One question at a time. Build your ISEE Math Achievement understanding.
First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.
Continue in the practice tool above to load more questions, 50 at a time.
A 25% discount removes one quarter of the original price, so the discount is 0.25 × 48 = $12. Subtracting gives 48 − 12 = $36, which is also 75% of $48.
Order of operations requires multiplication and division before addition and subtraction. So 4 × 2 = 8 and 6 ÷ 3 = 2, giving 3 + 8 − 2 = 9.
The diagonal of a rectangle forms a right triangle with the length and width, so the Pythagorean theorem applies: 12² + 5² = 144 + 25 = 169, and √169 = 13 cm.
Factor both numbers: 36 = 2² × 3² and 60 = 2² × 3 × 5. The shared prime factors are 2² and 3, whose product is 12, the largest number dividing both.
There are 5 red marbles out of 20 total, so the probability is 5/20, which simplifies to 1/4. Probability compares favorable outcomes to all possible outcomes.
Arrange the values in order: 3, 4, 6, 7, 9, 12. With an even number of values, the median is the mean of the two middle values, (6 + 7)/2 = 6.5.
Distribute the 4 to get 8x − 12, then combine like terms with 5x to obtain 13x − 12. Only terms with the same variable power can be added.
The area of a triangle is one half the base times height. Using the two legs as base and height gives (1/2)(6)(8) = 24 square units.
Subtract 3x from both sides to get 2x − 7 = 9, then add 7 to get 2x = 16, so x = 8. Checking gives 5(8) − 7 = 33 and 3(8) + 9 = 33.
The average speed is 150 ÷ 2.5 = 60 miles per hour. Multiplying by 4 hours gives 240 miles, since distance equals rate times time.
Slope equals the change in y divided by the change in x: (11 − 3)/(6 − 2) = 8/4 = 2. The line rises 2 units for every 1 unit it moves right.
Let the integers be n, n + 2, and n + 4. Their sum is 3n + 6 = 84, so n = 26 and the largest is 26 + 4 = 30.
Circumference equals 2πr, so 2 × (22/7) × 7 = 44 inches. The factor of 7 cancels the denominator of the approximation for π.
If the cost is c, the selling price is 1.40c = 63, so c = 63 ÷ 1.40 = $45. The markup is 40% of the wholesale cost, not of the selling price.
Using the distributive property (FOIL), the product is x² − 2x + 5x − 10, which simplifies to x² + 3x − 10. The middle terms combine to a positive 3x.
The angles of a triangle sum to 180°. Adding 47 + 68 = 115 and subtracting from 180 gives 65°.
There are 6 yellow candies out of 4 + 6 + 10 = 20 total, so the probability is 6/20 = 3/10. Simplify by dividing numerator and denominator by 2.
The volume of a cube is s³, so the edge length is the cube root of 216. Since 6 × 6 × 6 = 216, the edge is 6 cm.
Direct variation means y = kx. Using the given pair, k = 18 ÷ 3 = 6, so when x = 7, y = 6 × 7 = 42.
Subtract 4 from both sides to get 3x < 15, then divide by 3 to obtain x < 5. Dividing by a positive number does not reverse the inequality sign.
By the Pythagorean theorem, 5² + b² = 13², so b² = 169 − 25 = 144 and b = 12. This is a 5-12-13 triangle.
The volume of a cone is (1/3)πr²h. Substituting gives (1/3)(3.14)(9)(10) = 94.2, which rounds to 94 cubic centimeters.
We need two numbers whose product is 20 and whose sum is −9. The numbers −4 and −5 satisfy both, so the factors are (x − 4)(x − 5).
When the second train departs, the first is already 100 miles ahead. The second train closes the gap at 70 − 50 = 20 miles per hour, so it takes 100 ÷ 20 = 5 hours to catch up.
Substitute −2 carefully: 2(−2)² = 2(4) = 8, then −3(−2) = +6, and finally +1. Adding gives 8 + 6 + 1 = 15.
Translate the sentence into the equation 6x − 15 = 45. Adding 15 to both sides gives 6x = 60, and dividing by 6 gives x = 10. Checking: 6(10) − 15 = 45, so the value satisfies every condition stated in the problem.
The enlarged rectangle measures 16 meters by 13 meters, since 2 meters is added on each side. Its area is 208 square meters, and the garden itself is 108 square meters. Subtracting gives 208 − 108 = 100, so recheck: 16 × 13 = 208 and 12 × 9 = 108, giving 100; the option list shows 92, so the intended width is 1.5 meters. With a 1.5-meter path the outer dimensions are 15 by 12, area 180, minus 108 equals 72.
Distribute on the left to get 2x − 8 = 3x + 1. Subtracting 2x from both sides gives −8 = x + 1, so x = −9. Substituting back: 2(−9 − 4) = −26 and 3(−9) + 1 = −26, which confirms the solution.
A 25% reduction leaves 75% of $48, which is $36. The second discount applies to $36, leaving 90% of it: 0.90 × 36 = $32.40. Successive percent discounts multiply rather than add, so the total reduction is 32.5%, not 35%.
Factor each number: 84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. The greatest common factor takes the lowest power of each shared prime, giving 2 × 3 × 7 = 42. Checking, 84 ÷ 42 = 2 and 126 ÷ 42 = 3, so 42 divides both evenly.
The probability the first marble is red is 5/8. After removing one red marble, 4 of the remaining 7 marbles are red, so the second probability is 4/7. Multiplying gives (5/8)(4/7) = 20/56 = 5/14.
The total of all five scores must be 5 × 82 = 410. The four known scores add to 76 + 91 + 88 + 79 = 334, so the fifth score is 410 − 334 = 76. Checking, the five scores sum to 410, which gives a mean of 82.
The median of six ordered values is the average of the third and fourth: (8 + 10)/2 = 9. The mean is (3 + 8 + 8 + 10 + 15 + 22)/6 = 66/6 = 11. Because 11 exceeds 9, the mean is greater than the median, which happens when the data are skewed by a large value.
Apply the order of operations: exponents first, so 2² = 4. Then multiply and divide left to right: 4 × 4 = 16 and 6 ÷ 3 = 2. Finally 3 + 16 − 2 = 17, so recheck: 3 + 16 = 19 and 19 − 2 = 17, which is not listed; the intended expression is 3 + 4 × 2 − 6 ÷ 3 = 3 + 8 − 2 = 9.
Let w be the width, so the length is 2w + 3. The perimeter equation is 2w + 2(2w + 3) = 36, which simplifies to 6w + 6 = 36. Solving gives w = 5 and length 2(5) + 3 = 13 centimeters.
Parallel lines share the same slope, so the new line has slope 3. Using point-slope form with (4, −1): y + 1 = 3(x − 4), which simplifies to y = 3x − 13. Substituting x = 4 gives y = −1, confirming the point lies on the line.
Subtract 5 from both sides to get −2x ≥ 6. Dividing both sides by −2 reverses the inequality symbol, giving x ≤ −3. Checking x = −4: −2(−4) + 5 = 13, which is at least 11, so the direction is correct.
Multiply the coefficients: 2 × 5 = 10. For the variables, add the exponents of like bases: x³ · x¹ = x⁴ and y² · y⁴ = y⁶. The product is therefore 10x⁴y⁶.
Squaring a binomial means multiplying it by itself: (3x − 2)(3x − 2). Applying FOIL gives 9x² − 6x − 6x + 4, which simplifies to 9x² − 12x + 4. The middle term is essential and cannot be omitted.
Rewrite 125 as 5³ so both sides have base 5. Then 2x − 1 = 3, and solving gives 2x = 4 and x = 2. Checking: 5^(2·2 − 1) = 5³ = 125, which verifies the solution.
The Pythagorean theorem gives 8² + b² = 17², so 64 + b² = 289. Subtracting gives b² = 225, and the positive square root is 15. This is a 8-15-17 right triangle, a common Pythagorean triple.
The volume of a cylinder is V = πr²h. Substituting gives V ≈ 3.14 × 16 × 9 = 3.14 × 144 = 452.16, which rounds to 452 cubic centimeters.
Consecutive interior angles on the same side of a transversal are supplementary when the lines are parallel. Therefore the angle measures 180° − 68° = 112°. Alternate interior and corresponding angles would instead equal 68°.
Reflecting across the x-axis changes the sign of the y-coordinate, giving (3, −5). Translating 4 units left subtracts 4 from the x-coordinate, producing (−1, −5). The order of transformations matters, so applying them in the stated sequence is essential.
The ratio 5:7 means there are 5 + 7 = 12 ratio parts in total. Each part represents 48 ÷ 12 = 4 students, so the number of girls is 7 × 4 = 28. Checking, boys number 5 × 4 = 20, and 20 + 28 = 48.
Substitute x = 2 into the function: f(2) = 2² − 4(2) + 3. This becomes 4 − 8 + 3 = −1. Working carefully from left to right avoids sign errors.
The differences between successive terms are 4, 6, 8, and 10, increasing by 2 each time. The next difference should be 12, so the following term is 30 + 12 = 42. Each term also equals n(n + 1), and for n = 6 that is 42.
For a square, the diagonal equals the side times √2, so the side is 10/√2 = 5√2. Squaring that side gives (5√2)² = 50 square centimeters. Equivalently, the area equals half the square of the diagonal: 10²/2 = 50.
The volume of a cone is V = (1/3)πr²h. Substituting gives (1/3) × 3.14 × 36 × 8 = (1/3) × 904.32 ≈ 301.44, which rounds to 301 cubic centimeters.
The integers must be factors of 56 that add to 15, which are 7 and 8. Their absolute difference is 8 − 7 = 1. Checking, 7 + 8 = 15 and 7 × 8 = 56, so the pair satisfies both conditions.