A Summary of Concepts Needed to be Successful in Mathematics
The following sheets list the key concepts that are taught in the specified math course. The sheets
present concepts in the order they are taught and give examples of their use.
WHY THESE SHEETS ARE USEFUL –
• To help refresh your memory on old math skills you may have forgotten.
• To prepare for math placement test.
• To help you decide which math course is best for you.
A Summary of Concepts Needed to be Successful in Mathematics
The following sheets list the key concepts that are taught in the specified math course. The sheets
present concepts in the order they are taught and give examples of their use.
WHY THESE SHEETS ARE USEFUL –
• To help refresh your memory on old math skills you may have forgotten.
• To prepare for math placement test.
• To help you decide which math course is best for you.
Directions Please show all of your work for each problem.If.docxkimberly691
Directions
: Please show all of your work for each problem.
If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word.
There is a tutorial on using this equation editor in Module 1 Lecture Notes.
You also have the option of hand writing your work and scanning it.
1.
Find the greatest common factor.
4, 6, 12.
2.
Factor.
24
x
3
+ 30
x
2
3.
Factor out the GCF with a negative coefficient.
–24
m
2
n
6
– 8
mn
5
– 32
n
4
4.
Factor completely by factoring out any common factors and then factoring by grouping.
6
x
2
– 5
xy
+ 6
x
– 5
y
5.
The GCF of 15
y
+ 20 is 5.
The GCF of 15
y
+ 21 is 3.
Find the GCF of the product (15
y
+ 20)(15
y
+ 21).
6.
The area of a rectangle of length
x
is given by 15
x
–
x
2
.
Find the width of the rectangle in terms of
x
.
7.
Factor the trinomial completely.
x
2
+ 8
x
– 9
8.
Factor the trinomial completely.
2
x
2
+ 16
x
+ 32
9.
Complete the following statement.
6
a
2
– 5
a
+ 1 = (3
a
– 1)(__
?
__)
10.
State whether the following is true or false.
x
2
– 7
x
– 30 = (
x
+ 3)(
x
– 10)
11.
Factor completely.
x
2
+ 11
x
+ 28
12.
Factor completely.
15
x
2
+ 23
x
+ 4
13.
Factor completely.
6
z
3
– 27
z
2
+ 12
z
14.
The number of hot dogs sold at the concession stand during each hour
ii
h
after opening at a soccer tournament is given by the polynomial 2
h
2
– 19
h
+ 24.
Write this polynomial in factored form.
15.
Find a positive value for
k
for which the polynomial can be factored.
x
2
–
kx
+ 29
16.
Factor completely.
9
x
2
+ 4
17.
Determine whether the following trinomial is a perfect square.
If it is, factor the binomial.
x
2
– 12
x
+ 36
18.
Factor completely.
25
x
2
+ 40
xy
+ 16
y
2
19.
Factor.
s
2
(
t
–
u
) – 9
t
2
(
t
–
u
)
20.
State which method should be applied as the first step for factoring the polynomial.
6
x
3
+ 9
x
21.
State which method should be applied as the first step for factoring the polynomial.
2
a
2
+ 9
a
+ 10
22.
Solve the quadratic equation.
5
x
2
+ 17
x =
–6
23.
Solve the quadratic equation.
3
x
(2
x
– 15) = –84
24.
The sum of an integer and its square is 30.
Find the integer.
25.
If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm
2
.
What were the dimensions of the original square?
26.
Write in simplest form.
27.
Write in simplest form.
28.
Write the expression in simplest form.
29.
The area of the rectangle is represented by 5
x
2
+ 19
x
+ 12.
What is the length?
5
x
+ 4
30.
Multiply.
31.
Multiply.
32.
Divide.
33.
Divide.
34.
Perform the indicated operations.
35.
Find the area of the rectangle shown.
36.
Subtract.
Express your answer in simplest form.
37.
Subtract.
Express your answer in simplest form.
38.
Add.
Express your answer in simplest form.
39.
Add.
Express yo.
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1. MATHS
SAMPLE QUESTION PAPER
Class: I Maximum Marks: 45
Time duration: 90 minutes No of pages:2
General Instructions:
All questions are compulsory.
Choose the correct option and write inside the space given
Maintain clean Handwriting, 3m are given for handwriting.
1. What number comes after this numbers ? 5m
85 99
52 87
36 19
91 45
42 30
2. Ring the greater number 3m
a) 25,35,12,20,23
b) 56,45,52,46,32
c)100,121,99,132,145
3. Add 6m
11 16 45 23
24 23 16 45
+ 26 19 18 16
▬ ▬ ▬ ▬
▬ ▬ ▬ ▬
4. Subtract using number line 3m
a) 15-7
b) 12-6
c) 20-16
5. complete the following using hundred grid 5m
34+14=
67+30=
78+16=
6+39=
40-26=
71-36=
84-16=
6. Multiply 6m
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2
2. 50 82 93
X 4 X 6 X 4
▬▬ ▬▬ ▬▬
▬▬ ▬▬ ▬▬
7. Draw both hour hand and minute hand to show time. 6m
a) 4:30 b) 7.30 c) 11.20
8. A farmer had 318 sheep. 150 of them were black. 72 of them were white, while the rest of the
sheep were brown in color. How many sheep were brown in color? 3m
9. Answer the following for for given pictograph 5m
a) What is the total number of fruits in the store
b) How many apple are there
c) What is the total number of mango
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