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The diagram below, not drawn to scale shows part of the curve y = x² + 5 and the line y = 8.2x. The line...
(Solved)
The diagram below, not drawn to scale shows part of the curve y = x² + 5 and the line y = 8.2x. The line intersects the
curve at points C and D. Lines AC and BD are parallel to the y-axis.
(a) Determine the coordinates of C and D.
(b) Use integration to calculate the area bounded by the curve and the x-axis between the points C and D.
(c) Calculate the area enclosed by the lines CD, CA, BD and the x-axis.
(d) Hence determine the area of the shaded region.
Date posted:
April 26, 2019
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Answers (1)
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In the figure below O is the centre of the circle. Angle SPQ = 530 and angle PQO = 300.
(Solved)
In the figure below O is the centre of the circle. Angle SPQ = 530 and angle PQO = 300.
(a) Giving reasons find the size of angles:
(i) SOQ.
(ii) PSO.
(iii) SRT.
(b) If the radius of the circle is 14cm, find the area of the quadrilateral OQPS.
Date posted:
April 26, 2019
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Answers (1)
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The figure above shows the structure of a building under construction.
(Solved)
The figure above shows the structure of a building under construction. HA = IB = JC = ED = 12m and BC = AD = IJ =
HE 16m; and AB = DC = HI = EJ = 10m and HG = IG = FJ = FE = 7m and GF = 9m.
Calculate:
(a) the angle face GHI makes with base ABCD.
(b) vertical height of ridge GF above base ABCD.
(c) angle face GFJI makes with ABCD.
(d) M is midpoint of AB. What is the projection of MF to the base ABCD?
Date posted:
April 25, 2019
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Answers (1)
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(a) P, Q and R are three quantities such that P varies directly as the square of Q and inversely as the square root of...
(Solved)
(a) P, Q and R are three quantities such that P varies directly as the square of Q and inversely as the square root of R.
(i) Given that P = 12 when Q = 24 and R = 36, find P when Q = 27 and R = 121.
(ii) If Q increases by 10% and R decreases by 25%, find the percentage increase in P.
(b) If Q is inversely proportional to the square root of P and P = 4 when Q = 3.
Calculate the value of P when Q = 8.
Date posted:
April 25, 2019
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Answers (1)
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complete the table below for the functions;
(Solved)
Date posted:
April 25, 2019
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Answers (1)
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The table below shows the height of 50 athletes in a college.
(Solved)
The table below shows the height of 50 athletes in a college.
Calculate the median height of the athletes.
Date posted:
April 25, 2019
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Answers (1)
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In a race of 100km, John beats James by 10km and beats David by 13km. By how much will James beat David in a race
of...
(Solved)
In a race of 100km, John beats James by 10km and beats David by 13km. By how much will James beat David in a race
of 120km assuming all run at constant speeds throughout?
Date posted:
April 25, 2019
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Answers (1)
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The G.C.D of three numbers is 30 and their L.C.M is 900. If two of the numbers are 150 and 60, what are the other
three...
(Solved)
The G.C.D of three numbers is 30 and their L.C.M is 900. If two of the numbers are 150 and 60, what are the other
three possible third numbers?
Date posted:
April 25, 2019
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Answers (1)
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XYZ is a triangle. Draw the locus of a point M such that angle XYZ is equal to angle XMZ and Y must lie on...
(Solved)
XYZ is a triangle. Draw the locus of a point M such that angle XYZ is equal to angle XMZ and Y must lie on the locus of
M.
Date posted:
April 25, 2019
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Answers (1)
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Three angles of a polygon are 1250, 1400 and 1600. The remaining angles are 1450 each. Calculate the sum of the interior angles of the...
(Solved)
Three angles of a polygon are 1250, 1400 and 1600. The remaining angles are 1450 each. Calculate the sum of the interior angles of the polygon.
Date posted:
April 25, 2019
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Answers (1)
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Express in surd form and simplify by rationalizing the denominator.
(Solved)
Express in surd form and simplify by rationalizing the denominator.
Date posted:
April 25, 2019
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Answers (1)
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Expand (1 + 2X)8 in ascending powers of X up to and including the term in X³. Hence evaluate (1.02)8.
(Solved)
Expand (1 + 2X)8 in ascending powers of X up to and including the term in X³. Hence evaluate (1.02)8.
Date posted:
April 25, 2019
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Answers (1)
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The equation below represents an equation of a circle.
(Solved)
The equation 
represents a circle. Determine the coordinates of the centre and the length of it’s diameter.
Date posted:
April 25, 2019
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Answers (1)
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List all the integral values of X which satisfy the inequalities.
(Solved)
List all the integral values of X which satisfy the inequalities.
Date posted:
April 25, 2019
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Answers (1)
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The figure below shows a triangular prism. The measurements are in cm.
(Solved)
The figure below shows a triangular prism. The measurements are in cm.
Draw the net of the prism and hence find the total surface area.
Date posted:
April 25, 2019
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Answers (1)
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A bag contains 3 red and 5 green marbles. Two marbles are picked at random from the bag one at a time without
replacement. Find the...
(Solved)
A bag contains 3 red and 5 green marbles. Two marbles are picked at random from the bag one at a time without
replacement. Find the probability that two marbles picked will be of different colors.
Date posted:
April 25, 2019
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Answers (1)
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Use logarithms to 4 decimal places to evaluate:
(Solved)
Use logarithms to 4 decimal places to evaluate:
Date posted:
April 25, 2019
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Answers (1)
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The height and radius of a cone are measured as 21cm and 14.0cm respectively. Taking pi = 3.142, find the percentage error in the volume...
(Solved)
The height and radius of a cone are measured as 21cm and 14.0cm respectively. Taking pi = 3.142, find the percentage error in the volume of the cone.
Date posted:
April 25, 2019
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Answers (1)
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Simplify:
(Solved)
Simplify:
Date posted:
April 25, 2019
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Answers (1)
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Evaluate:
(Solved)
Evaluate:
Date posted:
April 25, 2019
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Answers (1)