__LOCI,LINEAR INEQUALITIES__

__CALCULUS: CURVE SKETCHING,AREA APPROXIMATIONS__

- The equation of the curve is y
– 2x^{3}+ 3x + 5.^{2} - (i) Determine the stationary points of the curve. (3 marks)

(ii) For each point in a (i) above determine the nature of the points hence sketch the curve. (4 marks)

- Find the equation of the tangent to the curve at x = 2. (3 marks)

*2018 Mocks PP1/87*

**2.**a) i) Find the coordinates of the stationary points on the curve y=x^{3}-3x+2. (3 marks)

- ii) For each stationary point determine whether it is a minimum or a maximum.

(4 marks)

- b) In the space provided, sketch the graph of the function y=x
^{3}-3x+2. (3 marks)

*2018 Mocks PP1/72*

3.The equation of a curve is y = -2*x*^{2} + *x* + 1

- Find

- The gradient of the curve at P(5, -44) (3mks)

- The
*y*intercept (1mk)

(b) (i) Determine the stationary point of the curve (3mks)

(ii) Sketch the curve (3mks)

*2018 Mocks PP1/48*

4.Using a ruler and pair of compas only construct :

(a) An equilateral triangle ABC of side 6cm

(b) The focus of a point P inside the triangle such that AP __<__ PB

(c) The locus of a point Q such that AQ > 4cm

(d) Mark and label the region x inside the triangle which satisfy the two loci. (4mks)

2018/31 PP2

5.Above line AB = 10cm drawn below, construct and label in a single diagram, using a pair of a compasses and ruler only;

- The locus of a point X such that the area of a triangle ABX is 15cm
^{2}. - The locus of a point Y such that angle AYB = 90
^{o}. - Locate points P and Q where loci X and Y intersect. Measure PQ.
- Show by shading and labeling the region R which satisfies the conditions below simultaneously:
- Angle ARB ≥ 90
^{o} - Area of triangle ABR ≥ 15cm
^{2} - Calculate the area of the shaded region R in (d) above. (Take = 3.142) (10 marks)

2018/24/PP2

6.(a)Construct rectangle **ABCD **with side**AB**= 6.4cm and diagonal **AC** = 8cm. (3mks)

(b)Locus,**L _{1}**

_{,}is a set of points equidistant from

**A**and

**B**and locus,

**L**is a set of points equidistant from

_{2,}**BC**and

**BA**.If

**L**and

_{1}**L**meets at

_{2}**N**inside the rectangle, locate point

**N**.(3mks)

(c)A point ** x** is to be located inside the rectangle such that it is nearer

**B**than

**A**and also nearer

**AB**than**BC**. If its not greater than 3cm from **N**shade the region where the points could be located. (4mks)

2018/21/PP2

7.Using a ruler and a pair of compasses only construct

- Triangle ABC, such that AB = 9cm, AC = 7cm and < CAB = 60° (2mks)

- The locus of P , such that AP ≤ BP (2mks)

iii. The locus of Q such that CQ ≤ 3.5cm

- Locus of R such that angle ACR ≤ angle BCR (2mks)

2018/11/PP2

8.The line segment BC = 7.5 cm long is one side of triangle ABC.

- a) Use a ruler and compasses only to complete the construction of triangle ABC in which

ÐABC = 45^{o}, AC = 5.6 cm and angle BAC is obtuse. {3 marks}

- b) Draw the locus of a point P such that P is equidistant from a point O and passes through the vertices of triangle ABC. {3 marks}
- c) Locate point D on the locus of P equidistant from lines BC and BO. Q lies in the region enclosed by lines BD, BO extended and the locus of P. Shade the locus of Q. {4 marks}