ACT MATH PRACTICE TEST ONLINE

Here, we give the questions whose qualities  are in high standard and practicing these questions will definitely make the students to reach their goal in ACT. 

Now, you can take ACT math practice test online  by clicking the following links.

• ACT Math Practice Test - 1
• ACT Math Practice Test - 2

About ACT test

The ACT is the leading US college admissions test which measures what the students have learned in high school and determines the students' academic readiness to the college.

Why do we need ACT test?

Since ACT is the leading US college admissions test which measures what the students have learned in high school and determines the students' academic readiness to the college, it is very important for all the students to have better score in ACT. 

ACT Math

Even though ACT test contains four multiple-choice tests: English, mathematics, reading, and science, the crucial part for almost all the students is math.

Most of the students who write ACT test find it difficult to answer the questions in math.

To overcome the above problems, students must know answer for the two questions.

1. What is the syllabus for ACT math?

2. Where can i get ACT math practice questions?

Here students can get clear answer for the above two questions. 

ACT math syllabus

1. Pre-Algebra

• Basic operations using whole numbers, decimals, fractions, and integers
• Place value
• Square roots and approximations
• The concept of exponents
• Scientific notation
• Factors
• Ratio, proportion and percent
• Linear equations in one variable
• Absolute value and ordering numbers by value
• Elementary counting techniques and simple probability
• Data collection, representation, and interpretation
• Understanding simple descriptive statistics

2. Elementary Algebra

• Properties of exponents and square roots
• Evaluation of algebraic expressions through substitution
• Using variables to express functional relationships
• Understanding algebraic operations
• The solution of quadratic equations by factoring

3. Intermediate Algebra

• The quadratic formula
• Rational and radical expressions
• Absolute value equations and inequalities
• Sequences and patterns
• Systems of equations
• Quadratic inequalities
• Functions and modeling
• Matrices
• Roots of polynomials
• Complex numbers

4. Co-ordinate Geometry

• Graphing and the relations between equations and graphs, including points, lines, polynomials, circles, and other curves
• Graphing inequalities
• Slope
• Parallel and perpendicular lines
• Distance
• Midpoints
• Conics

5. Pane Geometry

• Properties and relations of plane figures, including angles and relations among perpendicular and parallel lines
• Properties of circles, triangles, rectangles, parallelograms, and trapezoids
• Transformations
• The concept of proof and proof techniques
• Volume
• Applications of geometry to three dimensions

6. Trigonometry

• Trigonometric relations in right triangles
• Values and properties of trigonometric functions
• Graphing trigonometric functions
• Modeling using trigonometric functions
• Use of trigonometric identities
• Solving trigonometric equations

Problem 1 :

Armin is trying to decide whether to buy a season pass to his college basketball team’s 20 home games this season. The cost of an individual ticket is $14, and the cost of a season pass is $175. The season pass will admit Armin to any home basketball game at no additional cost. What is the minimum number of home basketball games Armin must attend this season in order for the cost of a season pass to be less than the total cost of buying an individual ticket for each game he attends?

a) 08      b)  09     c) 12    d) 13   e) 20

Solution :

Cost of individual tickets = $14

Cost of season pass = 175

Let x be the minimum number of basketball games Armin must attend this season.

14 x < 175

x < 175/14

x < 12.5

So, the correct answer is option c.

Problem 2 :

In triangle DEF, the length of DE is √30 inches, and the length of EF is 3 inches. If it can be determined, what is the length, in inches, of DF ?

a) 3      b) √30       c) √33       d) √39

e)  Cannot be determined from the given information

Solution :

If the given triangle is right triangle, it should satisfy Pythagorean theorem,

Case 1 :

EF = DF

3² + 3² =  √30²

9 + 9 = 30

18 ≠ 30

Case 2 :

DE = DF

√30² + √30² = 3²

30 + 30 = 9

60 ≠ 9

DF > DE + EF

DF > √30 + 3

Approximating √30 = 5.4

DF > 5.4 + 3

DF > 8.4

√39 = 6.2

It is not true. Since the type of triangle is not given clearly, it cannot be determined from the given information.

Problem 3 :

Laura plans to paint the 8-foot-high rectangular walls of her room, and before she buys paint she needs to know the area of the wall surface to be painted. Two walls are 10 feet wide, and the other 2 walls are 15 feet wide. The combined area of the 1 window and the 1 door in her room is 60 square feet. What is the area, in square feet, of the wall surface Laura plans to paint?

a) 200    b) 340   c) 360   d) 390    e) 400

Solution :

Length of one wall = 8 feet

Width of two walls = 10 feet

Width of other two walls = 15 feet

2 (8 x 10 + 8 x 15)

= 2(80 + 120)

= 2(200)

Area of walls = 400

Area of 1 window and 1 door should be subtracted from the total area

= 400 - 60

 = 340 square feet

Problem 4 :

Which of the following expressions is a factor of

x³ − 64 ?

a) x − 4   b) x + 4    c) x + 64    d) x² + 16

e) x² − 4x + 16

Solution :

x³ − 64 = x³ − 4³

a³ − b³ = (a - b) (a² + ab + b²)

= (x - 4) (x² + x(4) + 4²)

= (x - 4) (x² + 4x + 16)

So, (x - 4) is the factor and option a is correct.

Problem 5 :

The average of a list of 4 numbers is 90. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list  is 80, and the fourth number in the new list is 96. What is the average of this new list of numbers?

a) 90     b) 91.5    c) 94      d)  94.5    e) 94.8

Solution :

Average of 4 numbers = 90

Sum of 4 numbers / 4 = 90

Sum of 4 numbers = 90(4)

= 360

Sum of three numbers + fourth number = 360

Sum of three numbers + 80 = 360

Sum of three numbers = 360 - 80

= 280

Sum of 4 numbers in the new list = 280 + 96

= 376

Average of 4 numbers in the new list = 376/4

= 94

So, option c is correct.

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