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SS3 Term 1 Exam

The document contains 9 multipart questions about various math and geometry topics. Question 1 involves binary operations and solving equations. Question 2 involves calculating taxable income and monthly tax. Question 3 involves calculating lengths and trigonometric functions based on a diagram. Question 4 involves evaluating logarithmic and set theory expressions. The remaining questions cover topics like right pyramids, proportions, paper clip distributions, geometric constructions, and calculating distances and speeds based on latitude and longitude.

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114 views5 pages

SS3 Term 1 Exam

The document contains 9 multipart questions about various math and geometry topics. Question 1 involves binary operations and solving equations. Question 2 involves calculating taxable income and monthly tax. Question 3 involves calculating lengths and trigonometric functions based on a diagram. Question 4 involves evaluating logarithmic and set theory expressions. The remaining questions cover topics like right pyramids, proportions, paper clip distributions, geometric constructions, and calculating distances and speeds based on latitude and longitude.

Uploaded by

tommymakans
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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PART I [32 marks]

Answer ALL the questions in this part.


Each question carries equal marks.

1. (a) A binary operation is defined as p * q = q – 3p


Evaluate: (i) (1 * 2) * 3
ii. Find p if p*-4=5
iii. Is the operation * commutative?
(b) If 53y + 62y = 125y, what is the value of y?

2. A man has a wife and 6 Children and his total income in a year was GH¢ 850.00.

He was given the following tax free allowances:


Personal GH¢ 120.00;
Wife GH¢ 30.00;
Children GH¢ 25.00 per child, for a maximum of 4 children;
Medical GH¢ 40. 00.
The rest were taxed as follows:
First GH¢ 200.00 at 10%;
Next GH¢ 200.00 at 15%;
Next GH¢ 200.00 at 20%;
Remainder at 25%.
Calculate his:

a. Annual taxable income;


b. Monthly tax.

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3.
P

6 cm

S
4 cm

Q 5 cm R
T

In the diagram, PQ and QR are straight lines, |PS| = 6cm, |QS| = 4 cm,
|QT| = 5 cm and ∠QTS = ∠RPQ.
a. Calculate |TR|.
5
b. If sin x = , 00 ≤ x ≤ 90o, evaluate, without tables or calculator, to 4 significant figures
13

4. (a) Without using tables or calculator, evaluate:

log 10 ( 7510 ) – 2 log ( 59 ) +


10 log 10 ( 100
243 )

(b) Given that X = {x : 10 ≤ x < 15} and Y = { even numbers < 18 } are subsets of
the universal set U= {10, 11, 12, …, 20}, find:
(i) X ∩ Y;
(ii) n(X’ ∩ Y).

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PART II [48 marks]
Answer any 4 the questions in this part.
Each question carries equal marks.
5. The diagram shows a right pyramid with a rectangular base WXYZ and vertex O.

If |WX| = 8 cm, |ZW| = 6 cm and |OX| = 13 cm, calculate the:

c. height of the pyramid;


d. angle between the edge OY and the plane WXYZ, correct to the nearest degree;
e. Volume of the pyramid.

1 1
6. (a) In a class of 52 students, 16 are Science students. If of the boys and of the girls are Science
3 4
students, how many boys are in the class?

(b) The number of 100 packets of paper clips are counted and tabulated.

No. of
185 - 189 190 - 194 195 - 199 200 - 204 205 - 209
clips/packet
frequency 4 16 35 28 17
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Calculate:

(i) The mean number of paper clips;

(ii) The standard deviation of this distribution.

7. Using ruler and a pair of compasses only, construct:


a. Parallelogram PQRS with RS as the base such that |PQ| = 7.8 cm,

|QR| = 5.6 cm and angle QRS = 120o;

b. Rectangle ABRS, equal in area to parallelogram PQRS.


c. Measure:
(i) |AP|;
(ii) |AS|.

8. An airplane took 4 hours to fly from a town P (lat. 450N, long. 750E) to another town,
T (lat. 450, long. 150E).

The airplane changed course and 8 hours after leaving T, arrived at a third town

Q (lat. 00, long. 150E). If the flight from P to T was along the line of parallel of latitude, and that from T
to Q along the meridian, calculate, correct 3 significant figures:

a. The total length of the journey;


22
b. Average speed of the aircraft. (Take R = 6400 km/h and π = )
7

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9

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