Free Printable TSI Practice Problems

1.

What is the solution to the equation x² - 8x = -15?

a)

x = 3

b)

x = 5

c)

x = 7

d)

x = 9

2.

If 3t - 7 = 5t, what is the value of 6t?

a)

6t = 10

b)

6t = -21

c)

6t = 14

d)

6t = 0

3.

What is the formula for the area of a rectangle?

a)

Area = length × width.

b)

Area = length + width.

c)

Area = length - width.

d)

Area = length ÷ width.

4.

What is the difference between a rational and an irrational number?

a)

Rational numbers can be expressed as a fraction, while irrational numbers cannot.

b)

Irrational numbers can be expressed as a fraction, while rational numbers cannot.

c)

Rational numbers are always whole numbers, while irrational numbers are decimals.

d)

Rational numbers are infinite, while irrational numbers are finite.

5.

If y = x/2 and x = -2, what is (x + 2y)(x - y)?

a)

0

b)

2

c)

4

d)

-4

6.

What is the Pythagorean theorem?

a)

In a right triangle, a² + b² = c², where c is the hypotenuse.

b)

In any triangle, the sum of the angles equals 180 degrees.

c)

The area of a circle is πr², where r is the radius.

d)

The relationship between the sides of a triangle is given by a² + b² = c, where c is the longest side.

7.

If y varies inversely as x, and y = 4.5 when x = 10, what is x when y = 5?

a)

x = 7

b)

x = 8

c)

x = 9

d)

x = 10

8.

What is the process of solving a linear equation?

a)

Isolate the variable on one side of the equation using inverse operations.

b)

Add the same number to both sides of the equation.

c)

Multiply both sides of the equation by the same number.

d)

Graph the equation to find the solution.

9.

What is the definition of a function?

a)

A relation where each input has exactly one output.

b)

A set of ordered pairs with no restrictions.

c)

A collection of inputs and outputs that can be random.

d)

A mathematical operation that combines two numbers.

10.

What is the slope-intercept form of a linear equation?

a)

y = mx + b, where m is the slope and b is the y-intercept.

b)

y = ax^2 + bx + c, which is the quadratic form.

c)

y = mx + c, where m is the slope and c is the y-intercept.

d)

y = b/x + a, which is the inverse form.

11.

What does it mean for two variables to vary inversely?

a)

If one variable increases, the other decreases, such that their product is constant.

b)

Both variables increase or decrease together.

c)

The variables are unrelated and do not affect each other.

d)

One variable is always greater than the other.

12.

What is the formula for the circumference of a circle?

a)

Circumference = πd, where d is the diameter.

b)

Circumference = 2πr, where r is the radius.

c)

Circumference = πr^2, where r is the radius.

d)

Circumference = 2r, where r is the radius.

13.

What is the discounted price of a $3.80 large popcorn on sale for 25% off?

a)

$2.50

b)

$2.85

c)

$3.00

d)

$3.15

14.

What is the quadratic formula?

a)

x = (-b ± √(b² - 4ac)) / (2a)

b)

x = (b ± √(b² + 4ac)) / (2a)

c)

x = (-b ± √(b² + 4ac)) / (2a)

d)

x = (b ± √(b² - 4ac)) / (2a)

15.

What is the definition of a prime number?

a)

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

b)

A prime number is any integer that is divisible by 2.

c)

A prime number is a number that can be formed by multiplying two smaller natural numbers.

d)

A prime number is a natural number that is less than 1.

16.

If $\frac{x}{3}=\frac{x+2}{5}$ , then what is x ?

a)

-1

b)

0

c)

2

d)

3

17.

Given: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4

If a number is chosen at random from the list above, what's the probability of choosing 1 ?

a)

4/5

b)

2/5

c)

1/2

d)

1/5

18.

$8x^2-2x-1=$

a)

(x-1)(8x+1)

b)

(x+1)(8x-1)

c)

(2x-1)(4x+1)

d)

(2x+1)(4x-1)

19.

A tablet was on sale for 5% off the original price. If the original price is P, what is the sale price in terms of P?

a)

P-5

b)

P-0.5

c)

0.95P

d)

.05P

20.

In the x-y plane, midpoint M of segment AB has coordinates (-1,0), and point A has coordinates (-4,-1). What is the x-coordinate of point B?

a)

1

b)

2

c)

3

d)

4

21.

What is a factor of: $b^2+3b-18$

a)

b+3

b)

b-6

c)

b-18

d)

b+6

22.

a)

m>0, b>0

b)

m<0, b<0

c)

m>0, b<0

d)

m<0, b>0

23.

$\frac{a^9}{a^3}$

a)

3

b)

6

c)

$a^3$

d)

$a^6$

24.

The pie chart shows salad dressings chosen by customers at a restaurant. If 200 customers order salad each day, which of the following is the difference between the number who choose Italian and the number who choose vinaigrette?

a)

10

b)

16

c)

20

d)

30

25.

If $\frac{2}{5x}+\frac{1}{x}=35$ , what is x?

a)

1/25

b)

25

c)

5

d)

7

26.

If $x=3$ , then $\left(x-3\right)\left(2x-1\right)$ = ?

a)

-3

b)

-1

c)

0

d)

2

27.

If the length of a side of a square measures $\left(a-3b\right)$ , what is the area of the square in terms of a and b ?

a)

$a^2-3ab+3b^2$

b)

$a^2-6ab+9b^2$

c)

$a^2+9b^2$

d)

$a^2-6ab-9b^2$

28.

Which is a factor of: $3a^2+13a-10$

a)

3a-2

b)

3a-5

c)

3a-10

d)

a+2

29.

If $x-20=3x-20$ , what is $x^2-3$

a)

0

b)

3

c)

-3

d)

-20

30.

$r^2-16\ =\$

a)

(r+4)(r-4)

b)

(4+r)(4-r)

c)

(r-4)(r-4)

d)

(4-r)(4-r)

31.

a)

$x\le0,\ y\le0$

b)

$x\ge0,\ y\ge0$

c)

$x\le0,\ y\ge0$

d)

$x\ge0,\ y\le0$

32.

$x^2-2x-15=0$

a)

-3 or -5

b)

-1 or 15

c)

1 or 15

d)

5 or -3

33.

The ages of five friends are: 23, 36, 28, 36, and 27. How many are older than the average age?

a)

1

b)

2

c)

3

d)

4

34.

The relationship between a temperature in degree Celsius and in degrees Kelvin is given by K=C+273. What is the measure in degrees Celsius for a temperature of 14 degrees Kelvin?

a)

-287

b)

-259

c)

259

d)

289

35.

If a car travels at an average speed of x miles per hour, how far would the car travel in 75 minutes?

a)

75x/2

b)

5x/4

c)

4x/5

d)

6x/75

36.

Jacob loves to ride his bike, on this certain day he rode 5 miles. Jacob previously recorded that his average time per mile was 6.2 minutes. His times for the first 4 miles were: 7.3 minutes, 7 minutes, 4.9 minutes, and 5.1 minutes. What’s Jacob’s time for the last mile?

a)

6.7

b)

8.2

c)

5.3

d)

7.3

37.

In Zeroville, the population was 10,500 in the year 1995. Mathematicians predicted this formula $p\left(t\right)=\left(10500\right)\left(1.05\right)^t$ could be used to predict the population for the next 20 years where t is the number of years after 1995. What would the population of Zeroville be in 2000?

a)

13,400

b)

12,223

c)

8,223

d)

14,110

38.

If there are 2.2 pounds in 1 kilogram, how many pounds are there in x kilograms?

a)

$\frac{x}{2.2}$

b)

$2.2x$

c)

$2.2+x$

d)

$\frac{2.2}{x}$

39.

The bar graph shows the number of customers who shopped at a store Monday through Thursday of one week. If the number of customers on Friday was a one-fifth increase from the number of customers on Thursday, how many customers shopped at the store on Friday?

a)

$480$

b)

$500$

c)

$525$

d)

$600$

40.

Last year a bakery sold w loaves of bread. This year the bakery sold three more than twice the number of loaves of bread sold last year. If, next year, the bakery plans on selling twice the number of loaves of bread sold this year, how many loaves of bread does the bakery expect to sell next year?

a)

$2w$

b)

$2w+3$

c)

$4w+3$

d)

$4w+6$

41.

If $7p-4=8$ , what is the value of $p$ ?

a)

$\frac{4}{7}$

b)

$\frac{7}{12}$

c)

$\frac{12}{7}$

d)

$\frac{7}{4}$

42.

Running at an average rate of 6 miles per hour, how many minutes would it take Kyle to run 3 miles?

a)

$18$

b)

$30$

c)

$40$

d)

$45$

43.

The dot plot identifies the number of pets living with each of 20 families in an apartment building. What fraction of the families have more than 2 pets?

a)

$\frac{3}{20}$

b)

$\frac{1}{5}$

c)

$\frac{1}{4}$

d)

$\frac{9}{20}$

44.

The formula for the volume of the right circular cylinder is $V=\pi r^2h$ . If $r=2b$ and $h=5b+3$ , what is the volume of the cylinder in terms of $b$ ?

a)

$10\pi b^2+6\pi b$

b)

$20\pi b^3+12\pi b^2$

c)

$20\pi^2b^3+12\pi^2b^2$

d)

$50\pi b^3+20\pi b^2+90\pi b$

45.

Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50. How much would an order of 1 slice of cheese pizza and 3 sodas cost?

a)

$3.25

b)

$5.25

c)

$7.75

d)

$17.25

46.

If $5c-2=3c$ , then $24c$ = ?

a)

6

b)

18

c)

16

d)

24

47.

In the xy-plane, the slope of the line $y=mx-4$ is less than the slope of the line $y=x-4$ . Which of the following must be true about $m$ ?

a)

$m=-1$

b)

$m=1$

c)

$m<1$

d)

$m>1$

48.

A history class is made up of 12 tenth graders and 9 eleventh graders. The tenth graders averaged 77 on the midterm exam, and the eleventh graders averaged 91 on the midterm exam. What was the average grade on the midterm exam for the entire class?

a)

82

b)

83

c)

84

d)

85

49.

Reyna has 5 coins worth 10 cents each and 4 coins worth 25 cents each. If she chooses two of these coins at random, what is the probability that the two coins combined will be worth at least 35 cents?

a)

$\frac{5}{18}$

b)

$\frac{5}{9}$

c)

$\frac{13}{18}$

d)

$\frac{71}{72}$

50.

In the xy-plane, what is the y-intercept of the graph of the equation $y=6\left(x-\frac{1}{2}\right)\left(x+3\right)$ ?

a)

$-9$

b)

$-\frac{1}{2}$

c)

$3$

d)

$9$

51.

The area of the triangle is 21 square units. What is the value of x?

a)

3

b)

6

c)

7

d)

11

52.

Which of the following is not equivalent to $\left(3x-12\right)\left(x+4\right)$ ?

a)

$3\left(x^2-8x+16\right)$

b)

$3\left(x^2-16\right)$

c)

$3x^2-48$

d)

$3x\left(x+4\right)-12\left(x+4\right)$

53.

If the cost of carpeting a floor is $2.50 per square foot, how much will it cost to carpet a rectangular floor that is 10 feet by 12 feet?

a)

$112.00

b)

$120.00

c)

$250.00

d)

$300.00

54.

If n is the least of two consecutive odd integers, which of the following represents the sum of the two integers?

a)

$n+1$

b)

$n+2$

c)

$2n+1$

d)

$2n+2$

55.

$\left(\frac{x^{-5}y}{y^3}\right)^{-1\ }=$

a)

$\frac{x^5}{y^2}$

b)

$\frac{y^2}{x^5}$

c)

$x^5y^2$

d)

$x^5y^{-3}$

56.

For which of the following values of x is the function $f\left(x\right)=\sqrt[]{4-x^2}$ NOT defined as a real number?

a)

$-2$

b)

$0$

c)

$2$

d)

$4$

57.

Under ideal conditions, the population of a certain species doubles every nine years. If the population started with 100 individuals, which of the following expressions gives the population of the species t years after the population started , assuming that the population has been living under ideal conditions?

a)

$2x100^{9t}$

b)

$2x100^{\frac{t}{9}}$

c)

$100x2^{9t}$

d)

$100x2^{\frac{t}{9}}$

58.

Bill's new porch is rectangular and has an area of 50 square feet. If the length of the porch is two times the width, what is the perimeter of the porch?

a)

30 feet

b)

40 feet

c)

50 feet

d)

60 feet

59.

What is the probability of selecting a male from a group of 4 males and 8 females?

a)

$\frac{1}{3}$

b)

$\frac{1}{2}$

c)

$\frac{2}{3}$

d)

$\frac{4}{5}$

60.

Solve for x.

$3\left(x+1\right)=5\left(x-2\right)+7$

a)

$-2$

b)

$2$

c)

$\frac{1}{2}$

d)

$3$

61.

Line A passes through the point $\left(-1,2\right)$ . Which of the following CANNOT be the equation of Line A?

a)

$y=1-x$

b)

$y=x+1$

c)

$x=-1$

d)

$y=x+3$

62.

Diego's current age is five times Martina's age ten years ago. If Martina is currently m years old, what is Diego's current age in terms of m?

a)

$5m$

b)

$5m-10$

c)

$5m-50$

d)

$5m+\left(m-10\right)$

63.

If $2x+5=8x$ , then $12x$ =?

a)

5

b)

10

c)

15

d)

20

64.

An airline asked its agents to assign convenience ratings on a scale of 1-7 to 114 flights leaving one of its hub cities. The histogram shows the distribution of the ratings of the 114 flights. What is the median rating assigned by the agents?

a)

3

b)

4

c)

5

d)

6

65.

What is the value of x in the following equation?

$\sqrt[]{2x}=4$

a)

1

b)

4

c)

8

d)

16

66.

The market price of a house is directly proportional to the total area of the house in square feet. If the price of 1,500 square foot home is $300,000, what is the price of a 2,000 square foot home?

a)

$350,000

b)

$400,000

c)

$450,000

d)

$500,000

67.

Find the x-intercept of a line that has the following equation:

$2y=3x-6$

a)

$-2$

b)

$-1$

c)

1

d)

2

68.

There are 80 students in a school. Every student is taking either algebra or pre-calculus, and some students are taking both. There are 60 students in the algebra class. If 15 students are taking both algebra and pre-calculus, what is the probability that a randomly selected student is taking pre-calculus but not algebra?

a)

$\frac{1}{4}$

b)

$\frac{1}{3}$

c)

$\frac{3}{8}$

d)

$\frac{3}{4}$

69.

What are the solutions to the following equation?

$x^2+8x+15=0$

a)

2 and 3

b)

3 and 5

c)

-2 and -3

d)

-3 and -5

70.

Solve.

$\sqrt[]{5}\sqrt[]{3}$

a)

$\sqrt[]{2}$

b)

$\sqrt[]{8}$

c)

$\sqrt[]{15}$

d)

$8$

71.

An office supply superstore sells pens for 60 cents each and pencils for 40 cents each. Diane purchased a total of 17 items (pens and pencils) for $8.20. How many pens did Diane purchase?

a)

5

b)

7

c)

10

d)

12

72.

The points represented by the (x,y) coordinate pairs in the table all lie on Line k. What is the slope of Line k?

a)

-2

b)

-3

c)

2

d)

5

73.

If Goldy has 16m+8, and Fish has 1/4 of this, how much does Fish have?

a)

4m+2

b)

2m+4

c)

8m+2

d)

2m+8

74.

If you have an algebraic expression that states: two times a number added to six is equal to twelve times a number, what is the value of that number?

a)

3/5

b)

5/3

c)

1/4

d)

3

75.

What is the value of x when, $2\left(2x^2+3x\right)=10$

a)

1

b)

2

c)

-1

d)

3

76.

What is the value of x when: $x^2=9x$

a)

0, 9

b)

0, -9

c)

1, 9

d)

-1, 9

77.

What is one factor of: $\left(25x^2-16y^2\right)$

a)

5x+4y

b)

25x-4y

c)

4x-5y

d)

2x-7y

78.

$\frac{xy+y}{y}$

a)

x+1

b)

x

c)

y+x

d)

x+y

79.

Factor: $x^2-x-12$

a)

(x-4)(x+3)

b)

(x+4)(x-3)

c)

(x-6)(x+2)

d)

(x-2)(x+6)

80.

Solve for x: $x^2-6x-7$

a)

{7 and -1}

b)

{-7, and 1}

c)

{-7 and -1}

d)

{3 and -3}

81.

Factor: $2x^2-7x+3$

a)

(x-3)(2x-1)

b)

(x-1)(2x-3)

c)

(2x+1)(x-2)

d)

(x-3)(2x+2)

82.

Find a factor of: $2x^2+5x-12$

a)

(2x-3)

b)

(x-4)

c)

(2x+3)

d)

(x-2)

83.

Solve: $2x^2+3x-3=0$

a)

$\frac{-3\pm\sqrt{33}}{4}$

b)

$\frac{-3\pm\sqrt{12}}{4}$

c)

$\frac{-3\pm\sqrt{11}}{4}$

d)

$\frac{-3\pm\sqrt{-12}}{4}$

84.

Solve: $\frac{1}{x}=\frac{x}{10}$

a)

$\sqrt{10}$

b)

$\frac{1}{10}$

c)

10

d)

5

85.

Solve: $\frac{2}{4x}+\frac{1}{x}=1$

a)

$\frac{3}{2}$

b)

$\frac{2}{3}$

c)

$9$

d)

$\frac{1}{4}$

86.

$f\left(6\right)=\frac{1}{x}+\frac{x}{3}$

a)

$\frac{13}{6}$

b)

$\frac{7}{9}$

c)

$\frac{2}{3}$

d)

$\frac{15}{6}$

87.

What is the area of a square with a side length of : $2x-y$

a)

$4x^2-4xy+y^2$

b)

$4x^2+4xy+y^2$

c)

$4x^2-4xy+3y^2$

d)

$4x^2-7xy+y^2$

88.

Which equation belongs to this table?

a)

$x^2-2x+5$

b)

$x^2-2x-5$

c)

$x^2+2x-5$

d)

$2x-5$

89.

C=\frac{5}{9}\left(F-32\right)

If F = 68, solve for C.

a)

20

b)

18

c)

36

d)

12

90.

What is the median of the first 9 odd positive integers?

a)

9

b)

11

c)

13

d)

15

91.

A rectangular box is being fitted with a logo that measures $\left(x+6\right)\ by\ \left(x-4\right)$ What is the area of the logo?

a)

$x^2+2x-24$

b)

$x^2+2x+24$

c)

$x^2-2x-24$

d)

answer not here

92.

If: $2x-14=-3x-4$ what is $x^2+x$

a)

6

b)

4

c)

2

d)

0

TSI Practice Problems

Total questions: 92

Worksheet time: 1hrs 24mins

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