ACT MATH PRACTICE TEST ONLINE 2

Question 1 :

Mr. Daniel is paid $1500 salary. He spends 20% of the salary for his kids education, 35% for food, 15% for miscellaneous and he saves the rest. How much money does he save?

(a) $300     (b) $350     (c) $400     (d) $450     (e) $500 

Question 2 :

Let 'x' be a real number which satisfies the relations :

(2x - 5)  > 2 and (3x + 3) < 18

Which of the values can 'x' take?

(a) 4     (b) 5     (c) 6     (d) 7     (e) 8

Question 3 :

The retail price of a particular product is $3.00 per unit. What is the price of half of a box, if one box contains 42 units of the same product ?

(a) $63     (b) $67     (c) $56     (d) $72     (e) 49

Question 4 :

In the triangle given below, BD is perpendicular to AC. If the area of the triangle ABC is 30 square units, then find the area of the triangle DBC ?

(a) 20     (b) 24     (c) 27     (d) 35     (e) 54

Question 5 :

If one angle of a triangle is ∏/6 and another angle is ∏/3, then the third angle is

(a) π/6     (b) π/5     (c) π/4     (d) π/3     (e) π/2

Question 6 :

What is the ratio between the area of the square and circle given below ?

(a) 3/π     (b) π/4     (c) 5/2π     (d) π/5     (e) 2/π

Question 7 :

Find the radius of the circle which is described by the equation

x² + 2x + y² - 4y  =  4

(a) 1     (b) 2     (c) 3     (d) 4     (e) 5

Question 8 : 

(a) -2     (b) -1     (c) 0     (d) 1     (e) 2

Question 9 :

A square, a rectangle, a circle and a trapezoid are given. If we select one figure randomly, what is the probability that the figure has four right angles ?

(a) 0.5     (b) 0     (c) 0.75     (d) 1     (e) 0.25

Question 10 :

If the two lines y = mx + b and 2y + x = 8 are perpendicular to each other and both the lines are passing through the point (2, 2), find the value of 'b'.  

(a) -2     (b) 1     (c) 2     (d) -1     (e) 4

Question 11 :

To keep up with rising expenses, a motel manager needs to raise the $40 room rate by 22%. What will be the new rate ?

a) $40.22     b) $42.20   c) $48    d)  $48.8     e) $62

Solution :

Original amount = $40

Raise by 22%

= 122% of 40

= 1.22 (40)

= 48.8

So, option d is correct.

Question 12 :

As a sales person, your commission is directly proportional to the dollar amount of sales you make. If your sales are $800, your commission is $112. How much commission would you earn if you had $1400 in sales

a) $210     b) $196   c) $175    d)  $128     e) $64

Solution :

When sale = 800

Commission earned = 112

Let S be the sales and C be the commission.

S = kC

Applying S = 800 and C = 112

800 = k(112)

k = 800/112

k = 7.14

Applying the value of k, we get

S = 7.14 C

Applying S = 1400

1400 = 7.14 C

C = 1400/7.14

= 196.07

Approximately option b is correct.

Question 13 :

The total cost of renting a car is $30 for each day the car is rented plus 28.5 cents for each mile the car is driven. What is the total cost of renting the car for 5 days and driving 350 miles ?

a) $104.75      b) $159.98       c) $249.75     d)  $300

e) $1147.50

Solution :

Cost of renting for each day for car = $30

Amount changed for each mile = 28.5 cents

Converting into dollar, we get

= 0.285

Let x be the number of miles driven.

Let y the total cost.

Amount spent for renting car for 5 days = 30 (5)

= 150

y = 150 + 0.285x

When x = 350

y = 150 + 0.285(350)

= 150 + 99.75

= 249.75

So, option c is correct.

Question 14 :

In any parallelogram ABCD, it is always true that the measures of ∠ABC and ∠BCD

a) add upto 180°    b) add upto 90°

c) are each greater than 90°     d) are each 90°

e) are each less than 90°

Solution :

In parallelogram, the co-interior angles will be add upto 180 degree.

∠ABC + ∠BCD = 180

Option a is correct.

Question 15 :

In the isosceles right triangle below AB = 10 feet. What is the length in feet of AC ?

a) 5   b) 10   c) 20     d) √20    e) 10√2

Solution :

Since it is isosceles triangle, AB = BC = 10

AC² = AB² + BC²

AC² = 10² + 10²

= 100 + 100

= 200

AC = √200

= √(2 x 10 x 10)

= 10√2

So, option e is correct.

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