WorksheetsINTENSIVE 24/7 TOUR 1
Total questions: 131
Worksheet time: 1hrs 16mins
Which of the followings is NOT correct?
(x+a)(x+b)=x2+(a+b)x+ab
(a+b)3=a3+3a2b+3ab2+b3
(a+b)3=a3+3a2b−3ab2+b3
(a+b+c)2=a2+b2+c2+2ab+2ac+2bc
Which of the followings is CORRECT?
a3+b3=(a+b)(a2−ab+b2)
a3−b3=(a+b)(a2−ab−b2)
(a+b)3=a3−3a2b+3ab2−b3
(a−b)3=a3+2a2b−2ab2+b3
4−(4x−1)2x3x2(1−16x2)=
6+2x1
2+2x1
2−2x1
6−2x1
Simplification shortcut:
1) Find ______________.
2) Choose the smallest possible number belonging to this ___________.
etc.
domain
root
x
replacement
Fill in the blank.
The lowest (or least) common __________ of two or more numbers is the smallest number that they will all divide into exactly.
multiple
divide
addition
subtraction
To find the lowest common multiple, systematically test the multiples of the ________ number until you find the first one that all the other numbers go into.
largest
lowest
average
smallest
Find the lowest common multiple number of 6 and 8.
24
16
48
72
Being able to find highest common factors is useful in many areas of mathematics, such as _________ and algebra.
fractions
functions
geometry
percent
The highest common factor (HCF) of two or more numbers is the _________ whole number that divides exactly into them.
largest
smallest
lowest
average
What is the HCF of the three numbers 5, 20 and 25?
5
20
25
15
A recurring decimal is one in which a single digit, or a group of digits, is endlessly __________.
repeated
divided
multiplied
shortened
If the decimal has a single digit that repeats, place a dot above the ____________ digit.
repeating
shortened
multiple
endless
When the repeating pattern contains two or more digits, place a dot above the ______________ digits in the pattern.
first and last
first
last
first and second
The number of decimal places in a terminating decimal indicates the number of zeros in the _____________ when it is converted to fraction form.
denominator
nominator
There are three methods for converting recurring decimals to fractions are shown below:
calculator method
using denominators of 999
using nominators of 999
algebraic method
For a whole number that ends in zeros, you need extra information about how that number was rounded before determining how many significant figures it has.
TRUE
FALSE
Zeros at the ____ of a decimal are significant.
end
beginning
_______________ is used to approximate a number to a value that is easier to use but close to the real value.
Truncating
Rounding off
Trailing zeros
Rounding decimals
_______________ cuts off part of the number's value.
Truncating
Rounding off
Trailing zeros
Rounding decimals
Two directly ________________ quantities increase or decrease at the same rate; for example, if one doubles, so does the other.
proportional
constant
variable
rounding
The value of y is inversely proportional to x.
If y =20 when x=8, find y when x=10/
16
12
8
24
As the denominator of a fraction gets bigger, the value of the fraction itself gets ___________.
smaller
bigger
higher
You can use ___________________ to write very large and very small numbers.
standard form
rounding off
truncating
hyperbola
5 780 000 000 =
5.78 ×109
5.78 ×108
5.78 ×1010
5.78 ×1011
0.0000006123 =
6.123 ×10−7
6.123 ×10−8
6.123 ×10−9
6.123 ×10−6
(4×105)×(2×107)=
8×1012
6×1011
6×1012
6×1013
Exponents are ________________ when divided.
subtracted
multiplied
added
divided
(9.42×105)+(4.1×105)=
7.5 ×103
6.8 ×102
5.4 ×103
8.2 ×103
To increase a certain number by p%, just multiply it by ____________________
coefficient
denominator
nominator
percent
Money that is invested with a financial institution for a fixed length of time (or term) earns ____________.
percent
interest
investment
deposit
Choose the correct answer
Simple interest = principal x rate x time
Principal = simple interest x rate x time
Rate = simple interest x principal x time
Time = simple interest x principal x rate
Aruzhan invests $1000 for 4 years at 6% pa. Calculate the interest of Aruzhan earns on her investment.
$240
$280
$320
$160
Aidana invests $5000 for 3 years at 6.75% pa. Find the balance at the end of the term.
$ 6012.50
$ 5987.60
$ 5586.40
$ 5203.70
Which of the followings is TRUE?
Money put into a bank is called a deposit and is credited to your account.
Money put into a bank is called a withdrawal and is credited to your account.
Money put into a bank is called a deposit and is debited to your account.
Money put into a bank is called a withdrawal and is debited to your account.
Which of the followings is TRUE?
Money taken out of an account is called a withdrawal and is debited from the account.
Money taken out of an account is called a deposit and is debited from the account.
Money taken out of an account is called a withdrawal and is credited from the account.
Money taken out of an account is called a deposit and is credited from the account.
Compound interest is added to the _______________ at the end of each investment period
principal
rate
time
interest
Compound interest is added to the principal at the end of each investment period. For the next period, interest is calculated on this new amount giving you ____________ on your interest.
principal
rate
time
interest
Find the correct formula where
P is the principal
R is the interest rate for each period
A is the amount of the final balance
n is the total number of periods
A=P(1+R)n
A=n(1+R)P
P=A(n+1)R
R=P(1+A)n
Calculate how much $7500 accrues to if it is invested at4 %pa compounded annually for 5 years.
$ 9124.90
$ 9343.30
$ 8854.50
$ 9435.80
To calculate compound interest the R (rate) and n (number of periods) must both relate to the ___________ period.
same
different
average
quarterly
Paul has a classic car valued at $80,000 which is increasing in value at the rate of 421% pa .
What will the car be worth in 10 years to the nearest pound?
$ 124 238
$ 156 435
$ 176 235
$ 165 432
When a quantity grows in a fixed proportion (or percentage) a regular intervals, the growth is _______________.
exponential
proportional
appreciated
exceptional
Andrew invested $200 at a compound interest rate of 5% per annum. How much was Andrew's investment worth after 5 years?
$255.26
$253.78
$261.56
$218.20
When an item decreases in value, it is said to have _________________.
depreciated
appreciated
increased
decreased
Depreciation acts like ___________________, but in reverse.
compound interest
exponential growth
simple interest
investments
Choose the correct answer
y=a(1+r)x
a=y(1+r)x
y=r(1+a)x
y=x(1+r)a
Depreciation
Find the correct formula where
R is the interest rate for each period
V is the final value of the item
n - is the total number of periods
P is the total number of periods
V=P(1−R)n
P=R(1−V)n
R=V(1−P)n
n=R(1−P)V
When a population decreases over time, the decrease is called (a) .
The general formula for exponential decay is
y=a(1−r)n
a=r(1−y)n
r=y(1−n)a
n=r(1−a)y
If the base has a factor that is a square number, the surd can be rewritten with a simpler base. This is often called (a) the surd.
Simplify
x2y5
xy2y
y2x
x2xy
xyy
In some situations, it is convenient to include the (a) under the radical sign.
It is conventional to express a fractional surd so that it has a (a) denominator.
Rationalize the denominator of 253
25
2515
1015
523
(a) surds have the same root and the same base.
When adding or subtracting, only collect (a) surds.
Simplify 211×53
1033
133
103
1333
Simplify 3y15y7
5y3
3y6
15y
5y3
(a) means "two numbers" or "two terms"
Expand (5+37)(6−7)
9+137
9+7
13+97
7+913
Expand (5+37)(6−7)
54−145
54−5
14−545
54+145
The expression (x+y) is the (a) of (x−y)
Find the product of
(2−3) and its conjugate.
−1
2 +6
6+6
6
To rationalize the denominator of
a+b1
multiply the (a) and denominator by the conjugate of the denominator.
Write
5+21 with a rational denominator35−2
5+210
105−2
35+2
Numbers with the same base but with indices opposite in sign are (a) .
Write
5−1 as a simple fraction51
5
51
5
Write
91 in index form.3−2
9
32
9
When raising a term with an index to another power, (a) the indices.
When multiplying terms with the same base, (a) the powers.
When dividing terms with the same base, (a) the second power from the first power.
A (a) is a way of comparing quantities that are measured in the same units.
Write one word for both.
The (a) in a ration is important. Changing the order changes the result.
To compare ratios, it is often useful to write them in the form 1:n. This is called a (a) ratio.
The smallest possible value of the true measurement is called its lower bound and the largest, its upper bound. The (a) interval shows both the upper and lower bounds and the difference between them.
(a) variables can only take certain values, for example, numbers of people can only be whole numbers.
When a measurement has been (a) , the true value must be equal to or larger than the recorded value.
Objects have many different (a) you can measure such length, area, mass, volume, capacity, density and lifespan.
The metric system is a (a) system.
Prefixes in the metric system represent (a) of ten.
hecto means
one hundred
one hundredth
one thousand
one thousandth
IF ax = b
a=b → x=ab→
unique solution
no solution
infinitely many solutions
ax = b
a=0, b =0; 0 × x →
unique solution
no solution
infinitely many solutions
ax = b
a=0, b =0; 0 × x →
unique solution
no solution
infinitely many solutions
ax = b
a=0, b =0 → 0 × x =0; x ϵ R →
unique solution
no solution
infinitely many solutions
system has unique solution
system has no solutions
system has infinitely many solutions
system has unique solution
system has no solutions
system has infinitely many solutions
system has unique solution
system has no solutions
system has infinitely many solutions
ODD ONE OUT
sampling
discriminant
viet's rule
completing the square
pythagorean theorem
In discriminant, if D > 0, ....
two roots
no root
one root
In discriminant, if D < 0, ....
two roots
no root
one root
In discriminant, if D = 0, ....
two roots
no root
one root
Equation forms.
Standard form -
ax2 + bx + c = 0
ax2 + bx + c = a (x −x1)(x−x2)
ax2 + bx + c = (x−q)2+q
Equation forms.
Roots' form -
ax2 + bx + c = 0
ax2 + bx + c = a (x −x1)(x−x2)
ax2 + bx + c = (x−q)2+q
Equation forms.
Vertex form -
ax2 + bx + c = 0
ax2 + bx + c = a (x −x1)(x−x2)
ax2 + bx + c = (x−q)2+q
Distance Formula
(x2−x1)2−(y2−y1)2
(x2−x1)−(y2−y1)
(2x1+x2;2ay1+y2)
(2x1+x2;2y1+y2)
tanα =x2−x1y2−y1
Midpoint Formula
(x2−x1)2−(y2−y1)2
(x2−x1)−(y2−y1)
(2x1+x2;2ay1+y2)
(2x1+x2;2y1+y2)
tanα =x2−x1y2−y1
Slope
(x2−x1)2−(y2−y1)2
(x2−x1)−(y2−y1)
(2x1+x2;2ay1+y2)
(2x1+x2;2y1+y2)
tanα =x2−x1y2−y1
a is -----?
leading coefficient
second coefficient
free term
b is -----?
leading coefficient
second coefficient
free term
c is -----?
leading coefficient
second coefficient
free term
A function that is formed by the composition of two or more elementary functions is called a
composite function
linera function
quadratic function
inverse function
Linear function
Form:
Inverse?
f−1(x)=ax−b
f−1(x)=ax+b
f−1(x)=ab−x
f−1(x)=xa−b
f−1(x)=xa+b
Rational function
Form:
f(x)=cx+dax+b
Inverse?
f−1(x)=cx−a−dx+b
f1(x)=cx−a−dx+b
f−1(x)=cx+a−dx+b
f−1(x)=cx+a−dx−b
f−1(x)=dx−b−cx+a
Pythagorean triple
3-4-5
6-7-8
10-12-14
1-2-3
Area of triangle. Which one is INCORRECT?
A=21ab
A=21bccosα
A=21bcsinα
A=21base×height
Formula of the radius of prescribed circle
R =2a+b+c
R =2c
R=2a+b−c
R=2c−2
sin α =
adjacentopposite
hypotenuseopposite
oppositeadjacent
oppositehypotenuse
tg α =
adjacentopposite
hypotenuseopposite
oppositeadjacent
oppositehypotenuse
ctg α =
adjacentopposite
hypotenuseopposite
oppositeadjacent
oppositehypotenuse
Triangle is right isosceles, a = 3, b = 3, what is c?
33
3
3
32
Triangle is right isosceles, a = 5, b = 5, c = ?
53
5
50
25
Theorem of external angle
γ=α+β
γ=α−β
γ=180 −α+β
γ=180−(α+β)
If triangle is equilateral, find area.
2a23
6a23
3a3
4a23
If triangle is equilateral, find area.
2a23
6a3
3a3
4a23
If triangle is equilateral, find the height.
2a3
6a3
3a3
4a23
If triangle is equilateral, find the radius of prescribed circle.
2a3
6a3
3a3
4a23
Formula of circumference
C=2πR
C=πR2
C=2πR2
C=4πR2
Area of sector
A=2πR2⋅360α
A=πR2⋅180α
A=πR2⋅360α
A=2πR⋅360α
Central angle is
Half of internal angle
90
two times internal angle
half of sector
The angle between radius and tangent?
180
90
360
270
Formula of the sum of internal angles
180(n-2)
360(n-2)
180(2-n)
360(2-n)
What is NOT true about tangents of circle?
T⊥R
T=T
T⊥D
T=R
Cos rule:
a2=b2+c2−2bc⋅cosα
c2=b2+a2−2bc⋅cosα
b2=a2+c2−2ab⋅cosα
a2=b2−c2+2bc⋅cosα
Median rule: at the intersection point, ...
medians are divided in proportion to 2 to 1 starting from vertex
medians are divided in proportion to 2 to 1 starting from vertex
medians are multiplied in proportion to 2 to 1 starting from vertex
medians are divided in proportion to 2 to 3 starting from vertex
Bisector rule (sides of triangle a,b,c)
ax=by
xa=by
cx=ya
ay=cx
Area of parallelogram
A=a⋅h
A=21a⋅h
A=a⋅b
A=21d1⋅d2
Area of parallelogram
A=a2⋅ha
A=21a2⋅sinα
A=a2⋅sinα
A=21d1⋅d2
Diagonal of rectangle (sides are a,b)
d=a2+b2
d=a2−b2
d=a2+b2
d=a2−b2
Diagonal of square
a2
a2
2a
a2+b2
What is common between Rhombus and Parallelogram?
diagonals are bisect
diagonals are perpendicular
Area = 21d1d2
All sides are equal
