Algebra
Basic Calculations
1. a. Solve the following equation:
5 ( 3 x  2)  (x  3) =  4 (4 x + 5) + 13
b. Simplify the following equation:
2(a 3) + 4b  2(a b 3) + 5
2. Solve the following:
a. 0.06x+0.02 = 0.25x1.5
b. 0.65k0.1 = 0.4k0.35
3. Find the LCD of 5/6 and 1/4
Square Numbers, Roots and Powers
1. Solve the following:
a. √36
b. √256
c. √25
d. √144
e. √94
f. √704
2. Find the value of the following powers:
a. 104
b. 1010
c. 1015
d. 101
Radicals and Surds
1. Simplify the following expressions:
a. √ 400 × √ 90
b. √ 40 × √ 200 (
c. 90 × √ 600000
d. √ 1000/ √ 40
e. (1 − √ 5)(1 + √ 5)
f. ( √ 7 + 3)(√ 7 − 3)
2. Rationalize the following expressions:
a. 1 √ 5 − √ 3
b. √ 11
c. 30/ √ 3
d. 1/(1 − √ 3)
e. 1/( √ 7 + √ 2)
f. 2/( √ 5 − √ 7)
Proportionality
Direct Proportionality
1. Given the pairs of numbers, answer to the following questions:
X  2  3  6  7  8 
Y  14  21  42  49  56 
(Source: Esercizi sulle grandezze direttamente proporzionali (impariamoinsieme.com))
1.1. Which kind of proportionality these pair of numbers represent?
a. Inverse
b. Direct
1.2. Which, among the following, represents the right equation?
a. y= 7x
b. y=9x
c. y=5x
d. y=4x
2. Given the pairs of numbers, answer to the following questions:
X  3  7  8  10  11 
Y  27  63  72  90  99 
2.1. Which kind of proportionality these pair of numbers represent?
a. Inverse
b. Direct
2.2. Which, among the following, represents the right equation?
a. Y=8x
b. Y=7x
c. Y=10x
d. Y=9x
3. Given the following X values, write the Y in the chart
Y=6x
X  7  2  13  29  4 
Y 





Inverse Proportionality
4. Given the pairs of numbers, answer to the following questions:
X  2  1  4  6  8 
Y  24  48  12  8  6 
4.1. Which kind of proportions are these pairs of numbers representing?
a. Direct
b. Inverse
4.2. Which, among the following, is the right equation?
a. y= 48/x
b. y=28/x
c. y=7/x
d. y=11/x
5. Given these pairs of numbers, choose the right equation:
X  2  1  8  4  5 
Y  60  120  15  30  24 
a. Y=160/x
b. y=80/x
c. y=120/x
d. y=60/x
6. Given the following X value, write the Y in the chart
Y=x/150
X  1  2  3  5  10  15 
Y 






Representations of Direct and Inverse Proportions
7. Which proportion does the graph below represent?
a. Direct
b. Inverse
(Source: internal)
8. Which proportion does the graph below represent?
a. Direct
b. Inverse
(Source: directandinverseproportion.png (750×350) (byjus.com)
Linear Models
Functions and Relations
1. Given the graph represented in the image below, answer to the following questions:
(Source: Questions on Functions with Solutions (analyzemath.com)
1.1. Is the graphs a function?
a. Yes
b. No
1.2. Write the correct equation that correspond to the graph:
2. Given the image below, answer the following questions:
(Source: funzione pari e funzione dispari  mathnotes)
2.1. Is the equation a function?
a. Yes
b. No
2.2. Write the correct equation:
^{}
Variables and Parameters
3. State whether the following statements are true or false:
3.1. 12 is a constant and z is a variable but 12z is variable.
a. True
b. False
3.2. 7 is constant and p is variable but together 7 + p is a variable.
a. True
b. False
3.3. 13 is constant and m is variable but together 13  m is a constant.
a. True
b. False
3.4. 11 is constant and n is variable but together 11 n is a constant.
a. True
b. False
3.5. 0 is a variable.
a. True
b. False
3.6. Combination of both a constant and a variable is also variable.
a. True
b. False
3.7. A quantity which takes a fix numerical value is called variable.
a. True
b. False
3.8. A quantity or symbol which has a no fixed value but it can represent any numerical values is called variable.
a. True
b. False
3.9. 15x, z/3, 7/m are some of the examples of constants.
a. True
b. False
3.10. x, a + b, c – 2, a 13 are some of the examples of variables.
a. True
b. False
(Source: Worksheet on Constants and Variables  Constants and Variables  Answers (mathonlymath.com) )
Linear Graphs
4. Write the Cartesian coordinates of each point shown in the following graph (write the correct answer)
4.1.
A: (_;_), B: (_;_)4.2.
A: (_;_)
Linear Equations
Simultaneous Equation
1. Solve the following systems of simultaneous equations (write the right answer)
1.1.
a. 2y+3x=6
b. Y=4x2
x=
y=
1.2.
a. 3x+4y=12
b. 2x3y=8
x=
y=
1.3.
a. 3x2y+3z=16
b. X+2yz=6
c. 2xy+3z=13
x=
y=
z=
1.4.
a. x+4=15
b. x2y=12
x=
y=
(Source: BestMaths)
Polynomials
Polynomial expressions
1. Which polynomials are in a standard form?
2. Which of the following expressions is not a polynomial?
(Source: Polynomials intro (practice)  Khan Academy)
3. Write the degree of each of the following polynomial expressions in the following table:
(Source: Polynomial Expressions  Basics & Definition  Solved Examples  Cuemath)
Quadratic expressions
4. Factorize the quadratic expressions and write the results:
(Source: 07QuadraticEquations.pdf (une.edu.au) )