G 11/12 MATHS TEST 2

Evaluate

Solve the equation   

Simplify

Given that ,

find               

(i) The determinant of B            [1]

(ii) B­²                                                          [2]

Express K 75.00 as a percentage of K 50.00

solve the equation  m² – m – 5 = 0,  giving your answer correct to two decimal places

In the diagram below, PAQ is a tangent to the circle at point A.  AC bisects BCD, ABC = 81^o and              PAB = 30^o

Calculate

ACB       [1]

ADC       [1]

DAQ     [1]

CAQ    [2]

Express the expression below as a single fraction in its simplest form. write the numerator as the solution.

In the diagram below, OAB is a triangle in which OA = a and OB = b. the point X on AB is such that AX: XB = 3: 1.

Express in terms of a and/or b

BO      [1]

AB      [1]

AX      [2]

In the diagram below, OAB is a triangle in which OA = a and OB = b. the point X on AB is such that AX: XB = 3: 1.

Express in terms of a and/or b

OX       [2]

At gender technical secondary school, a group of 70 girls take optional subjects as illustrated in the Venn diagram below.

1. Calculate the value of x.
2.  Find the number of girls who

a) History only 

b) Commerce

A box has 14 identical balls, three of which are blue. Two balls are drawn at random from the box, one after the other without replacement.

Calculate the probability that (expressing your answer as a fraction)

a) the two balls are both blue 

b) at least one ball drawn is blue.

The diagram below shows a triangular garden OAB where OA = 1.7m, AB = 1.1m and angle OAB = 114^o

Calculate

a) The area of triangle OAB correct to 1 decimal place,                                     

b) The distance OB

c) the shortest distance from A to OB

A rectangular maize field has a length of 1.5km and a width of 1.1km. Calculate the length of its diagonal.

Mofu, Kopa and Nora are partners in business. Mofu owns 50% of the shares while Kopa and Nora own the remaining shares equally. Given that Mofu’s shares are valued at K 1 800.00,

a) Calculate the sum of all the shares,                                                                                         

b) Express the shares of Mofu, Kopa and Nora as a ratio in its simplest form

Chakudya has a food warmer made up of a cylindrical bowl and a conical lid, as shown in the diagram below. The bowl has a height of 20cm and a diameter of 32cm. the height of the lid is 5cm.

Taking π = 3.142, calculate

a) The surface area of the cylindrical bowl, [4]

b) The volume of the lid (volume of cone = 1/3 πr²h)

Evaluate

Factorise complete 2x² – 3x + 2cx – 3c