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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The Best Books to Ace the ISEE Upper Level Math Test

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.

Frequently Asked Questions

How many math sections are on the ISEE Upper Level?

Two: Quantitative Reasoning (37 questions in 35 minutes) and Mathematics Achievement (47 questions in 40 minutes). Quantitative Reasoning focuses on word problems, quantitative comparisons, and number sense. Mathematics Achievement tests school-curriculum topics like algebra, geometry, and data.

Is a calculator allowed on the ISEE?

No. Calculators are not allowed on any portion of the ISEE, including both math sections. Practice arithmetic, fraction work, and basic algebra by hand throughout your prep.

Does the ISEE penalize guessing?

No. The ISEE has no guessing penalty. Wrong answers don’t subtract from your score, so answer every single question even if you have to guess blindly. Mark uncertain questions and come back if time allows.

What grades take the ISEE Upper Level?

Students applying for admission to grades 9 through 12. Most are currently in grades 8-11. Younger students take the Middle Level (apply to grades 7-8), Lower Level (apply to grades 5-6), or Primary Level (apply to grades 2-4) versions.

How is the ISEE scored?

Each section gets a scaled score (760-940) and a stanine (1-9, with 9 being highest). The stanine compares your performance against other ISEE-takers in your same grade applying to the same level. Most competitive schools focus heavily on stanine.

What’s the difference between Quantitative Reasoning and Mathematics Achievement?

Quantitative Reasoning tests math reasoning — word problems, quantitative comparisons (column A vs column B), and problem-solving with less heavy computation. Mathematics Achievement tests school-curriculum knowledge: algebra mechanics, geometry formulas, and data analysis. Two different angles on the same math.

How long is the full ISEE Upper Level test?

About 2 hours 40 minutes of actual testing. It covers Verbal Reasoning (20 min), Quantitative Reasoning (35 min), Reading Comprehension (35 min), Mathematics Achievement (40 min), and an Essay (30 min), with two 5-10 minute breaks between sections.

Can my child retake the ISEE?

Yes — but only once per testing season (Fall, Winter, Spring/Summer). The ERB caps you at 3 attempts per 12-month period across those windows. Schools typically receive your most recent score, not your highest.

What math topics are on the ISEE Upper Level?

Algebra (linear and quadratic equations, exponents, polynomials), geometry (area, volume, angles, triangles, coordinate geometry), data analysis (mean, median, mode, probability, charts), and number sense (fractions, decimals, ratios, percents). Difficulty reaches into Algebra I and early Algebra II content.

How long should we prepare for the ISEE Upper Level?

For most middle and high schoolers, 6-10 weeks of consistent practice at 30-45 minutes per day works well. Start with a diagnostic test, identify the weakest topics, drill those, then build up to full timed practice in the last 2-3 weeks.

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)