TSI Math Test Prep – Practice Questions & Detailed Solutions
(Updated 2025/2026 Edition)
One third of the candidates for a job were 25 years old or younger. Two sevenths of the
candidates were at least 50 years old. If 84 people applied for the job, how many were
between 25 and 50? - correct answerOne third of 84 is 84 × 1/3 = 84÷3 = 28. 28 people
25 years old or younger applied for the job. Two seventh of 84 is 84 × 2/7= 2×84÷7 =
24.
24 people who were at least 50 years old applied for the job. 84 - 28 - 24 = 32.
32 people applied for the job who were between 25 and 50.
Which of the following is a factor of 450 and multiple of 25? - correct answerIt can be
confirmed by division that (a), (b) and (c) are factors of 450, while 100 is not. The
multiples of 25 are 25, 50, 75,....
75 is both a factor of 450 and multiple of 25.
The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting.
Which is the rate at which the plant's height is increasing? - correct answerh =15 + 3.2t
gives the height of a shrub in inches after t weeks. When planting occurs the height is
15 + 3.2× 0 = 15 inches
After one week the height is 15 + 3.2× 1 = 18.2 inches
The rate at which the height increases is 18.2 - 15 = 3.2 inches
the formula h-15 =3.2t gives the height h inches of a plant t weeks after planting
how high was the initial height of the shrub - correct answernitial me ans at the
beginning. At the beginning t is 0. h =15 + 3.2t gives the height of a shrub in inches after
t weeks. When planting occurs the height is 15 + 3.2× 0 = 15 inches
The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting.
When was the height 31 inches? - correct answerh =15 + 3.2t gives the height of a
shrub in inches after t weeks. When the height is 31 inches 31 = 15 + 3.2t
3.2t = 16
t = 16÷3.2
t=5
The height is 31 inches after 5 weeks
A graph of the temperature T (degrees Fahrenheit) in a refrigerator t hours after midday.
What is the equation of the axis of symmetry of this graph? - correct answerIt is clear
from the diagram that the T -axis is the mirror line or axis of symmetry of this diagram.
The equation of the T- axis is t = 0.
The equation of the axis of symmetry of this graph is t = 0
A graph of the temperature T (degrees Fahrenheit) in a refrigerator t hours after midday.
It is necessary to find the times when the temperature is 8o F. Which of the following is
the correct equation to do this. - correct answerIt is apparent from the graph that it is not
, linear hence the answer cannot be (A) If an attempt is made to solve (B) it will be found
there is no real solution. One of the solutions to (D) is 8, which gives a negative value.
(C) is the only possible solution.
9+t2=8
Which of the following is the equation of the straight line joining the points on the graph
corresponding to t = 2 and t = 1? - correct answerThe point on the graph corresponding
to t = 1 is (1,8). The point on the graph corresponding to t = 2 is (2,5). The slope of the
straight line joining them is (5 - 8)÷(2 - 1) = -3.
The equation is T = -3t + c As (2,5) lies the line we can substitute for t and T.
5 = -3×2 + c
c = 11
Equation is T = -3t + 11 which is the same as (a)
T+3t=11
The formula for the volume V of the sphere = 4(pi)r. Which of the following is the
closest approximation to the volume when r, the radius, is 11 inches? - correct answerIt
is necessary to substitute 11 for r in the formula.
The calculation is V = 4/3 x (pi=3.14) x 113 = 5572.45.......
Clearly the closest approximation to this is (c)
5573 cubic inches
If the radius of the sphere were doubled by what factor would the surface area be
enlarged? - correct answerIf r = 1 then the surface area of the smaller sphere is
12.56......
If the radius is doubled the surface area is 50.26......
The factor is 50.26... ÷ 12.56.... = 4.
The surface area is enlarged by a factor of 4.
10 people can paint a building in 5 days. If each person paints as quickly as the others
then how much of the building could 7 people paint in 5 days? - correct answer10
people can paint a building in 5 days. Each person paints 1/10 of the building in 5 days.
In 5 days 7 people would paint 7 × 1/10 of the building In 5 days 7 people would paint
7/10 of the building.
how many meters are there in 21 ft? - correct answer3.25 feet = 1 meter
1 foot = 1÷3.25 meters
21 feet = 21×1÷3.25 = 6.4615 meters
what is the x value such that y=15-3x and y=0 - correct answery =15 - 3x and y = 0
Hence 15 - 3x = 0
Hence 3x = 15 x = 5
(Updated 2025/2026 Edition)
One third of the candidates for a job were 25 years old or younger. Two sevenths of the
candidates were at least 50 years old. If 84 people applied for the job, how many were
between 25 and 50? - correct answerOne third of 84 is 84 × 1/3 = 84÷3 = 28. 28 people
25 years old or younger applied for the job. Two seventh of 84 is 84 × 2/7= 2×84÷7 =
24.
24 people who were at least 50 years old applied for the job. 84 - 28 - 24 = 32.
32 people applied for the job who were between 25 and 50.
Which of the following is a factor of 450 and multiple of 25? - correct answerIt can be
confirmed by division that (a), (b) and (c) are factors of 450, while 100 is not. The
multiples of 25 are 25, 50, 75,....
75 is both a factor of 450 and multiple of 25.
The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting.
Which is the rate at which the plant's height is increasing? - correct answerh =15 + 3.2t
gives the height of a shrub in inches after t weeks. When planting occurs the height is
15 + 3.2× 0 = 15 inches
After one week the height is 15 + 3.2× 1 = 18.2 inches
The rate at which the height increases is 18.2 - 15 = 3.2 inches
the formula h-15 =3.2t gives the height h inches of a plant t weeks after planting
how high was the initial height of the shrub - correct answernitial me ans at the
beginning. At the beginning t is 0. h =15 + 3.2t gives the height of a shrub in inches after
t weeks. When planting occurs the height is 15 + 3.2× 0 = 15 inches
The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting.
When was the height 31 inches? - correct answerh =15 + 3.2t gives the height of a
shrub in inches after t weeks. When the height is 31 inches 31 = 15 + 3.2t
3.2t = 16
t = 16÷3.2
t=5
The height is 31 inches after 5 weeks
A graph of the temperature T (degrees Fahrenheit) in a refrigerator t hours after midday.
What is the equation of the axis of symmetry of this graph? - correct answerIt is clear
from the diagram that the T -axis is the mirror line or axis of symmetry of this diagram.
The equation of the T- axis is t = 0.
The equation of the axis of symmetry of this graph is t = 0
A graph of the temperature T (degrees Fahrenheit) in a refrigerator t hours after midday.
It is necessary to find the times when the temperature is 8o F. Which of the following is
the correct equation to do this. - correct answerIt is apparent from the graph that it is not
, linear hence the answer cannot be (A) If an attempt is made to solve (B) it will be found
there is no real solution. One of the solutions to (D) is 8, which gives a negative value.
(C) is the only possible solution.
9+t2=8
Which of the following is the equation of the straight line joining the points on the graph
corresponding to t = 2 and t = 1? - correct answerThe point on the graph corresponding
to t = 1 is (1,8). The point on the graph corresponding to t = 2 is (2,5). The slope of the
straight line joining them is (5 - 8)÷(2 - 1) = -3.
The equation is T = -3t + c As (2,5) lies the line we can substitute for t and T.
5 = -3×2 + c
c = 11
Equation is T = -3t + 11 which is the same as (a)
T+3t=11
The formula for the volume V of the sphere = 4(pi)r. Which of the following is the
closest approximation to the volume when r, the radius, is 11 inches? - correct answerIt
is necessary to substitute 11 for r in the formula.
The calculation is V = 4/3 x (pi=3.14) x 113 = 5572.45.......
Clearly the closest approximation to this is (c)
5573 cubic inches
If the radius of the sphere were doubled by what factor would the surface area be
enlarged? - correct answerIf r = 1 then the surface area of the smaller sphere is
12.56......
If the radius is doubled the surface area is 50.26......
The factor is 50.26... ÷ 12.56.... = 4.
The surface area is enlarged by a factor of 4.
10 people can paint a building in 5 days. If each person paints as quickly as the others
then how much of the building could 7 people paint in 5 days? - correct answer10
people can paint a building in 5 days. Each person paints 1/10 of the building in 5 days.
In 5 days 7 people would paint 7 × 1/10 of the building In 5 days 7 people would paint
7/10 of the building.
how many meters are there in 21 ft? - correct answer3.25 feet = 1 meter
1 foot = 1÷3.25 meters
21 feet = 21×1÷3.25 = 6.4615 meters
what is the x value such that y=15-3x and y=0 - correct answery =15 - 3x and y = 0
Hence 15 - 3x = 0
Hence 3x = 15 x = 5
