SS2: MATHEMATICS HOLIDAY ASSIGNMENT. (TEST 01 - 40 marks)
1.
(a) ABCD is a rectangle in which /AB) = 2.8 cm and /AD/ = 3.3 cm. E is a point on
DC produced such that AAED and rectangle ABCD are equal in area. Calculate
() /DE/ (ii) /AE/
A
2.9
13
(b) Solve the equation * = x - 5+
3.3
2
D
2.
(a) The floor of a classroom measures 6m by 8m. The walls are 3m high and
they contain tour windows measuring 1.2m by 75 cm. There is a door which
measures 2m by 80 cm. What percentage of the total wall area is taken up by
the windows and doors? Give your answers to two s. f.
(b) The cost(c) of producing n bricks is the sum of a fixed amount, hand a
variable amount y, where y varies directly as n. If it costs N950.00 to produce
600 bricks and N1030.00 to produce 1000 bricks.
(i) Find the relationship between c, h and y
(ii) Calculate the cost of producing 500 bricks.
k
3.
Solve for x given thatx2
x = 2p, where k and p are real constants
(a) the surface area of a closed cone of height h and base radius r is given by
the formula,
A - Ter2 + tor Vh2 + r2, show that
A
2nr 2
h =
L.
1 .Hence calculate the height of the cone of surface area
157cm’and base radius 3 cm. (1 = 3)
(b) If x is the average of m and 9, y is the average of 2m and 15 and z is the
average of 3m and 18, What is the average of x, y and z.
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After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).