Edexcel GCE Core Mathematics C1 January 2012 exam answers review

1. dy/dx(3)
2. \(\int\)y dx(3)

1. Simplify

   √32 + √18

   giving your answer in the form a √2 , where a is an integer.

   (2)

2. Simplify

   √32 + √18/3 + √2

   giving your answer in the form b √2 + c , where b and c are integers.

   (4)

Find the set of values of x for which

1. 4x − 5 > 15 − x(2)
2. x(x − 4) > 12(4)

A sequence x₁, x₂, x₃,… is defined by

where a is a constant.

1. Write down an expression for x₂ in terms of a.(1)
2. Show that x₃ = a² + 5a + 5 (2)

Given that x₃ = 41

3. find the possible values of a.(3)

The curve C has equation y = x(5 − x) and the line L has equation 2y = 5x + 4

1. Use algebra to show that C and L do not intersect.(4)
2. In the space on page 11, sketch C and L on the same diagram, showing the coordinates of the points at which C and L meet the axes.(4)

The line l₁ has equation 2x − 3y +12 = 0

1. Find the gradient of l₁.(1)

The line l₁ crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure 1.

The line l₂ is perpendicular to l1 and passes through B.

2. Find an equation of l₂.(3)

The line l₂ crosses the x-axis at the point C.

3. Find the area of triangle ABC.(4)

A curve with equation y = f (x) passes through the point (2, 10). Given that

find the value of f (1).

(5)

The curve C₁ has equation

1. Find dy/dx(2)
2. Sketch C₁, showing the coordinates of the points where C₁ meets the x-axis.(3)
3. Find the gradient of C₁ at each point where C₁ meets the x-axis.

The curve C₂ has equation

y = (x − k)²(x − k + 2)

where k is a constant and k > 2

4. Sketch C₂ , showing the coordinates of the points where C₂ meets the x and y axes.(3)

A company offers two salary schemes for a 10-year period, Year 1 to Year 10 inclusive.

1. Show that the total earned under Salary Scheme 1 for the 10-year period is;

   £(10P + 90T)

   (2)

For the 10-year period, the total earned is the same for both salary schemes.

2. Find the value of T.

For this value of T, the salary in Year 10 under Salary Scheme 2 is £29 850

3. Find the value of P.(3)

Figure 2 shows a sketch of the curve C with equation

The curve crosses the x-axis at the point A.

1. Find the coordinates of A. (1)

2. Show that the equation of the normal to C at A can be written as

   2x + 8y −1 = 0

   (6)

The normal to C at A meets C again at the point B, as shown in Figure 2.

3. Find the coordinates of B.(4)