### 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.**

**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.**

**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.**

**(b) Evaluate the shaded area.**

**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.**

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