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‫ دبي‬, ‫العالمية‬
‫مدرسة جيه اس اس‬
ِ
JSS INTERNATIONAL SCHOOL, DUBAI
GRADE: 09
Max Marks: 80
FIRST TERM EXAM (Model question paper)
MATHEMATICS
(Two hours and Thirty minutes)
(Candidates are allowed additional 15 minutes for only reading the paper. You
are NOT allowed to start writing during this time.)
The Question Paper consists of two sections A and B. Candidates are required to
attempt all the questions from Section A and Any FOUR from Section B.
All working, including rough work, should be done on the same sheet as, and adjacent to,
the rest of the answer. The intended marks for questions or parts of questions are given in
brackets [ ].
SECTION A
(4*10 = 40)
(ANSWER ALL THE FOUR)
Question 1
3+ √2
(a) Find the value of m and n if
3− √2
= m + n√2
(3)
(b) On what sum of money will the difference between simple interest and compound interest
for 2 years at 5% per annum is 50$ ?
(4)
1
1
𝑎
𝑎2
(c) If a - = 3 find 𝑎2 + 3a +
-
3
𝑎
(3)
Question 2
(a) Factorise (2𝑥 − 𝑦)2 – 14x + 7y – 18
(3)
(b) Solve the following simultaneous equations by cross multiplication method
8x + 13y – 29 = 0 and 12x – 7y – 17 = 0
(4)
(c) Use method of contradiction to show that 5 is an irrational number.
(3)
1|5
Question 3
(a) If a+b+c= 14 and a²+b²+c² = 74 find the value of ab+bc+ca.
(b) Two pillars 15 feet and 35 feet high are 15 feet apart. Find the distance between the
tops.[3]
(3)
(c)A certain sum amounts to Rs 5292 in 2 years and to Rs 5556.60 in 3 years at compound
interest. Find the rate and sum.
(4)
Question 4
(a) The difference between simple interest and compound interest on a certain sum is 54.40$
for 2 years at 8 percent per annum,find the sum.
(3)
(b) Evaluate
(4)
(c ) If a – b = 4 and a + b = 6; find :
(3)
SECTION B
(4*10 = 40)
(ANSWER ANY FOUR)
Question 5
(a)
Solve the following equations by substitution method
6x  7 y  7
7y  x  8
(4)
(b)Find the compound interest on Rs7600 for 2 ½ years at 10% per annum compounded
annually.
(3)
(c) Factorize
a 2 (b  c)  (b  c)3
9a 2 
Question 6
2|5
1
4
 2  12a 
2
9a
3a
(3)
(a) A is 20 years older than B.5 years ago,A was 3 times as old as B.
Find their present ages.
(b)Rationalise the denominator of
(3)
1
√6+√5√11
(c)State and prove Pythagoras theorem.
(4)
Question 7
(a)Solve for x and y,
8x . 4y = 1 and 27y = 9 . 3x
(3)
(b)Solve by cross multiplication method :
2
𝑥
3
5
4
𝑦
𝑥
𝑦
+ = 13 ; − = −2
(3)
(c )The sum of the two digit number and the number obtained by reversing the order of the
digits is 99. Find the number,if the digits differ by 3.
(4)
Question 8
(a) Simplify (3+2) (4+7)
(3)
(b)2x . 5y . 7z = 98x103, find x+y+z.
(4)
(c) Find the values of “a” and “b” in
5+3√2
5−3√2
= a + b 2
(3)
Question 9
3
(a) Simplify 5−
√3
2
+ 5+√3
(3)
(b) Find the amount for 36000aed compounded annually for two years if the rate of interest
are 10% for first year and 12% for second year.
(4)
(c) If x – y = 7 and 𝑥 3 - 𝑦 3 = 133 find the value of xy and 𝑥 2 + 𝑦 2
(3)
Question 10
(a) Factorise (𝑥 2 + 𝑦 2 − 𝑧 2 )2 - 4𝑥 2 𝑦 2
(3)
(b) Seven times a two-digit number is equal to four times the number obtained by reversing
the order of digits. Find the number if the difference between its digits is 3.
(4)
(c) If a  0 and a 
3|5
1
= 4 find
a
i) a 2 
1
a2
ii) a 4 
1
a4
iii) a 3 
1
a3
(3)
Question 11
(a) Solve the following by elimination method
5y x
 8
2 3
y 5x

 12
2 3
(b) Evaluate
4−Ö5
4+Ö5
(3)
4+Ö5
+ 7−Ö5
(3)
(c) Find the amount and the compound interest on 12,000aed in 3 years at 5%; interest
being compound annually.
(4)
…………………………………………………………………………………………………
4|5