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Mathematics Question Paper
Mathematics
Course:Secondary Level
Institution: Mock question papers
Exam Year:2010
MATHEMATICS PAST PAPER
1. (a) The volume of a cylinder of height 20cm is 720p cm3 .
?? Find the radius of the cylinder.
(b) A square of side length 8cm is circumscribed by a circle.
(i) ?? Find the length of the diagonal, d of the square in surd form.
(ii) ?? Hence, write down the radius of the circle in surd form.
(iii) ?? Find the area of the shaded region correct to one decimal place, taking
p = 3·14 .
(c) A cone has a height of 12cm and has a slant height of 153 cm.
(i) ?? Verify that the radius of the cone is 3cm.
(ii) ?? Show that the volume of the cone is 36p cm3 .
(iii) ?? One half of the volume of the cone drips into
a hemisphere and fills it. Calculate the radius
of the hemisphere.
153
Page 3 of 7
2. (a) Prove that a diagonal bisects the area of a parallelogram.
(b) Using the points m(-3, 5) and n(2, -1).
(i) ?? find the slope nm.
(ii) ?? find the equation of the line nm.
(iii) ?? If c (q, - 4) is on the line nm find the value of q.
(c) P is the line x - 3y + 5 = 0 .
Q is the line 3x + y = 0 .
(i) ?? Verify that P ? Q.
(ii) ?? Find the coordinates of r the point of intersection of P and Q.
(iii) ?? Find s, the image of the point t (-3, 5) , under a central symmetry in
the point (-2, 3) .
(iv) ?? rstu forms a parallelogram. Find the coordinates of the point u.
Page 4 of 7
3. (a) The line M is parallel to L.
?? Calculate the value of x and the value of y in the diagram.
(b) (i) ?? Copy the diagram below and sketch the image of the letter F under an axial
symmetry in the line P.
(ii) ?? Calculate the value of p and q in the diagram.
(c) (i) ?? Construct a triangle pqr where:
?pqr = 80°, pq = 6cm and qr = 4cm.
(ii) ?? Construct the circumcentre of the triangle and hence draw the circumcircle.
P
o
Page 5 of 7
4. (a) ?? xyzw is a parallelogram.
Find the value of A and B in the parallelogram in the following diagram.
(b) Prove that if two triangles are equiangular, the lengths of corresponding sides are in
proportion.
(c) x, y, z,w are all points on a circle, as shown.
o is the centre of the circle.
?xy z = 70° and xw = wz
Find
(i) ?xoz
(ii) ?? ?xwz
(iii) ?? By joining x to z, or otherwise, find ?wxo .
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5. (a) ?? If tan 1
3
A = - , find the two values for the angle A where 0 = A = 360° .
(b) In a right angled triangle pqr, pr = 4·8cm and ?pq r = 32° .
(i) ?? Find rq , to the nearest cm.
The line qr is extended to t.
(ii) ?? If pt = 12cm, find ?ptr to the nearest degree.
(c) defg is a parallelogram df =12cm, ?dg f =124° and ?dfg = 24° .
(i) ?? Find dg , correct to the nearest cm.
(ii) ?? Find the area of parallelogram defg to one decimal place.
Page 7 of 7
6. (a) A survey was done of the number of downloads made by students over
a one month period. The results of this survey are in the table below.
Number of Downloads 0 – 10 10 – 20 20 – 40 40 – 70
Number of Students 6 8 10 15
Draw a histogram to illustrate the above information.
(b) The table below shows the amount of time in minutes taken by 100 shoppers to
complete their shopping in a supermarket
Time in Minutes 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
Number of shoppers 10 25 35 18 12
(i) Copy the table below into your answer book and using the table above complete it.
Time in seconds = 10 = 20 = 30 = 40 = 500
Number of shoppers
(ii) On graph paper construct the cumulative frequency curve.
Use the curve to estimate:
(iii) ?? the interquartile range.
(iv) ?? the number of shoppers that spent more than 35 minutes shopping.
(c) A survey was done of the number of text messages made by mobile phone users over
a weekend.
Number of texts 0 – 4 4 – 10 10 – 20 20 – 30 30 – 50
Number of users 15 6 6 x 9
(Note: 10 – 20 means 10 texts or more but less than 20 texts.)
Taking mid-interval values, it was found that the mean number of texts made per
user was 16.
?? Find the value of x.
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