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Evaluate:
(Solved)
Evaluate:
Date posted:
August 20, 2019
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Answers (1)
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The figure below shows a frustrum PQRSTUVW of a right pyramid. PQ = 20cm, QR = 15cm,UV = 10cm, UT = 7.5cm and PU =...
(Solved)
The figure below shows a frustum PQRSTUVW of a right pyramid. PQ = 20cm, QR = 15cm,UV = 10cm, UT = 7.5cm and PU = QV = RW = ST = 12cm.
Leave all your answer to 4 s.f.
(a) Find the altitude of the pyramid from which the frustum was cut.
(b) Find the angle between
(i) PW and base PQRS
(ii) PQVU and the base PQRS
Date posted:
August 20, 2019
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Answers (1)
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Solve the pair of simultaneous equations using elimination method.
4x+9y=5
3x+3y=2
(Solved)
Solve the pair of simultaneous equations using elimination method.
4x+9y=5
3x+3y=2
Date posted:
August 20, 2019
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Answers (1)
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Express the number 935 and 19845 as a product of their prime factors hence evaluate the following expression leaving your answer in prime factor form.
(Solved)
Express the number 935 and 19845 as a product of their prime factors hence evaluate the following expression
leaving your answer in prime factor form.
Date posted:
August 20, 2019
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Answers (1)
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Given 2.421=2a/b. determine the values of a and b.
(Solved)
Given 2.421=2a/b. determine the values of a and b.
Date posted:
August 20, 2019
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Answers (1)
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Find the length of AC in the figure below.
(Solved)
Find the length of AC in the figure below.
Date posted:
August 20, 2019
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Answers (1)
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A circle of radius 4.9cm fits exactly inside a square. Find the area of the space between the circle and the square.
(Solved)
A circle of radius 4.9cm fits exactly inside a square. Find the area of the space between the circle and the square.
Date posted:
August 20, 2019
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Answers (1)
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Express y in terms of x given that:-
10x2 - 9xy + 2y2 = 0
(Solved)
Express y in terms of x given that:-
10x2 - 9xy + 2y2 = 0
Date posted:
August 20, 2019
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Answers (1)
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The distance from town A to town B is 360km. A bus left town A and traveled towards town B at an average speed of...
(Solved)
The distance from town A to town B is 360km. A bus left town A and traveled towards town B at an average speed of 60km/h. After 1½ hours, a car left town A and traveled along the same road at an average speed of 100km/h.
(a) Determine:
(i) The distance of the bus from town A when the car took off.
(ii) The distance the car traveled to catch up with the bus.
(b) The distance from P to Q is 160km. If an express train was 16km/h slower it would take 20 minutes longer on the journey. Find the average speed of the express train.
Date posted:
August 20, 2019
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Answers (1)
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Use mathematical tables to evaluate
(Solved)
Use mathematical tables to evaluate
Date posted:
August 20, 2019
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Answers (1)
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A transformation represented by the matrix
(Solved)
A transformation represented by the matrix 
maps the points A(0, 0), B(2, 0), C(2, 3) and D(0, 3) of the quad ABCD onto A¹B¹C¹D¹ respectively.
(a) Draw the quadrilateral ABCD and its image A¹B¹C¹D¹.
(b) Hence or otherwise determine the area of A¹B¹C¹D¹.
(c) Another transformation 
maps A¹B¹C¹D¹ onto A¹¹B¹¹C¹¹D¹¹. Draw the image A¹¹B¹¹C¹¹D¹¹.
(d) Determine the single matrix which maps A¹¹B¹¹C¹¹D¹¹ back to ABCD.
Date posted:
August 20, 2019
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Answers (1)
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In the given figure, 0, 0 and 0.
(Solved)
In the given figure, 0, 0 and 0. BAF is a straight line.
Giving reasons where necessary, calculate the size of:-
(i) (ii) (iii) (iv)
Date posted:
August 20, 2019
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Answers (1)
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A tetrahedron has equilateral triangular base ABC of side 10cm.
(Solved)
A tetrahedron has equilateral triangular base ABC of side 10cm. The vertex V is such that VA = VB = VC = 8cm. Calculate:
(a) The angle between the planes ABC and BCV
(b) The vertical height of the vertex V above the base ABC.
(c) Volume of the tetrahedron.
Date posted:
August 20, 2019
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Answers (1)
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On the grid provided below, draw the graph of y = (x + 4)(1 - 2x) for the range
(Solved)
(a) On the grid provided below, draw the graph of y = (x + 4)(1 - 2x) for the range 
(b) On the same grid draw the line y + 3x = 2.
(c) Use your graph to solve the equations:
(i) (x + 4)(1 - 2x) = -5
(ii) -2 - 4x - 2x² = 0
Date posted:
August 20, 2019
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Answers (1)
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Two aeroplanes, T and S leave an airport A at the same time.
(Solved)
Two aeroplanes, T and S leave an airport A at the same time. S flies on a bearing of 0600 at 750km/h while T flies on a bearing of 2100 at 900 km/h.
(a) Use a suitable scale, to draw a diagram showing the relative position of the aeroplanes
after two hours.
(b) Use your diagram to determine:
(i) the distance between the two aeroplanes.
(ii) the bearing of T from S.
(c) Aeroplane T later flew to the East at the same speed for one hour. Show its final position
on the diagram in (a) above.
Determine:
(i) Its final distance from A.
(ii) Its final bearing from S.
Date posted:
August 20, 2019
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Answers (1)
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The figure below shows a solid frustum with a rectangular base measuring 18cm by 24cm and the top
measuring 6 cm by 8cm. The slant edges...
(Solved)
The figure below shows a solid frustum with a rectangular base measuring 18cm by 24cm and the top
measuring 6 cm by 8cm. The slant edges are each 26cm long.
Determine:
a) Height of the original pyramid.
b) Volume of the frustum.
c) Density in g/cm3 if the solid has a mass of 7.488kg
Date posted:
August 20, 2019
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Answers (1)
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Sketch and label the net of the prism shown below.
(Solved)
Sketch and label the net of the prism shown below.
Date posted:
August 20, 2019
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Answers (1)
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The gradient of a curve at any point (x, y) is given by 3x² + 2x. If the curve passes through the point (-2, 1).
(Solved)
The gradient of a curve at any point (x, y) is given by 3x² + 2x. If the curve passes through the point (-2, 1). Find its equation.
Date posted:
August 20, 2019
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Answers (1)
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In the figure below O is the centre of a circle and PS is the diameter. QR is parallel to PS. If anglePSQ = 25o...
(Solved)
In the figure below O is the centre of a circle and PS is the diameter. QR is parallel to PS. If angle PSQ = 25o and angle POT = 120o.
a) Angle QRP
b) Angle PTO
c) Angle QPT
d) Angle QPS
c) Angle PTS
Date posted:
August 20, 2019
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Answers (1)
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A circle of radius 7 units has it’s centre at the point of intersection between the lines x + 2y + 1 = 0 and...
(Solved)
A circle of radius 7 units has it’s centre at the point of intersection between the lines x + 2y + 1 = 0 and 2x + 3y – 3 = 0. Find the equation of the circle expressing it in the form x² + y² + yx + fy + c = 0.
Date posted:
August 20, 2019
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Answers (1)