### Higher Mathematics  Paper 1 2019

There is a total of 17 Questions for the Higher Mathematics Paper 1 with proper solutions.

1. Find the x-coordinates of the stationary points on the curve with equation Solution: 2. The equation xk x + − += ( ) 2 5 10 has equal roots.
Determine the possible values of k.  3. The radius of C2 is equal to the radius of C1.
Find the equation of circle C2.  Maths Paper 1 National 5

4. A sequence is generated by the recurrence relation
where the first three terms of the sequence are 6, 9, and 11.
(a) Find the values of m and c.
(b) Hence, calculate the fourth term of the sequence.  NATIONAL MATHEMATICS PAPER 1 2019

5. (a) Show that the points A(1,5,-3), B(4,-1,0) and C(8,-9,4) are collinear.
(b) State the ratio in which B divides AC. 6. Given that  7. The line, L, makes an angle of 30° with the positive direction of the x-axis.
Find the equation of the line perpendicular to L, passing through (0,-4). 8.The graphs intersect at the points where x x =− = 1 2 and.
(a) Express the shaded area, enclosed between the curves, as an integral.  Q9:
(a) (i) Find an expression for u.v.
(ii) Determine the values of p for which u and v are perpendicular.
(b) Determine the value of p for which u and v are parallel  10. The diagram shows the graphs with equations y = f (x) and  y = kf(x) a     13. Triangles ABC and ADE are both right-angled.
Angles p and q are as shown in the diagram.      16. The point P has coordinates (4,k).
C is the center of the circle with equation
(a) Show that the distance between the points P and C is given by
(b) Hence, or otherwise, find the range of values of k such that P lies outside the
circle.    