Subject: Mathematics
MYP Year: 4
Revision Sheet for holidays
Level 1
1. If p and q represent rational numbers in the equation :
1
3
+ 2+1
2−1
√
√
appropriate mathematical strategy , show that p = -2 and q= 4
2. Example :
Understand above example to solve following equations :
3.
= 𝑝 + 𝑞√2, then using
Answer :
1. A. x= 1
b. x= 2
c. x=3
d. x=0
e. x= -1
f. x=-1
g. x= -4
h. x=0
i. x=-4
j. x= -2
k. x= 6
l.
x= -2
m. 4x+2= -1 hence , x = -3/4
n. 2x-6=3 hence, x = 9/2
o. x= 0
p. -2+x= 2 hence, x= 4
4. A. x= 3
b. x= 0
c. x=-2
d. x= 3
e. x=3
f. x= -2
g. 2-5x=2x hence, x= 2/7
h. x-1= -3 hence, x= -2
i. 2(x-2)=-3x+1 hence, 2x-4 = -3x+1 , x= 1
5.
ans
a. X^2+x-12
b. -2x^2+11x-15
6. Factorize the following expressions :
a. 4-9y2
b. 9a-16a3
c. 4x2y2-1
Ans
a. (2-3y)(2+3y)
b. A(3-4a)(3+4a)
c. (2xy-1)(2xy+1)
7.
Ans
a. Y = (10-5y)/2
b. Y= (20-3x)/4
c. Y= 2x-8
d. Y= (14-2x)/7
e. Y= (20-5x)/2
f. Y= (2x+12)/3
8.
Ans
a. a+2
b. 1/(a-2b)
c.
Ans:
3𝑥−1
12
9.
A is the set of prime numbers less than 10, B is the set of odd numbers less than 10
and C is the set of even numbers less than 10.
Identify the correct statement from following ?
A⊂B
B⊂A
A⊂C
C⊂A
B⊂C
C⊂A
None
Level 2:
10.
Ans
11.
Ans
i.
ii.
iii.
iv.
v.
X= y/(1-y)
X= (2y+3)/ (1-y)
X= (3y+1)/(3-y)
X= (y-2)/(y-5)
X= (2y+1)/(y+4)
vi.
vii.
viii.
ix.
X= (3y-7)/(2y+3)
X= (3y-1)/(y-1)
X= (-4y-3)/(y+2)
X= 2y/(y+3)
12.
Answer : Gradient = 5/4
Gradient implies that Tan takes 5 seconds to walk 4 meter distance.
Speed = distance / time which is the gradient of line hence constant. Can justify finding speed in any
case from graph.
13.
70 people were asked whether they like running, cycling or swimming. 32 people answered
they like running, 31 people like cycling and 36 people like swimming. 9 people answered
both running and cycling, 15 people answered both running and swimming, 12 people
answered cycling and swimming both and two people liked none of the three sports.
i) Represent the above information in Venn Diagram.
ii) Apply appropriate mathematical strategy to find the number people who liked all three
sports. Ans 5
Use appropriate mathematical strategy to find the number of people who likes exactly two
types of sports. Ans Exactly two = 4+11+7 = 22
Level 3:
14. When you work in a job that pays an hourly wage, you receive a certain dollar amount for
each hour you work. You may receive a higher overtime rate for hours you work beyond a
stated number of hours per week.
When you work in a job that pays a salary, you receive a certain dollar amount per week or per month. You
may be expected to be at work between certain hours of the day, but earnings are not directly linked to the
number of hours you work.
Commissions are often earned by salespersons and are usually a certain percentage of the value of sales in
dollars.
Maria is starting a job in a company. She is offered 3 options for her pay. Choose one option and
answer the questions.
Option A: Maria earns a monthly salary of $1800 plus a 4% commission on her total monthly
sales(in dollars).
Option B Maria earns 9% commission on her total monthly sales(in dollars).
Option C: Maria earns a monthly salary of $1800 regardless of her total monthly sales(in dollars).
Keeping in view all the three options, answer the following questions.
a) Model an equation connecting monthly sales(s) with the monthly income earned (e) in all
the three options.
b) Compare and contrast all three payment/salary options for the average monthly sales of
$40000.
c) Previous year records show that monthly sales of company generally fluctuate
between$25000-$40000. Use appropriate mathematical strategy to estimate range of her
monthly salary for both Options A and B.
Answer :
a. Option A: e = 1800+0.04s
Option B: e= 0.09s
Option C : e= 1800
b. for sales of $40000
Option A
$3400
Option B
$3600
Option C
1800
Option B would be paying her the most.
c. For the range of sales as $25000-40000,
Option A
$2800-3400
Cr B and C
Option B
$2250-3600
Option C
1800
1. Describe any three patterns observed in the table above
2. Generalize the formula connecting T and L
3. Generalize the formula connecting T and B, when
a) B is an even number
b) B is an odd number
4.
5. Verify the formula for Q3
6. Justify the formula for T and L
ANS