AI en Translation, Pages 26-50
Page 26
Shamash Secondary School
3rd Quarter + 4th Quarter Examination
Page. 1
Subject: Algebra
Date: 7/4/1969
Class: 4th Year, scientific
Time: 8:30 - 10:30 a.m.
Answer all questions:
1. (i) By first taking the square root and then the cube root, find the sixth
root of:
(a³ - 1/a³)² - 6(a - 1/a)(a³ - 1/a³) + 9(a - 1/a)² (12 marks)
(ii) Prove that the left hand side is always equal to the right hand side
in the following equation:
bc(b-c) + ca(c-a) + ab(a-b) = -(b-c)(c-a)(a-b) (13 marks)
2. (i) solve the equation : (x-1)/(√x -1) = 3 + (√x +1)/2 (12 marks)
(ii) Rationalise the denominator and then find the value of:
(√1+x + √1-x) / (√1+x - √1-x) , when x = 2b / (b²+1) (13 marks)
3. (i) Compute : ⁷√[ (6.002001)³ (sin 16° 23')² / (1.003)⁵ (tan 41° 16')² ] (12 marks)
(ii) Solve the following equation for x:
2(log x)² - 5(log x) + 2 = 0 (13 marks)
4. (i) In an arithmetic Progression the first term is 3 and the common difference
is 6 . Show that the sum of 2n terms is always equal to four times
the sum of n terms . (12 marks)
(ii) In an A.P. the ratio of the 3rd term to the 6th term is 11:26 and
the sum of the first 4 terms is 34 . Find the progression and the sum
of the first 8 terms . (13 marks)
Page 27
SHAMASH SECONDARY SCHOOL
3rd & 4th quarter Examination.
Subject: Algebra
Class: 4th Year Scientific
Date: 7/4/1969.
Time: 8:30-10:30 a.m.
⟦line⟧
Answer all Questions :
1. (i) By first taking the square root and then the cube root, find the sixth
root of :
( a³ - 1/a³ )² - 6( a - 1/a )( a³ - 1/a³ ) + 9( a - 1/a )². (12 marks).
(ii) Prove that the left-hand side is always equal to the right-hand side
in the following equation :
bc(b - c) + ca(c - a) + ab(a - b) = - (b - c)(c - a)(a - b).
(13 marks).
2. (i) Solve the equation : (x - 1)/(√x - 1) = 3 + (√x + 1)/2. (12 marks).
(ii) Rationalise the denominator and then find the value of :
(√(1 + x) + √(1 - x)) / (√(1 + x) - √(1 - x)) , when x = 2b / (b² + 1) . (13 marks).
3. (i) Compute by logarithms : ⁷√[ (0.⟦002001⟧)³(sin16° 23')² / (1.003)⁵(tan41° 16')² ] (12 marks).
(ii) Solve the following equation for x :
2(log x)² - 5(log x) + 2 = 0 . (13 marks).
4. (i) In an Arithmetic Progression the first term is 3 and the common
difference is 6. Show that the sum of 2n terms is always equal to
four times the sum of n terms. (12 marks).
(ii) In an A. P. the ratio of the 3rd term to the 6th term is 11:26 and the
sum of the first 4 terms is 34. Find the progression and the sum of
the first 8 terms. (13 marks).
⟦line⟧
Page 28
Solutions to Mid-year Exam., in Algebra
4th Secondary year, February, 1969.
1
1. Let the time now be x minutes after 5 o'clock.
then x = 25 + x/12 + 30 (ACB = 30)
∴ x - x/12 = 55 ∴ 11x/12 = 55 ∴ x = 60 minutes after 5
∴ the time now is exactly 6 o'clock Ans.
⟦Diagram of a clock with labels: B at 12, A at 6, C at 9, and an arrow at 5 labeled x min.⟧
2. (i) solve 6 x³+19 x²+x-6 = 0
By trial + error we discover that x = -3 satisfies the equation. Hence by
the remainder + factor theorems, (x+3) is a factor. Factoring, we get
(x+3) (6x² + x - 2) = 0 or (x+3) (3x+2) (2x-1) = 0
∴ x = -3
x = - 2/3 } Ans.
x = 1/2
(ii) (3x-7)/(x-2) + (2x-5)/(x-3) = (3x+7)/(x+2) + (2x+5)/(x+3)
∴ (3(x-2)-1)/(x-2) + (2(x-3)+1)/(x-3) = (3(x+2)+1)/(x+2) + (2(x+3)-1)/(x+3)
∴ 3 - 1/(x-2) + 2 + 1/(x-3) = 3 + 1/(x+2) + 2 - 1/(x+3)
1/(x-3) - 1/(x-2) = 1/(x+2) - 1/(x+3) ∴ (x-2-x+3)/((x-2)(x-3)) = (x+3-x-2)/((x+2)(x+3))
∴ 1/((x-2)(x-3)) = 1/((x+2)(x+3)) ∴ (x+2)(x+3) = (x-2)(x-3)
∴ x²+5x+6 = x²-5x+6 ∴ 10x = 0 ∴ x = 0 Ans.
Page 29
2
3. (i) A (x² - 2x) + B (x + 4) + C = 3x² + x + 25
∴ Ax² - 2Ax + Bx + 4B + C = 3x² + x + 25
∴ Ax² + (B - 2A) x + 4B + C = 3x² + x + 25 . Equating coefficients of like terms,
∴ A = 3 , B - 2A = 1 ∴ B - 6 = 1 or B = 7
4B + C = 25 ∴ 4 x 7 + C = 25 or C = -3
∴ A = 3 , B = 7 and C = -3 Ans.
Another method :
In the original identity, let x = 0 , then 4B + C = 25 ... ①
again let x = 2 , then 6B + C = 12 + 2 + 25 = 39 ... ②
6B + C = 39 ... ②
4B + C = 25 ... ① } subtract 2B = 14 ∴ B = 7 and C = -3
now let x = 1 , then A (1 - 2) + B (1 + 4) + C = 3 + 1 + 25 or
-A + 5 x 7 - 3 = 29
∴ A = 32 - 29 ∴ A = 3 , B = 7 and C = -3 Ans.
(ii) Solve : x² + xy + 2y² = 8 ... ①
2x² - 2xy - 3y² = 1 ... ②
Let y = mx ∴ x² + mx² + 2m²x² = 8 from ① ..... (1.a)
2x² - 2m x² - 3m²x² = 1 from ② ..... (2.a)
x² (1 + m + 2m²) = 8 } dividing, (1 + m + 2m²) / (2 - 2m - 3m²) = 8 / 1
x² (2 - 2m - 3m²) = 1 }
∴ 1 + m + 2m² = 16 - 16m - 24m² ∴ 26m² + 17m - 15 = 0
∴ (13m + 15) (2m - 1) = 0 ∴ m = 1/2 or m = -15/13
when m = 1/2 , from (1.a) , we get: x² + x²/2 + x²/2 = 8 or 2x² = 8
∴ x² = 4 ∴ x = ± 2 when x = 2 , y = mx = 1/2 x 2 = 1
and when x = -2 , y = 1/2 (-2) = -1
x = 2 } Ans. 1 x = -2 } Ans. 2
y = 1 } y = -1 }
when m = -15/13 then x² (1 - 15/13 + 2 x 225/169) = 8 or x² ( (169 - 13 x 15 + 450) / 169 ) = 8
∴ x² ( (169 - 195 + 450) / 169 ) = 8 ∴ x² ( 424 / 169 ) = 8 ∴ x² = (8 x 169) / 424 = 169 / 53
∴ x = ± 13 / √53 when x = 13 / √53 , y = -15/13 . 13 / √53 = -15 / √53 and when x = -13 / √53 , y = (-15/13) (-13 / √53) = 15 / √53
x = 13 / √53 } Ans. 3 x = -13 / √53 } Ans. 4
y = -15 / √53 } y = 15 / √53 }
Page 30
3
An alternative method
x² + xy + 2y² = 8 ⟦line⟧ ①
2x² - 2xy - 3y² = 1 ⟦line⟧ ②
multiply Eq (2) by 8 :
Subtract { 16x² - 16xy - 24y² = 8 ⟦line⟧ ③
{ x² + xy + 2y² = 8 ⟦line⟧ ①
15x² - 17xy - 26y² = 0 ⟦line⟧ ④
∴ (x - 2y) (15x + 13y) = 0
∴ y = 1/2 x or y = - 15/13 x
When y = x/2 from Eq. ① : x² + x(x/2) + 2(x/2)² = 8 or x² + x²/2 + x²/2 = 8
or 2x² = 8 ∴ x² = 4 ∴ x = ± 2 ∴ y = x/2 = ± 2/2 = ± 1
∴ x = 2 } Ans. 1 x = -2 } Ans. 2
y = 1 } y = -1 }
When y = - 15/13 x from Eq. ① : x² + x(- 15/13 x) + 2(- 15/13 x)² = 8 or
x² - 15/13 x² + 450/169 x² = 8 ∴ 169x² - 15x13x² + 450x² = 8 x 169
∴ 169x² - 195x² + 450x² = 1352 ∴ 424x² = 1352 ∴ x² = 1352/424
∴ x² = 169/53 ∴ x = ± 13/√53
When x = 13/√53 ∴ y = - 15/13 x or y = - 15/13 (13/√53) = - 15/√53
and when x = - 13/√53 ∴ y = - 15/13 x or y = - 15/13 (- 13/√53) = 15/√53
∴ x = 13/√53 } Ans. 3 x = - 13/√53 } Ans. 4
y = - 15/√53 } y = 15/√53 }
Page 31
4
4 (i) x³ + y³ + 1/x³ + 1/y³ = (x³ + 1/x³) + (y³ + 1/y³) = [(x + 1/x)³ - 3(x + 1/x)] + [(y + 1/y)³ - 3(y + 1/y)]
= a³ - 3a + b³ - 3b = a³ + b³ - 3(a + b)
= (a + b)(a² - ab + b² - 3) Ans. 1
= (1 + 2)(1² - 1x2 + 2² - 3)
= (3)(1 - 2 + 4 - 3) = 3 x zero = 0 Ans. 2
(ii) a³ + a - 8b³ - 2b + c + 6abc + c³ = a³ - 8b³ + c³ + 6abc + a - 2b + c
= [a³ + (-2b)³ + c³ - 3a(-2b)c] + [a - 2b + c]
= (a - 2b + c)(a² + 4b² + c² + 2ab - ac + 2bc) + (a - 2b + c)
= (a - 2b + c) [(a² + 4b² + c² + 2ab - ac + 2bc) + 1]
= (a - 2b + c)(a² + 4b² + c² + 2ab - ac + 2bc + 1) Ans.
5. after the first replacement, there are
x/2 gall. of Brandy in Cask P and
(50 - x/2) gall. " " " Q
At the beginning of the 2nd operation:
100 gall water P
50 gall Brandy Q
(x²/200) gall. of Brandy are removed from Cask P and
x(50 - x/2) / 50 gall. " " " " Q
Mixture Brandy
100 x/2 gall. ? = x * x/2 / 100
x ? = x²/200 gall.
50 gall. (50 - x/2) gall.
x ? ? = x(50 - x/2) / 50
x²/200 + x(50 - x/2) / 50 / 2 gall. of Brandy are deposited in P after 2nd replacement.
∴ (x/2 - x²/200) + (x²/200 + x(50 - x/2) / 50) / 2 = 17 or
100x - x² / 200 + x² + 4x(50 - x/2) / 2 = 17 ∴ 100x - x² / 200 + x² + 200x - 2x² / 2 = 17
∴ 100x - x² / 200 + 200x - x² / 400 = 17 ∴ 200x - 2x² + 200x - x² = 6800
∴ 3x² - 400x + 6800 = 0 ∴ (3x - 340)(x - 20) = 0
∴ x = 340/3 = 113 1/3 inadmissible
x = 20 gallons Ans.
Page 32
45
6. speed of train A = 22.5 mi/h = 22.5 x 22/15 ft/sec = 45/2 x 22/15 = 33 ft/sec.
speed " " B = 15 mi/h = 15 x 22/15 ft/sec = 22 ft/sec.
(i) when the two trains are travelling in
opposite directions (see Fig. I), points C and D
are separating at the rate of (33+22) ft/sec
= 55 ft/sec.
When the rear cars A and B just clear away
from each other, (see Fig. II) points C and D
have already separated by a distance
= (240+200) ft = 440 ft.
Time taken = total distance / rate of separation = 440 / 55 = 8 sec. Ans. 1
v₁ = 33 ft/sec. C
A ⟦line⟧→
240 ft v₂ = 22 ft/sec
Fig. I ←⟦line⟧ B
200 ft
A ⟦line⟧→ C
D ←⟦line⟧ B
Fig. II
(ii) When the two trains are travelling in the
same direction, (See Fig. III), points C and D
are separating at the rate of (33-22) ft/sec
= 11 ft/sec.
When the rear car A of the faster train
and the front car D of the slower train
just clear away from each other,
(see Fig. IV), points C and D have already
separated by a distance of 240 ft which
is the length of the faster train.
240 ft
A ⟦line⟧→ C v₁ = 33 ft/sec
200 ft
B ⟦line⟧→ D v₂ = 22 ft/sec
Fig. III
A 240 ft
⟦line⟧→ C
B 200 ft
⟦line⟧→ D
Fig. IV
∴ Time taken = distance / rate of separation = 240 / 11 = 21 9/11 sec. Ans. 2
Page 33
SHAMASH SECONDARY SCHOOL
Mid-Year Examination, February, 1969.
Subject: Algebra
Date: 17/2/1969.
Class: 4th Year, Secondary
Time: 8:30-11:30 a.m.
Five questions only are to be attempted.
1. The time now is x minutes after five and the two hands of the watch
stand in a straight line on opposite sides of the centre of the dial of the
watch. Find x and state, in words, the correct time. (20 marks)
2. (i) Find the value of x from the following equation :
6 x³ + 19 x² + x - 6 = 0. (10 marks)
(ii) Solve the following equation, using the shortest possible method,
by first reducing each fraction to a simpler form :
3 x - 7 2 x - 5 3 x + 7 2 x + 5
⟦line⟧ + ⟦line⟧ = ⟦line⟧ + ⟦line⟧ . (10 marks)
x - 2 x - 3 x + 2 x + 3
3. (i) In the following equation, A, B, and C are constants and the
equation is true for all values of x. Find the values of A, B and C.
A(x² - 2x) + B(x + 4) + C = 3x² + x + 25. (10 marks)
(ii) Solve the following equations simultaneously :
x² + xy + 2y² = 8 ...............(1)
2x² - 2xy - 3y² = 1 ...............(2) (10 marks)
4. (i) If x + 1/x = a and y + 1/y = b , find the value of the expression
(x³ + y³ + 1/x³ + 1/y³) in terms of "a" and "b". Hence or otherwise find the
value of (x³ + y³ + 1/x³ + 1/y³) if a = 1 and b = 2. (10 marks)
(ii) Resolve the expression a³ + a - 8 b³ - 2b + c + 6abc + c³ into two
factors one of which is (a - 2b + c). (10 marks)
5. A cask P is filled with 100 gallons of water, and a cask Q with
50 gallons of brandy; x gallons are drawn from each cask, mixed and replaced;
and the same operation is repeated. Find x when there are 17 gallons of
brandy in P after the second replacement. (20 marks)
6. Two trains A and B are travelling on two railway tracks which are
parallel to each other. Train A is 240 ft long and it is travelling at 22.5
miles per hour. Train B is 200 ft long and is travelling at the rate 15 miles
per hour. Find the length of time in seconds from the instant when the heads
of the front cars of the two trains are together, to the instant when the
P. T. O.
Page 34
- 2 -
Mid-Year Exam. Cont., in Algebra ; 4th Year, Secondary, 17/2/1969.
two trains just clear away from each other in the two cases :
(i) When the two trains are travelling in opposite directions.
(ii) when the two trains are travelling in the same direction.
(20 marks).
⟦line⟧
2. (i) Find the value of x from the following equation :
⟦illegible⟧
(10 marks)
(ii) Solve the following equation, using the shortest possible method,
by first reducing each fraction to a simpler form :
⟦illegible⟧
(10 marks)
3. (i) In the following equation, A, B and C are constants and the
equation is true for all values of x. Find the values of A, B and C.
A(x - 2)(x - 3) + B(x + 4) + C = x² + x + 25. (10 marks)
(ii) Solve the following equations simultaneously :
x² + xy + 2y² = 8 ........... (1)
2x² - 3xy - 5y² = 7 ........... (2)
(10 marks)
4. (i) If x + y = 5 and xy = 4 find the value of the expression
x³ + y³. Hence or otherwise find the
value of (x² + y² + ⟦illegible⟧) (x + y + ⟦illegible⟧) if x = 4 and y = 1. (10 marks)
(ii) Resolve the expression a² - b² + 2a - 4b - 3 into two
factors one of which is (a - 2b + 1). (10 marks)
5. A cask B is filled with ⟦illegible⟧ gallons of water and a cask A with
80 gallons of brandy. x gallons are drawn from each cask, mixed and replaced,
and the same operation is repeated. Find x when there are 17 gallons of
brandy in A after the second replacement. (20 marks)
6. Trains A and B are travelling on two railway tracks which are
parallel to each other. Train A is 240 ft long and it is travelling at 22.5
miles per hour. Train B is 270 ft long and is travelling at the rate 15 miles
per hour. Find the length of time in seconds from the instant when the
of the front ends of the two trains are opposite to the instant when the
P.T.O.
Page 37
Make-up Exam. 2nd Quarter ⟦Fourth Grade⟧
17/1/1969
I. (i) Find the value of x² - 1/y when x = -1/2 & y = -3 (6 marks)
(ii) Solve the equation x/3 + (x-1)/2 = 7 (7 marks)
(iii) Find x if 2x + y = 4 and 3y + 4 = 6x (7 marks)
II (i) If t = ∛((x² + 4y) / 2yz) , find z in terms of x, y and t. (10 marks)
(ii) If F = av - b/v² and if F = 4 when v = 5 and F = 36 when
v = 10, find the values of "a" and "b" and the value of F when v = 20
(10 marks)
III. a man can cycle at x m.p.h. in still air. His speed increases
y m.p.h. when he cycles with the wind, and decreases y m.p.h. when
he cycles against the wind. The difference in his time to cycle one mile
with the wind and one mile against the wind is z hours. Find a
formula for z in terms of x and y, and find x if y = 2, z = 1/3.
(20 marks)
IV. In how many days will "a" horses eat 1/n th of the corn of a field
the whole of which can be eaten by "b" horses in "c" days.
(20 marks)
V. Find the square root of:
16x⁴ + 16/3 x²y + 8x² + 4/9 y² + 4/3 y + 1
showing your steps neatly. (20 marks)
Page 38
SHAMASH SECONDARY SCHOOL
Subject: Algebra
Class: 4th Year Secondary
Date: 7/1/1969
Time: 10:15-11:45
Attempt all questions:
1. The expression 2 x³ + Ax² + Bx - 4 is exactly divisible by x²-4.
Find the values of A and B and find the remaining factor.
(20 marks)
2. Find the square root of:
4x⁴ - 3x⁵ - 3x³ + 9/4 x⁶ + 5/3 x² - 2/3 x + 1/9
(20 marks)
3. Which of the following equations is always true, which is sometimes
true and which is never true? Find the values of x which satisfy the
equatioh which is sometimes true.
(a) 4(x²-1) + 2(x + 3) = 2 + 2x(1 + 2x)
(b) x(6x + 1) = 2x + 1
(c) x(x + 2) = 2(x - 2)
(20 marks)
4. (i) Solve simultaneously the following equations:
1/x + 1/y + 3/z = 2½ ⟦line⟧ (1)
2/x + 4/y - 6/z = 2 ⟦line⟧ (2)
3/x + 5/y + 7/z = 2 5/6 ⟦line⟧ (3)
(ii) Simplify the following expression to simplest form:
x/y + y/x - 1 / (x²/y² + x/y + 1) . (1 + y/x) / (x - y) ÷ (1 + y³/x³) / (x²/y - y²/x)
(20 marks)
5. A man bought "A" lbs of coffee for a certain sum of money. He
kept "B" lbs to himself and sold the remainder at "C" shillings a pound
more than he paid for it. He found that he received for this portion
an amount equal to the original sum of money which he paid for the whole.
Find the original sum of money which he paid for the whole. (20 marks)
Page 40
SHAMASH SECONDARY SCHOOL
Monthly Examination, November 1968
Subject: General Mathematics Date: 18/11/1968.
Class : 4th Year Secondary Time: 8:30 - 10:00 a.m.
Number:
Name:
1. Give the English Equivalent of the following, filling the blanks in
this sheet and hand it over with your examination book.
Numerals = figures | 1- Numerals
Digits | 2- Digits
Subtraction | 3- Subtraction
Factors | 4- Factors
The index or exponent of the power | 5- Exponent of the power
Multiple | 6- Multiple
Consecutive even numbers | 7- Consecutive even numbers
⟦Consecutive⟧ odd ⟦numbers⟧ | 8- Consecutive odd numbers
The integral part of a number | 9- The integral part of the number
Prime numbers | 10- Prime numbers
The least common Denominator | 11- The least common denominator
An improper fraction | 12- Improper fraction
The reciprocal of a number | 13- The reciprocal of the number
Terminating decimals | 14- Terminating decimal fractions
Recurring or Repeating decimals | 15- Recurring decimal fractions
The percentage error | 16- The percentage error
Ratio + Proportion | 17- Ratio and Proportion
The mean proportional between two numbers | 18- The mean proportional between two numbers
The Dividend | 19- Shareholder's profit (stockholder's profit)
Axiom | 20- Axiom
Postulate | 21- Postulate
an acute angle | 22- Acute angle
an obtuse ⟦angle⟧ | 23- Obtuse angle
a Reflex ⟦angle⟧ | 24- Reflex angle
a segment of a circle | 25- Segment of a circle
a Sector ⟦of a circle⟧ | 26- Sector of a circle
The Data | 27- Knowns
The unknowns | 28- Unknowns
Two Complementary angles | 29- Two complementary angles
⟦Two⟧ Supplementary ⟦angles⟧ | 30- Two supplementary angles
an equilateral polygon | 31- Equilateral polygon
an isosceles triangle | 32- Isosceles triangle
The rhombus | 33- The rhombus
The Locus | 34- The geometric locus
The secant to a circle | 35- The secant line to the circle
The removal + insertion of brackets | 36- Removal and insertion of brackets
Transposition from one side of an equation to the other | 37- Transposing equation terms from one side to the other
Identity | 38- Identity
Inequality | 39- Inequality
- To be continued -
Page 41
- 2 -
Number:
Name:
40- A homogeneous algebraic expression ⟦line⟧ 1 mark
A homogeneous algebraic expression
41- The degree of an algebraic expression ⟦line⟧ "
The degree or the dimension of an algebraic expression
42- The literal coefficient ⟦line⟧ "
The literal coefficient
43- An algebraic expression of the second degree ⟦line⟧ "
An algebraic expression of the second degree
or a quadratic expression
44- The two terms of a fraction are its numerator and denominator ⟦line⟧ 2 marks
The two terms of a fraction are its numerator
and denominator
45- In every process of division there is a dividend, a divisor, a quotient, and in some cases a remainder. 5 marks
In every process of division there is a dividend, a divisor, a quotient + in some
cases a remainder
46- The perpendicular bisectors of the sides of a triangle meet at the center of the circumscribed circle ⟦line⟧ "
The perpendicular bisectors of the sides of a triangle meet at the centre
of the circumscribed circle.
47- The medians of a triangle meet at one point which divides each of them into two-thirds from the vertex "
and one-third from the base. This point is called the centroid of the triangle.
The medians of a triangle meet at a point which divides each of them
two thirds from the vertex and one third from the base. This point is
called the centroid of the triangle.
48- We measure the length of a straight line and find it equals 61.5 cm. Then we later find its exact length is 60 cm. "
In this case we say the absolute error is ⟦line⟧
and the relative error is ⟦line⟧ and the percentage error is ⟦line⟧
We measure the length of a st. line + we find that it is equal 61.5 cms. We then find that
its exact length is 60 cms. In this case we say that the absolute error is 1.5 cm, the relative error is 1.5/60
and the percentage error is 2.5%
49- The value of the expression 5309.72 to the nearest four significant figures is ⟦line⟧ 5 marks
The value of 5309.72 correct to 4 significant figures is 5310.00
50- The equation 3x² - 2xy + y = 5z - 3z is an equation of degree ⟦line⟧ in ⟦line⟧ "
unknowns ⟦line⟧
The equation 3x² - 2xy + y = 5z - 3z is a quadratic equation in three unknowns.
(75 marks)
(II) Fill in the blanks in the following equations:-
(2.5 marks) | 1. | one furlong = | ( 10 ) | chains= | ( 1/8 ) | mile
" | 2. | one chain = | ( 22 ) | yards = | ( 100 ) | links
" | 3. | one statute mile = | ( 1760 ) | yds. = | ( 5280 ) | ft.
" | 4. | one nautical mile = | ( 6080 ) | ft.
" | 5. | one sq. chain = | ( 484 ) | sq. yds.
" | 6. | one acre = | ( 10 ) | sq. ch. = | ( 4840 ) | sq. yds.
" | 7. | one gallon = | ( 8 ) | pints
" | 8. | one bushel = | ( 8 ) | gallons = | ( 4 ) | pecks
" | 9. | one English ton = | ( 2240 ) | lbs. = | ( 1016 ) | kilograms
" | 10. | one English ton = | ( 20 ) | cwt. = | ( 80 ) | qr. = | ( 160 ) | stones.
1 quarter = 1/4 of one cwt = 28 lbs = 2 stones
1 stone = 14 lbs
(25 marks).
Page 42
SHAMASH SECONDARY SCHOOL
Monthly Examination, November 1968
No.::
Name::
Subject:: General Mathematics
Date:: 18/11/1968.
Class :: 4th Year Secondary
Time:: 8:30 - 10:00 a.m.
1. Give the English Equivalent of the followinh, filling the blanks in
this sheet and hand it over with your examination book.
1- Digits
2- Places
3- Subtraction
4- Factors
5- Exponent of power
6- Multiple
7- Consecutive even numbers
8- Consecutive odd numbers
9- The integer part of the number
10- Prime numbers
11- Lowest common denominator
12- Vulgar fraction
13- Reciprocal of the number
14- Terminating decimals
15- <del>Decimals</del> ⟦Recurring⟧
16- Percentage error
17- Ratio and proportion
18- Mean proportional between two numbers
19- Shareholder's profit (dividend)
20- Axiom
21- Postulate
22- Acute angle
23- Obtuse angle
24- Reflex angle
25- Segment of a circle
26- Sector of a circle
27- Knowns
28- Unknowns
29- Two complementary angles
30- Two supplementary angles
31- Equilateral polygon
32- Isosceles triangle
33- Rhombus
34- Locus
35- Secant line of the circle
36- Removing and inserting brackets
37- Transposing terms of the equation from one side to the other
38- Identity
39- Inequality
- Continued -
Page 43
- 2 -
Number::
Name::
40 - Homogeneous algebraic expression
41 - Degree of the algebraic expression
42 - Literal coefficient
43 - Algebraic expression of the second degree
44 - The terms of a fraction are its numerator and its denominator
45 - In every division process, there is a dividend, a divisor, a quotient, and in some cases, a remainder.
46 - The perpendicular bisectors of the sides of a triangle meet at the center of the drawn circle ⟦line⟧
47 - The medians of a triangle meet at a single point that divides each of them into two-thirds from the vertex side
and one-third from the base side. This point is called the center of gravity (centroid) of the triangle.
48 - We measure the length of a straight line and find it equals 61.5 cm. Then we later find that its exact length is 60 cm.
In this case, we say the absolute error is ⟦line⟧
and the relative error is ⟦line⟧ and the percentage error is ⟦line⟧
49 - The value of the expression 53.072 to the nearest four significant figures is ⟦line⟧
50 - The equation 3x^2 - 2xy + y^2 = 45 - 4z is an equation of the ⟦line⟧ degree in
⟦line⟧ unknowns.
(75 marks)
(II) Fill in the blanks in the following equations:-
1. one furling = ( ) chains = ( ) mile
2. one chain = ( ) yards = ( ) links
3. one statute mile = ( ) yds. = ( )
4. one nautical mile = ( ) ft.
5. one sq. chain = ( ) sq. yds.
6. one acre = ( ) sq. ch. = ( ) sq. yds.
7. one gallon = ( ) pints
8. one bushel = ( ) gallons = ( ) pecks
9. one English ton = ( ) lbs. = ( ) kilograms
10. one English ton = ( ) cwt. = ( ) qr. = ( ) stones.
Page 44
SHAMASH SECONDARY SCHOOL:
Number ::
Name ::
Monthly Examination, November 1968:
Subject: General Mathematics:
Date: 18/11/1968.:
Class : 4th Year Secondary:
Time: 8:30 - 10:00 a.m.:
1. Give the English Equivalent of the followinh, filling the blanks in
this sheet and hand it over with your examination book.
1- Digits
2- Places
3- Subtraction
4- Factors
5- Exponent of power
6- Multiple
7- Consecutive even numbers
8- Consecutive odd numbers
9- The integer part of the number
10- Prime numbers
11- Lowest common denominator
12- Vulgar fraction
13- Reciprocal of the number
14- Terminating decimals
15- <del>Recurring decimals</del>
16- Percentage error
17- Ratio and proportion
18- Mean proportional between two numbers
19- Shareholder's profit (dividend)
20- Axiom
21- Postulate
22- Acute angle
23- Obtuse angle
24- Reflex angle
25- Segment of a circle
26- Sector of a circle
27- Knowns
28- Unknowns
29- Complementary angles
30- Supplementary angles
31- Equilateral polygon
32- Isosceles triangle
33- Rhombus
34- Locus
35- Secant line of a circle
36- Removing and inserting brackets
37- Transposing terms of the equation from one side to the other
38- Identity
39- Inequality
To be continued
Page 45
- 2 -
Number ::
Name ::
40- Homogeneous algebraic expression
41- Degree of the algebraic expression
42- Literal coefficient
43- Second-degree algebraic expression
44- The two terms of a fraction are its numerator and denominator
45- In every division process there is a dividend, a divisor, and a quotient, and in some cases a remainder of the division.
46- The perpendicular bisectors of the sides of a triangle meet at the center of the circumscribed circle ⟦line⟧
47- The medians of a triangle meet at a single point that divides each of them into two-thirds from the vertex side and one-third from the base side. This point is called the centroid of the triangle.
48- We measure the length of a straight line and find it equals 61.5 cm. Then we find later that its exact length is 60 cm.
In this case we say that the absolute error is ⟦line⟧
And the relative error is ⟦line⟧ and the percentage error is ⟦line⟧
49- The value of the quantity 5309.72 to the nearest four significant figures is ⟦line⟧
50- The equation 3x2 - 2xy + y2 = 45 - xz is an equation of degree ⟦line⟧ in ⟦line⟧ unknowns.
(75 marks)
(II) Fill in the blanks in the following equations:-
1. one furlong = ( ) chains= ( ) mile
2. one chain = ( ) yards = ( ) links
3. one statute mile = ( ) yds. = ( ) ft.
4. one nautical mile = ( ) ft.
5. one sq. chain = ( ) sq. yds.
6. one acre =( ) sq. ch. = ( ) sq. yds.
7. one gallon = ( ) pints
8. one bushel = ( ) gallons = ( ) pecks
9. one English ton = ( ) lbs. ⟦=⟧ ( ) kilograms
10. one English ton = ( ) cwt. = ( ) qr. = ( ) stones.
(25 marks).