FREE ISEE Upper Level Math Practice Test

Interactive ISEE Upper Level Math Practice Test (Timed, Both Sections)

Take our free, full-length ISEE Upper Level Math practice test below — both math sections (Quantitative Reasoning and Mathematics Achievement) in one timed exam, with no calculator and no penalty for wrong answers. You’ll get an estimated scaled score (760–940), a stanine, full step-by-step explanations, and a personalized study plan. Scroll down for more practice and tips.

C.

D.

3- The rectangle on the coordinate grid is translated 5 units down and 4 units to the left.

Which of the following describes this transformation?

A. \((x,y) ⇒ (x-4,y+5)\)

B. \( (x,y) ⇒ (x-4,y-5)\)

C. \( (x,y) ⇒ (x+4,y+5)\)

D. \( (x,y) ⇒ (x+4,y-5)\)

4- A girl 160 cm tall, stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamp post?

A. 240

B. 400

C. 600

D. 800

5- Which value of \(x\) makes the following inequality true?
\(\frac{3}{22}≤ x < 19%\)

A. 0.13

B. \(\frac{5}{36}\)

C. \(\sqrt{0.044}\)

D. 0.124

6- The ratio of boys to girls in a school is 5:3. If there are 640 students in a school, how many boys are in the school?

A. 240

B. 360

C. 400

D. 540

7- The width of a box is one-third of its length. The height of the box is one-third of its width. If the length of the box is 27 cm, what is the volume of the box?

A. 81 cm\(^3\)

B. 162 cm\(^3\)

C. 243 cm\(^3\)

D. 729 cm\(^3\)

8- The drivers at G & G trucking must report the mileage on their trucks each week. The mileage reading of Ed’s vehicle was 40,907 at the beginning of one week, and 41,053 at the end of the same week. What was the total number of miles driven by Ed that week?

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A. 46 miles

B. 145 miles

C. 146 miles

D. 1046 miles

9- Which equation represents the statement Three plus the sum of the squares of \(w\) and \(x\) is 32.

A. 42

B. \(3(w^2 + x) = 32\)

C. 126

D. 130

10- What is the solution of the following system of equations?
\(-2x- y = -9 \)
\(5x-2y= 18\)

A. \((-1, 2)\)

B. \((4, 1)\)

C. \((1, 4)\)

D. \((4, -2)\)

11- What is the area of an isosceles right triangle that has one leg that measures 6 cm?

A. 18 cm

B. 36 cm

C. 6 \(\sqrt{2}\) cm

D. 72 cm

12- Which of the following is a factor of both \(x^2 – 2x – 8\) and \(x^2 – 6x + 8\)?

A. \((x – 4)\)

B. \((x + 4)\)

C. \((x – 2)\)

D. \((x + 2)\)

13- \(\frac{1}{6b^2} + \frac{1}{6b} = \frac{1}{b^2}\)

A. \(-\frac{16}{15}\)

B. 5

C. \(-\frac{15}{16}\)

D. 8

14- \(\frac{|3+x|}{7}≤ 5, \space then \space x =?\)

A. \(-38 ≤ x ≤ 35\)

B. \(-38 ≤ x ≤ 32\)

C. \(-32 ≤ x ≤ 38\)

D. \(-32 ≤ x ≤ 32\)

15- The cost, in thousand of dollars, of producing \(x\) thousands of textbooks is \(C (x) = x^2 + 10x + 30\). The revenue, also in thousands of dollars, is \(R(x) = 4x\). Find the profit or loss if 3,000 textbooks are produced. (profit \(=\) revenue \(-\) cost)

A. $21,000 loss

B. $57,000 profit

C. $3,000 profit

D. $240 loss

16- Ella (E) is 4 years older than her friend Ava (A) who is 3 years younger than her sister Sofia (S). If E, A, and S denote their ages, which one of the following represents the given information?

A. \(E=A+4\)
\(S=A-3\)

B. \(E=A+4\)
\(A=S+3\)

C. \(A=E+4\)
\(S=A-3\)

D. \(E=A+4\)
\(A=S-3\)

17- Which is the longest time?

A. 23 hours

B. 1520 minutes

C. 2 days

D. 4200 seconds

18- Write 523 in expanded form, using exponents.

A. \((5 × 10^3) + (2 × 10^2) + (3 × 10)\)

B. \((5 × 10^2) + (2 × 10^1) – 5\)

C. \( (5 × 10^2) + (2 × 10^1) + 3\)

D. \((5 × 10^1) + (2 × 10^2) + 3\)

19- A company pays its writer $4 for every 400 words written. How much will a writer earn for an article with 960 words?

A. $11

B. $5.6

C. $9.6

D. $8.7

20- A circular logo is enlarged to fit the lid of a jar. The new diameter is \(60\%\) larger than the original. By what percentage has the area of the logo increased?

A. \(40\%\)

B. \(30\%\)

C. \(60\%\)

D. \(20\%\)

Best ISEE Upper Level Math Prep Resource for 2026

Answers:

2- B
A linear equation is a relationship between two variables, \(x\) and \(y\), and can be written in the form of \(y = mx + b\).
A non-proportional linear relationship takes on the form \(y=mx + b\), where \(b ≠ 0\) and its graph is a line that does not cross through the origin.

3- B
Translated 5 units down and 4 units to the left means: \((x.y) ⇒ (x-4,y-5)\)

4- D
Write the proportion and solve for the missing side.
\(\frac{Smaller \space triangle \space height}{Smaller \space triangle \space base}=\frac{Bigger \space triangle \space height}{Bigger \space triangle \space base} ⇒\frac{90 \space cm}{160 \space cm}=\frac{90 + 360 \space cm}{x} ⇒ x = 800 \space\) cm

5- B
\(\frac{3}{22} = 0.136 \)And \(19\% = 0.19\) therefore \(x\) should be between 0.136 and 0.19
Choice B. \(5/36 = 0.138\) is between 0.136 and 0.19

6- A
The ratio of boys to girls is 2:3. Therefore, there are 2 boys out of 5 students. To find the answer, first divide the total number of students by 5, then multiply the result by 2.
\(600 ÷ 5 = 120 ⇒ 120 × 2 = 240\)

7- D
If the length of the box is 27, then the width of the box is one-third of it, 9, and the height of the box is 3 (one-third of the width). The volume of the box is:
V = lwh = \((27) (9) (3) = 729\)

8- C
To find the total number of miles driven by Ed that week, you only need to subtract 40,907 from 41,053.
\(41,053-40,907=146\)

9- B
\(3(w^2 + x) = 32\)

10- B
\(-2x- y = -9\)
\(5x-2y= 18\)
⇒ Multiplication \((–2)\) in first equation ⇒
\(4x +2y =18\)
\(5x-2y= 18 \)
Add two equations together \(⇒ 9x =36 ⇒ x= 4\) then: \(y = 1\)

11- A
First, draw an isosceles triangle. Remember that two sides of the triangle are equal.
Let’s put a for the legs. Then:
\(a=6⇒\) area of the triangle is = \(\frac{1}{2}(6×6)=\frac{36}{2} = 18 \)Cm\(^2\)

12- A
Factor each trinomial \(x^2 – 2x – 8\) and \(x^2 – 6x + 8\)
\(x^2 – 2x – 8 ⇒ (x – 4)(x + 2) \)
\(x^2 – 6x + 8 ⇒ (x – 2)(x – 4)\)

13- B
Subtract \(\frac{1}{6b}\) and \(\frac{1}{b^2}\) from both sides of the equation. Then:
\(\frac{1}{6b^2}+\frac{1}{6b}=\frac{1}{b^2}→\frac{1}{6b^2}-\frac{1}{b^2}=-\frac{1}{6b}\)
Multiply both the numerator and denominator of the fraction \(\frac{1}{b^2}\) by 6. Then:
\(\frac{1}{6b^2}-\frac{6}{6b^2}=-\frac{1}{6b}\)
Simplify the first side of the equation:
\(-\frac{5}{6b^2}=-\frac{1}{6b}\)
Use cross multiplication method: \( 30b=6b^2→30=6b→b=5\)

14- B
First, multiply both sides of the inequality by 7. Then:
\(\frac{|3+x|}{7}≤ 5→|3+x|≤35\)
Since \(3+x\) can be positive or negative, then:
\(3+x≤35\) or \(3+x≥-35\)
Then:
\(x≤32\) or \(x≥-38\)
Choice B is correct.

15- D
Plug in the value of \(x=30\) into both equations. Then:
\(C(x) = x^2+2x=(30)^2+2(30)=900+60=960\)
\(R(x)=40x=40×30=1,200 \)
\(1,200 – 960 = 240\)

16- D
\(E = 4 + A\)
\(A = S – 3\)

17- C
\(23\) hours \(= 82,800\) seconds
\(1520\) minutes \(= 91,200\) seconds
\(2\) days\( = 48\) hours \(= 172,800\) seconds
4200 seconds

18- C
Let’s review the choices provided:
A. \((5 × 103) + (2 × 102) + (3 × 10) = 5,000 + 200 + 30 = 5,230\)
B. \((5 × 102) + (2 × 101) – 5 = 500 + 20 – 5 = 515\)
C. \((5 × 102) + (2 × 101) + 3 = 500 + 20 + 3 = 523\)
D. \((5 × 101) + (2 × 102) + 3 = 50 + 20 + 3 = 73\)
Only choice C equals to 523.

19- C
\(\frac{4}{400}=\frac{x}{960}\)
\(x = \frac{4 × 960}{400} = 9.6\)

20- B
The area of a circle equals:
\(A=πr^2\)
The new diameter is \(30\%\) larger than the original then the new radius is also \(30\%\) larger than the original.
\(30\%\) larger than r is \(1.3r\).
Then, the area of the larger circle is:
\(A=πr^2=π(1.3r)^2=π(1.69r^2 )=1.69πr^2\)
\(1.69πr^2\) is \(69\%\) bigger than \(πr^2\).

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ISEE Upper Level Math Practice Workbook 2026 The Most Comprehensive Review for the Math Section of the ISEE Upper Level Test

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Recommended EffortlessMath Books

For a workbook your child can use alongside this practice test, the ISEE Upper Level Math for Beginners covers every topic across both math sections with worked examples. For full admissions prep with multiple timed practice tests, see the ISEE Upper Level Math Test Prep Bundle (resource currently unavailable).

Frequently Asked Questions

Is there a free ISEE Upper Level practice test?

Yes. You can take a free, full-length ISEE Upper Level math practice test online that combines Quantitative Reasoning and Mathematics Achievement in one timed session. Work it without a calculator, just like the real exam, then check every step-by-step explanation to see which skills, such as ratios or similar triangles, still need work.

Is there an ISEE Upper Level math practice test PDF?

Printable ISEE Upper Level math practice is available, and many families like working on paper because the real test is done without a calculator. If you print questions, set a timer for each section: 35 minutes for 37 Quantitative Reasoning items and 40 minutes for 47 Mathematics Achievement items. Grade your work afterward and redo any missed problem from scratch.

What math topics are on the ISEE Upper Level?

The ISEE Upper Level math covers algebra (linear and quadratic equations, exponents, polynomials), geometry (area, volume, angles, coordinate transformations), data analysis and probability, and number sense with fractions, decimals and percents. Quantitative Reasoning leans on word problems and quantitative comparisons, while Mathematics Achievement checks curriculum skills more directly. A shadow problem using similar triangles is a typical example.

What is the timing for the ISEE Upper Level?

The two ISEE Upper Level math sections give you 35 minutes for 37 Quantitative Reasoning questions and 40 minutes for 47 Mathematics Achievement questions, or 84 questions in 75 minutes. That is a little under a minute per question, so practice skipping a tough item and coming back. The full test also includes verbal, reading and essay sections with short breaks.

How should I use ISEE Upper Level practice tests?

Start with one timed ISEE Upper Level practice test as a diagnostic, then spend a few weeks drilling the topics you missed most before taking another full test. Since there is no guessing penalty, practice answering every question, even when you have to make an educated guess. Review each wrong answer by reworking it by hand without a calculator.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• ISEE Upper Level Math Formula Cheat Sheet
• How to find the slope of a line
• How to use the Pythagorean theorem
• Rules of exponents
• Order of operations (PEMDAS)