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- The diagram below represents a community water tank made up of cylindrical and regular hexagonal parts.(Solved)
The diagram below represents a community water tank made up of cylindrical and regular hexagonal parts. The diameter and the height of the cylindrical part are 7m and 5m respectively. The side of the regular hexagonal face is 2m and the height of the hexagonal part is 10m. (Take pi= 22/7)
(a) Determine:-
(i) Cylindrical part.
(ii) Hexagonal part.
(iii) The whole tank.
(b) An identical structure is to be built with a hollow cross-sectional area of 1.5m2 and mass of 440kgs. Calculate the density of this structure.
Date posted: September 10, 2019. Answers (1)
- A quadrilateral ABCD has the coordinates A (1,1), B(4,1), C(5,3) and D(2,3)(Solved)
A quadrilateral ABCD has the coordinates A (1,1), B(4,1), C(5,3) and D(2,3).
(a) On the graph provided draw the quadrilateral ABCD.
(b) AIBICIDI is the image of ABCD under a transformation matrix represented by: 
write down the coordinates of AIBICIDI and on the same grid draw quadrilateral AIBICIDI.
(c) AIIBIICIIDII with coordinates AII(1,-2), BII(4,1), CII(5,-4), DII(2,-7) is the image of AIBICIDI under transformation whose matrix is T. Find matrix T.
(d)
(i) On the same grid, draw quadrilateral AIIBIICIIDII.
(ii) A single transformation matrix K maps ABCD onto AIIBIICIIDII. Determine the matrix K.
Date posted: September 10, 2019. Answers (1)
- The turns ratio of primary to secondary coils in a 100% efficient transformer is 3: 1. Calculate the current through the primary coil if the...(Solved)
The turns ratio of primary to secondary coils in a 100% efficient transformer is 3: 1. Calculate the current through the primary coil if the current in the secondary coil is 5A.
Date posted: September 10, 2019. Answers (1)
- A school has two students whose age difference is 9. Twice the sum of their ages is equal to the age of their teacher.(Solved)
A school has two students whose age difference is 9. Twice the sum of their ages is equal to the age of their teacher.
(a) By letting the age of the younger student be y, write an expression of the:
(i) Age of the elder student.
(ii) Age of their teacher.
(b) If in 19 years time, the product of the ages of the two students is equal to 14 times the age of their teacher;
(i) Form an equation in y and hence determine the present possible age of the younger student.
(ii) Determine the possible age of the elder student in 19 years time.
(iii) Find the possible age of the teacher.
Date posted: September 10, 2019. Answers (1)
- The table below shows the masses of population randomly chosen in a certain town in kilogrammes.(Solved)
The table below shows the masses of population randomly chosen in a certain town in kilogrammes.
(a) Represent this information on a histogram.
(b) Draw a frequency polygon.
(c) Calculate the mean of the population in this town.
Date posted: September 10, 2019. Answers (1)
- (a) Complete the table below to 2 decimal places for
y = -x3 – x2 + 3x + 1(Solved)
(a) Complete the table below to 2 decimal places for
y = -x3 – x2 + 3x + 1
(b) On the grid provided, draw the graph for y = -x3 – x2 + 3x + 1 for -4 < x < 3.
(c) Use the graph to solve the equation -x3 – x2 + 3x + 1=0
(d) By drawing a suitable straight line on the graph, solve -x3 – x2 + 3x + 1 = -2x
Date posted: September 10, 2019. Answers (1)
- A metallic cuboid 8cm by 10cm by 14cm is melted.(Solved)
A metallic cuboid 8cm by 10cm by 14cm is melted. Half of it is used to make a cylinder of radius 4.2cm, the remaining is used to make a sphere. Determine using pi= 22/7
(a) The height and surface area of the cylinder to 1 decimal place.
(b) The radius and surface area of the sphere correct to 1 decimal place.
Date posted: September 10, 2019. Answers (1)
- A and B are two points 10cm apart.(Solved)
A and B are two points 10cm apart.
(a) Draw a circle centre A, radius 2cm and a circle centre B, radius 4cm.
(b) Draw a transverse common tangent to the two circles.
(c) Find by calculation the length of a direct common tangent correct to 3 significant figures.
Date posted: September 10, 2019. Answers (1)
- In the figure below, SP is parallel to QR.(Solved)
In the figure below, SP is parallel to QR.
(i) Show that triangles SPX and RQX are similar.
(ii) If PS = 8cm, PX = 6cm, SX = 4cm and RX = 3cm, find the length of RQ and QX.
Date posted: September 10, 2019. Answers (1)
- The ratio of a spherical balloon increases by 4%. Find the percentage increase in its;(Solved)
The ratio of a spherical balloon increases by 4%. Find the percentage increase in its;
(a) Surface area.
(b) Volume
Date posted: September 10, 2019. Answers (1)
- The diagram ABCD is a parallelogram. Line BE is parallel to line FD.(Solved)
The diagram ABCD is a parallelogram. Line BE is parallel to line FD. Show that triangles ABE and CDF are congruent. Show that triangles ABE and CDF are congruent.
Date posted: September 10, 2019. Answers (1)
- How many terms of the arithmetic series 2, 5, 8, 11 …. May be added to make their sum 301?(Solved)
How many terms of the arithmetic series 2, 5, 8, 11 …. May be added to make their sum 301?
Date posted: September 10, 2019. Answers (1)
- The graph below is a velocity time graph(Solved)
The graph below is a velocity time graph
Determine the acceleration in the sections:
(a)
(i) CD
(ii) DE
(b) Calculate the total distance covered.
Date posted: September 10, 2019. Answers (1)
- The gradient of the curve is ax2 + 3x at x = 2 is 8.(Solved)
The gradient of the curve is ax2 + 3x at x = 2 is 8. Find the value of a.
Date posted: September 10, 2019. Answers (1)
- Factorise xy – zy – xw + zw hence simplify the expression completely.(Solved)
Factorise xy – zy – xw + zw hence simplify the expression completely.
Date posted: September 10, 2019. Answers (1)
- Given the matrix(Solved)
Given the matrix 
(a) Determine y2
(b) If y2 = I, determine the possible values of c and d.
Date posted: September 10, 2019. Answers (1)
- Expand (v5 + v3) (v5 – v3) hence or otherwise simplify by rationalising the denominator of (Solved)
Expand (√5 + √3) (√5 – √3) hence or otherwise simplify by rationalising the denominator of
Date posted: September 10, 2019. Answers (1)
- The diagonal of a rectangular flower garden is 20m.(Solved)
The diagonal of a rectangular flower garden is 20m. If the width of this garden is 8m, calculate its length and perimeter to 4 s.figures.
Date posted: September 10, 2019. Answers (1)
- The diagram below shows the region enclosed by inequalities.(Solved)
The diagram below shows the region enclosed by inequalities.
Determine the inequalities that defines the regions R.
Date posted: September 10, 2019. Answers (1)
- The column vectors of b, c and d are given as:(Solved)
The column vectors of b, c and d are given as:
respectively and that P = b + 2c – d. Express vector P as a column vector and hence calculate the magnitude of P.
Date posted: September 10, 2019. Answers (1)