x + 3 a.   find the value of the discriminant of f(x). b.   Express f(x) in the form p(x + q)2 + r where p, q and r are integers to be found. The line y = 4x + c, where c is a constant, is a tangent […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#10

Question A curve with equation y=f(x) passes through the point (4,25). Given that a.   find f(x) simplifying each term. b.   Find an equation of the normal to the curve at the point (4, 25). Give your answer in the form ax + by + c = 0, where a, b and c are integers to […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#9

Question The line , shown in figure has equation 2x+3y = 26. The line  passes through the origin O and is perpendicular to . a.   Find an equation for the line . The line  intersects the line  at the point C. Line  crosses the y-axis at the point B as shown in Figure. b.   Find the area of triangle OBC. […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#8

Question In the year 2000 a shop sold 150 computers. Each year the shop sold 10 more computers than the  year before, so that the shop sold 160 computers in 2001, 170 computers in 2002, and so on  forming an arithmetic sequence. a.   Show that the shop sold 220 computers in 2007. b.   Calculate the total number of […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#7

Question Differentiate with respect to x, giving each answer in its simplest form. a)   b)  Solution a.     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; We have algebraic formula; Rule for differentiation is of […]

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 (C1-6663/01) | Year 2014 | June | Q#5

Question A sequence of numbers  is defined by  , for  Given that , .a)   Find the value of . b)  Find the value . Solution a.     We are given that sequence  is defined by We are required to find  when . We can utilize the given expression for general terms beyond first term as; We are given that ; b.   […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#4

Question Figure 1 shows a sketch of the curve C with equation  , x ≠ 0. The curve C crosses the x-axis at the point A. a.   State the x coordinate of the point A. The curve D has equation y = x2(x – 2), for all real values of x. b.   A copy of Figure 1 […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#3

Question Find the set of values of x for which a.   b.   c.  both  and . Solution a.   We are given; b.   We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are -3 & […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#2

Question a.   Write down the value of  . b.   Simplify fully . Solution a.   b.

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

Question Find giving each term in its simplest form. Solution We are given; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: