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Free ISEE Math Practice Test — Grade 6

Math only, deliberately — the real ISEE (published by ERB) also has verbal and reading sections, which we don't cover.

20 real practice questions at ISEE Lower Level difficulty, drawn from the same calibrated bank our adaptive practice uses. Work through them right here — every question has the answer and a step-by-step explanation one tap away.

Question 1 · Coordinate GraphsIntro
A worker at a hardware store marks shelf spots on a grid where each unit equals 1 foot. She wants to place a point one-half of a foot to the right of the y-axis and 3 feet above the x-axis. Which point shows that location?
A(1, 3)
B(12\frac{1}{2}, 3)
C(2, 3)
D(3, 12\frac{1}{2})
Show answer & explanation
Let's work it out
1.The description says one-half of a foot to the right of the y-axis, which is the x-coordinate, and 3 feet above the x-axis, which is the y-coordinate.
2.The ordered pair is written (x, y), so the correct location is (12\frac{1}{2}, 3).
Answer: B) (12\frac{1}{2}, 3)
Question 2 · Coordinate GraphsIntro
During a scooter trip around the neighborhood, Maya marks her progress on a coordinate grid. Each point on the grid shows how far she has traveled: the x-axis shows hours spent riding and the y-axis shows the total distance traveled in kilometers. The points she marks are listed below. Hours Ridden (x) | Distance Traveled in km (y) 0.2 | 0.6 0.4 | 1.2 0.6 | 1.8 0.8 | 2.4 According to the grid, how many kilometers has Maya traveled after riding for 0.6 hours?
A1.8
B1.5
C0.6
D1.2
Show answer & explanation
Let's work it out
1.To find the distance traveled after 0.6 hours, locate the row in the table where the Hours Ridden column equals 0.6.
2.Reading across that row, the corresponding Distance Traveled value is 1.8 kilometers.
3.Therefore, Maya has traveled 1.8 km after riding for 0.6 hours.
Answer: A) 1.8
Question 3 · Arithmetic & Number SenseEasy
A weather station recorded that a nature preserve received four and sixty-two thousandths inches of rain during a single storm. A student volunteer is entering this amount into a data log. Which decimal correctly represents this rainfall total?
A40.62
B4.062
C4.62
D4.602
Show answer & explanation
Let's work it out
1.To convert a number word to a decimal, identify each part by its place value.
2.Four and sixty-two thousandths means 4 ones, plus sixty-two in the thousandths position.
3.Because sixty-two thousandths occupies the hundredths and thousandths places (with nothing in the tenths place), a zero must be written as a placeholder in the tenths column.
4.This gives 4.062: the digit 0 in the tenths place, 6 in the hundredths place, and 2 in the thousandths place.
Answer: B) 4.062
Question 4 · Algebraic ExpressionsEasy
A builder is cutting a rectangular plank that is 4.5 feet long and 1.2 feet wide. She needs to attach a metal strip along twice the length of the plank and once across the width. How many feet of metal strip does she need in all?
A9.7
B7.7
C11.4
D10.2
Show answer & explanation
Let's work it out
1.The builder needs twice the length plus once the width, which is the expression 2L + W.
2.Substituting L = 4.5 and W = 1.2: 2(4.5) + 1.2 = 9.0 + 1.2 = 10.2 feet.
Answer: D) 10.2
Why the other choices are tempting: The value 5.7 comes from computing L + W, omitting the factor of 2 on the length. The value 7.7 comes from treating the coefficient 2 as a separate addend rather than a multiplier, giving 2 + 4.5 + 1.2. The value 9.7 comes from a place-value error that produces 8.5 instead of 9.0 for 2 times 4.5. The value 11.4 comes from computing the full perimeter 2L + 2W instead of 2L + W.
Question 5 · PercentagesEasy
A school is hosting a bake sale with 50 cookies. By lunchtime, 40% of the cookies have been sold. How many cookies are left after lunchtime?
A30 cookies
B10 cookies
C20 cookies
D25 cookies
Show answer & explanation
Let's work it out
1.Step 1: Find how many cookies were sold.
2.40% of 50 = 0.40 x 50 = 20 cookies sold.
3.Step 2: Subtract from the total.
4.50 - 20 = 30 cookies left.
Answer: A) 30 cookies
Why the other choices are tempting: The answer is 30 cookies.
Question 6 · Ratios & ProportionsEasy
A class makes red and yellow paper chains in a ratio of 2 to 3. If the class makes 8 red paper chains, how many yellow paper chains do they make?
A10 yellow chains
B5 yellow chains
C6 yellow chains
D12 yellow chains
Show answer & explanation
Let's work it out
1.The ratio of red to yellow chains is 2 to 3.
2.If there are 8 red chains, find how many times 2 fits into 8: 8 divided by 2 = 4.
3.Multiply the yellow chains by the same factor: 3 times 4 = 12.
4.So there are 12 yellow paper chains.
Answer: D) 12 yellow chains
Question 7 · Equations & InequalitiesStandard
Number lineNumber line from -10 to 0, marked every 1. A point is marked at -6. -10-9-8-7-6-5-4-3-2-10
During a winter wildlife survey, a number line marks a reference temperature. If the nighttime temperature t was warmer than the marked temperature, which could be the value of t?
A-8
B-6
C-7
D-5
Show answer & explanation
Let's work it out
A warmer temperature has a greater value and appears farther to the right on the number line.
Answer: D) -5
Why the other choices are tempting: The value -5 lies to the right of the marked temperature, so t could be -5.
Question 8 · Fractions & DecimalsStandard
QuadrilateralQuadrilateral. Side length: 9 feet. 9 feet
A wood plank in the school workshop is 9 feet long. A student cuts off a piece that is 2 and 56\frac{5}{6} feet long to build a shelf bracket. How many feet of the plank remain after the cut?
A1
B6 and 16\frac{1}{6}
C6 and 56\frac{5}{6}
D7
Show answer & explanation
Let's work it out
1.To find the remaining length, subtract 2 and 56\frac{5}{6} from 9.
2.Since 9 has no fractional part, rewrite it as 8 and 66\frac{6}{6}.
3.Then subtract the whole parts: 8 − 2 = 6, and subtract the fraction parts: 66\frac{6}{6} − 56\frac{5}{6} = 16\frac{1}{6}.
4.The remaining length is 6 and 16\frac{1}{6} feet, which is answer B.
Answer: B) 6 and 16\frac{1}{6}
Question 9 · GeometryStandard
QuadrilateralQuadrilateral. Side length: Base area: 144.0 square centimeters. Base area: 144.0 square centimeters
The figure shows the square base of a cube-shaped storage insert being built in a school maker space. The area of the base is labeled in the figure. The insert will be filled with small cube-shaped spacers, each with side length 3.0 centimeters. If the spacers fit without gaps, how many are needed?
A576
B4
C64
D16
Show answer & explanation
Let's work it out
1.Because 12.0 × 12.0 = 144.0, the larger cube has side length 12.0 centimeters and volume 12.0 × 12.0 × 12.0 = 1,728 cubic centimeters.
2.Each spacer has volume 3.0 × 3.0 × 3.0 = 27 cubic centimeters.
3.Therefore, the insert holds 1,728 ÷ 27 = 64 spacers.
Answer: C) 64
Question 10 · Pre-AlgebraStandard
QuadrilateralQuadrilateral. Side lengths: 3/4 ft, 5/4 ft, ? ft, 3/2 ft. 3/4 ft5/4 ft? ft3/2 ft
The figure shows a quadrilateral. Three of its side lengths and its perimeter are labeled. What is the length, in feet, of the missing side?
A54\frac{5}{4}
B114\frac{11}{4}
C72\frac{7}{2}
D194\frac{19}{4}
Show answer & explanation
Let's work it out
1.Let s equal the missing side length in feet.
2.The perimeter equals the sum of all four sides, so s + 34\frac{3}{4} + 54\frac{5}{4} + 32\frac{3}{2} = 194\frac{19}{4}.
3.Converting 32\frac{3}{2} to fourths gives 64\frac{6}{4}, so the three known sides sum to 34\frac{3}{4} + 54\frac{5}{4} + 64\frac{6}{4} = 144\frac{14}{4}.
4.Subtracting from the perimeter gives s = 194\frac{19}{4} - 144\frac{14}{4} = 54\frac{5}{4} feet.
Answer: A) 54\frac{5}{4}
Question 11 · Ratios & ProportionsStandard
Greenhouse Seedling Count
DayOak SeedlingsPine Seedlings
1610
245
31815
A class nature study tracked how many oak and pine seedlings sprouted in a greenhouse over three days. The results are shown. Day 1: 6 oak seedlings, 10 pine seedlings Day 2: 4 oak seedlings, 5 pine seedlings Day 3: 18 oak seedlings, 15 pine seedlings On which day was the ratio of oak seedlings to pine seedlings the greatest, and what is that ratio in simplest form?
A18:15
B22:15
C5:6
D6:5
Show answer & explanation
Let's work it out
1.Computing the oak-to-pine ratio for each day: Day 1 gives 6:10, which simplifies to 3:5 (0.6 as a decimal); Day 2 gives 4:5 (0.8); Day 3 gives 18:15, which simplifies by dividing both by 3 to get 6:5 (1.2).
2.Since 1.2 is the largest of the three values, Day 3 has the greatest ratio, and in simplest form it is 6:5.
Answer: D) 6:5
Why the other choices are tempting: The value 4:5 is the Day 2 ratio — a student who stopped comparing after Day 2 or misidentified the maximum would report this. The value 18:15 is the unsimplified Day 3 ratio, the result of skipping the GCF reduction step. The value 22:15 comes from mistakenly combining Day 2 and Day 3 oak counts (4 + 18 = 22) and using only Day 3 pine (15). The value 5:6 is the correct Day 3 ratio written in reverse, putting pine before oak.
Question 12 · Data & StatisticsStandard
A pet store sold the following number of fish each day for one week: 12, 9, 15, 9, 11, 14, and 9. What is the difference between the greatest number of fish sold in a day and the least number of fish sold in a day?
AA) 3
BB) 5
CC) 6
DD) 7
Show answer & explanation
Let's work it out
1.First find the greatest value: 15.
2.Then find the least value: 9.
3.Subtract: 15 - 9 = 6.
4.The difference (range) is 6.
Answer: C) C) 6
Question 13 · GeometryStandard
OctagonOctagon. Side lengths: 9 meters, 2 meters, 3 meters, 3 meters, 4 meters, 3 meters, 2 meters. 9 meters2 meters3 meters3 meters4 meters3 meters2 meters
During a class trip, students walk one complete lap along the right-angled boundary of the overlook shown. How far do they walk?
A17 meters
B44 meters
C34 meters
D42 meters
Show answer & explanation
Let's work it out
1.The vertical sides running upward total 2 + 3 + 3 = 8 meters, so the unlabeled side is 8 meters.
2.Adding the lengths of all eight sides gives a total distance of 34 meters.
Answer: C) 34 meters
Question 14 · Data & StatisticsStandard
Bar chart: Basketball Points by PlayerBar chart: Basketball Points by Player. Horizontal axis: Player. Vertical axis: Points Scored. Values: Player 1 8, Player 2 10, Player 3 12, Player 4 14, Player 5 16, Player 6 18, Player 7 20. Basketball Points by Player 051015208101214161820Player1Player2Player3Player4Player5Player6Player7PlayerPoints Scored
The bar chart shows the number of points scored by seven players in a basketball game. What is the mean (average) number of points scored per player?
AA) 10
BC) 14
CD) 16
DE. 13
Show answer & explanation
Let's work it out
1.The points scored by the seven players are: 8, 10, 12, 14, 16, 18, 20.
2.Sum = 8 + 10 + 12 + 14 + 16 + 18 + 20 = 98.
3.Mean = Sum ÷ Number of players = 98 ÷ 7 = 14.
4.The correct answer is 14.
Answer: B) C) 14
Question 15 · Arithmetic & Number SenseHard
A track coach calculates a relay team's score using the following rule: begin with a base score of 20 points, then add one-half point for each qualifying lap completed, then add one-third point for each bonus lap completed. In Saturday's meet, the team finished 8 qualifying laps and 6 bonus laps. What was the team's total score?
A30
B28
C24
D26
Show answer & explanation
Let's work it out
1.Apply the scoring rule step by step, completing each multiplication before adding.
2.First, multiply 8 qualifying laps by one-half point each: 8 × (12\frac{1}{2}) = 4 points.
3.Next, multiply 6 bonus laps by one-third point each: 6 × (13\frac{1}{3}) = 2 points.
4.Finally, add both results to the base score: 20 + 4 + 2 = 26.
5.The total score is 26.
6.Why the other answers are wrong: • 30 (A): The student awarded 1 full point per qualifying lap instead of 12\frac{1}{2}, computing 20 + (8 × 1) + (6 × 13\frac{1}{3}) = 20 + 8 + 2 = 30. • 28 (B): The student calculated the qualifying contribution twice and ignored bonus laps entirely, computing 20 + (8 × 12\frac{1}{2}) + (8 × 12\frac{1}{2}) = 20 + 4 + 4 = 28. • 24 (C): The student correctly added the qualifying contribution but omitted the bonus-lap term entirely, computing 20 + (8 × 12\frac{1}{2}) = 20 + 4 = 24. • 29 (E): The student applied both the 12\frac{1}{2} and 13\frac{1}{3} rates to the bonus laps in addition to the correct qualifying term, computing 20 + (8 × 12\frac{1}{2}) + (6 × 12\frac{1}{2}) + (6 × 13\frac{1}{3}) = 20 + 4 + 3 + 2 = 29.
Answer: D) 26
Question 16 · Equations & InequalitiesHard
x and y Values
xy
15
28
311
414
?20
A teacher writes a rule on the board and fills in part of the table. Every (x, y) pair in the table follows the rule y = 3x + 2. The table shows: when x = 1, y = 5; when x = 2, y = 8; when x = 3, y = 11; when x = 4, y = 14; and when y = 20, x =?. What is the missing value of x?
A7
B3
C18
D6
Show answer & explanation
Let's work it out
1.Every pair follows y = 3x + 2.
2.To find x when y = 20, substitute 20 for y: 20 = 3x + 2.
3.Subtract 2 from both sides: 18 = 3x.
4.Divide both sides by 3: x = 6.
5.You can verify: 3(6) + 2 = 18 + 2 = 20.
6.Extending the table pattern (x goes 1, 2, 3, 4, 5, 6 while y goes 5, 8, 11, 14, 17, 20) also confirms x = 6.
7.Stopping at x = 5 gives y = 17, not 20.
8.Dividing by 6 instead of 3 gives x = 3.
9.Forgetting to divide after subtracting gives 18, which is not the x-value.
Answer: D) 6
Question 17 · Algebraic ExpressionsHard
After-School Crafts Program
ClubStudentsSupply Cost per StudentInstructor Stipend
Pottery12$4$18
Weaving20$3$22
Jewelry15$5$30
An after-school crafts program runs three clubs. The table shows enrollment, supply cost per student, and a flat instructor stipend for each club. What is the total amount, in dollars, the program must spend on all three clubs combined?
A70
B228
C253
D183
Show answer & explanation
Let's work it out
1.For each club, multiply the number of enrolled students by the supply cost per student, then add the flat instructor stipend.
2.Pottery: 12 students × $4 per student + $18 stipend = $48 + $18 = $66.
3.Weaving: 20 students × $3 per student + $22 stipend = $60 + $22 = $82.
4.Jewelry: 15 students × $5 per student + $30 stipend = $75 + $30 = $105.
5.Adding all three clubs together: $66 + $82 + $105 = $253.
Answer: C) 253
Why the other choices are tempting: The answer is $253.
Question 18 · Fractions & DecimalsHard
Weather Balloon Cloud Observations
Cloud classificationNumber of observations
Low clouds30,000
Middle clouds42,000
High clouds24,000
A weather balloon classified its cloud observations by altitude, as shown in the table. What decimal represents the fraction of all observations classified as middle clouds?
A0.42
B0.3125
C0.4375
D0.75
Show answer & explanation
Let's work it out
1.The table contains 30,000 + 42,000 + 24,000 = 96,000 observations in all.
2.Middle clouds account for 42,00096\frac{000}{96},000 = 716\frac{7}{16} of the observations, and 716\frac{7}{16} equals 0.4375.
Answer: C) 0.4375
Question 19 · PercentagesHard
ItemOriginal PriceDiscount
Jacket$6014\frac{1}{4} off
Hat$4015\frac{1}{5} off
The table shows the original prices and sale discounts on two items at a school clothing fair. Jordan buys both items at their sale prices. How much does Jordan pay in total?
A100
B77
C92
D75
Show answer & explanation
Let's work it out
1.For the jacket, a 14\frac{1}{4} off discount means Jordan pays 34\frac{3}{4} of $60: (34\frac{3}{4}) x 60 = $45.
2.For the hat, a 15\frac{1}{5} off discount means Jordan pays 45\frac{4}{5} of $40: (45\frac{4}{5}) x 40 = $32.
3.The total is 45 + 32 = $77.
Answer: B) 77
Why the other choices are tempting: The value 75 comes from applying the jacket's 14\frac{1}{4} discount to both items instead of using 15\frac{1}{5} for the hat: (34\frac{3}{4}) x 60 + (34\frac{3}{4}) x 40 = 45 + 30 = 75. The value 92 comes from forgetting to discount the jacket and only discounting the hat: 60 + 32 = 92. The value 100 comes from paying full price for both items and applying no discounts at all. The value 78 comes from swapping the two discounts -- applying 15\frac{1}{5} off to the jacket and 14\frac{1}{4} off to the hat: 48 + 30 = 78.
Question 20 · Pre-AlgebraHard
DayChange
Monday-8 mm
Tuesday+5 mm
Wednesday-3 mm
Thursday+12 mm
Friday-6 mm
The table shows how the water level in a rain gauge changed each day compared to the previous day during a school week. What was the mean (average) daily change in water level over these five days?
A6.8 mm
B0 mm
C3.4 mm
D0.5 mm
Show answer & explanation
Let's work it out
1.Add all five daily changes together: −8 + 5 + (−3) + 12 + (−6).
2.Group the negative values: −8 − 3 − 6 = −17.
3.Group the positive values: 5 + 12 = 17.
4.The total is −17 + 17 = 0.
5.Divide by the number of days: 0 ÷ 5 = 0 mm.
6.The mean daily change in water level is 0 mm.
Answer: B) 0 mm

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