Mathematics revision Exercise 1

1. Find the size of each angle of a triangle PQR in which PQ = 9 cm, QR = 12 cm and RP = 6 cm.
2. R represents half-turn about the point (2, 3). H represents half-turn about the point (-2, -1). Find a single a single transformation equivalent to HR and state its inverse.
3. For each of the following wave functions, state the period and the amplitude;

          a) y = 2 Sin x

          b) y = Sin 2x

          c) y = 1/3 Sin x

         d) y = 1/3 Sin 3x

         e) y = Sin ½ x

         f) y = Sine 1/3 x

 

   4. Solve the following pair of simultaneous equations graphically;

5. A card is drawn at random from a normal pack of playing cards. what is the probability of drawing ;

a) a black card?

b) a red card?

c) an ace?

d) the queen of spades?

6. a pencil PQ is 20 cm long. The end P is placed on a horizontal flat surface such that PQ makes an angle of 47° with the surface. Calculate how far above the surface the pint Q is.

7. Solve the following inequalities and show your solutions on a number line;

a) 3x - 5 > 5

b) 2x + ½ < 3

c) - 4x - 6 > 7

8. Evaluate each of the following;

9. A quadrilateral has vertices at A(1, 2), B(1, 3), C(2, 3) and D(3, 1). Find the vertices of the image of the quadrilateral after a reflection in the following lines;

a) y = x + 1

11. ABC is an isosceles triangle with AB = AC and its perimeter is 64 cm. The altitude from A to BC IS 24 cm. Find the length of AC and BC.

12. Two variables x and y are connected by an equation of the form y = Axⁿ, where A and n are constants. If y = 80 when x = 2 and y = 52 when x = 3, find the values of A and n to 2 s.f.

13. Find the distance in nautical miles between point A(4° S, 50° E) and B(4°S, 80°E).

14. Draw a line AB = 4.5 cm. Construct a locus of a point P such that <APB = 40°.