SAT 数学与阅读练习

Subtract 5 from both sides of the equation to isolate x: x = 12 - 5, which simplifies to 7. Substituting 7 back into the original equation gives 7 + 5 = 12, confirming the answer.

Convert 25% to its decimal form 0.25, then multiply 80 by 0.25 to get 20. This follows the rule that a percentage of a number equals the number times the percentage expressed as a decimal.

Divide both sides of 3x = 18 by 3 to isolate x: x = 18 / 3 = 6. Check the result by substituting 6 into the original equation: 3 × 6 = 18.

Apply the distributive property by multiplying 2 by each term inside the parentheses: 2(x + 3) = 2x + 6. The x term and the constant term are both scaled by 2, so option b is the only equivalent expression.

An exponent tells you how many times to multiply the base by itself, so 4^2 means 4 × 4. Multiplying gives 16, which matches the correct choice.

The area of a rectangle is length times width. With length 6 and width 4, the area is 6 × 4 = 24 square units; the other options confuse area with perimeter or double-count the dimensions.

In y = mx + b, m is the slope, so the slope is 2.

Since x^2 = 49, x is the positive square root of 49. Because 7 × 7 = 49, one positive value of x is 7; the other possible value is -7.

The interior angles of a triangle always sum to 180 degrees.

The fraction 1/4 means 1 divided by 4, which is 0.25. Think of one dollar divided into four equal parts: each part is 25 cents, or 0.25.

The decimal 0.5 represents five tenths, which simplifies to 1/2. Dividing 1 by 2 gives 0.5, so 1/2 is the only equivalent fraction among the options.

Substitute the given value x = 4 into the equation y = 3x. This gives y = 3 × 4 = 12, so the correct value of y is 12.

Each term is multiplied by 2, so the next term is 32.

Express 60% as the decimal 0.6, then multiply 50 by 0.6 to find 60% of 50. The calculation 50 × 0.6 = 30 gives the correct result.

The median is the middle value after the numbers are arranged in order. The set 3, 7, 9 is already ordered, and 7 is in the middle, so the median is 7.

The mean is (2 + 4 + 6) / 3 = 12 / 3 = 4.

3^2 + 4^2 = 9 + 16 = 25 = 5^2, so it is a right triangle.

The perimeter of a square is the sum of all four equal sides, or 4 times the side length. For side length 5, perimeter = 4 × 5 = 20.

Add 4 to both sides: 2x = 12, so x = 6.

Absolute value measures distance from zero on the number line, so it is always nonnegative. The distance from -7 to 0 is 7, so |-7| = 7.

A prime number has exactly two distinct positive divisors: 1 and itself. Among the options, 9, 15, and 21 are composite, while 11 is divisible only by 1 and 11.

To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. Since 3/5 = 0.6, the equivalent percent is 0.6 × 100 = 60%.

Divide both sides of 5y = 20 by the coefficient 5 to isolate y. This gives y = 20 / 5 = 4; substituting 4 back into the equation confirms 5 × 4 = 20.

6/8 simplifies to 3/4 after dividing by 2.

Multiplication comes first: 3 × 4 = 12, then 2 + 12 = 14.

x > 5, so x = 6 is the only option that satisfies the inequality.

A slope of 0 means the line does not rise or fall; it is horizontal.

In y = mx + b, b is the y-intercept, so it is -4.

Average speed is total distance divided by total time. Traveling 60 miles in 1 hour gives 60 / 1 = 60 miles per hour, so the correct choice is 60 mph.

Ten percent means 10 out of every 100, or 0.1 in decimal form. Multiply 250 by 0.1 to find 10% of 250: 250 × 0.1 = 25.

The decimal 0.75 represents 75 hundredths, which simplifies to 3/4. Dividing 3 by 4 gives 0.75, so 3/4 is the only equivalent fraction listed.

The exponent 5 tells you to multiply the base 2 by itself five times: 2 × 2 × 2 × 2 × 2 = 32. Therefore, the value of 2^5 is 32.

The mode is the value that appears most often, which is 3.

The range of a data set is the largest value minus the smallest value. For {2, 5, 9}, the range is 9 - 2 = 7; the middle value 5 is not part of this calculation.

Divide both sides of 4x = 28 by 4 to isolate x: x = 28 / 4 = 7. Check by substituting 7 back: 4 × 7 = 28, so the answer is correct.

The area of a triangle is half the product of its base and height. With base 10 and height 6, area = (10 × 6) / 2 = 30 square units.

Circumference is the distance around a circle and equals 2πr, where r is the radius. With radius 7, circumference = 2 × 7 × π = 14π.

To solve x/4 = 3, multiply both sides by 4 to undo the division. This gives x = 3 × 4 = 12; substituting 12 back makes 12 / 4 = 3.

The factorial 7! equals 7 × 6!, so the fraction 7! / 6! simplifies to 7. Dividing both factorials cancels every common factor except the 7.

Subtract 3: 2a = 8, then divide by 2: a = 4.

An even integer is divisible by 2 with no remainder. Among the options, only 12 is even; 7, 9, and 15 are odd.

The exponent 3 means multiply the base 3 by itself three times: 3 × 3 × 3 = 27. Therefore, the value of 3^3 is 27.

When multiplying powers with the same base, add exponents: x^5.

Follow the order of operations: perform multiplication before subtraction. First compute 5 × 6 = 30, then subtract from 100 to get 100 - 30 = 70.

A 25% discount means the customer pays 25 percent less than the original price. Multiply the original price $40 by 0.25 to find the discount: 40 × 0.25 = $10.

Translate the sentence into the equation 4x + 3 = 15, since 15 is 3 more than 4x. Subtract 3 from both sides to get 4x = 12, then divide by 4 to find x = 3.

Slope is the change in y divided by the change in x between two points. From (0, 0) to (2, 4), the slope is (4 - 0) / (2 - 0) = 4 / 2 = 2.

√2 cannot be written as a ratio of two integers, so it is irrational.

The decimal 0.2 means 2 tenths, written as the fraction 2/10. Simplify by dividing the numerator and denominator by 2, giving 1/5.

Substitute x = 4 into x + y = 10 to get 4 + y = 10. Subtract 4 from both sides to isolate y: y = 10 - 4 = 6.

The largest factor shared by 12 and 18 is 6.

The smallest multiple shared by 4 and 6 is 12.

Probability is the number of favorable outcomes divided by the total number of outcomes. There are 3 red marbles out of 8 total, so the probability of picking red is 3/8.

Any nonzero number raised to the power 0 equals 1.

Divide both sides of 3(x + 2) = 21 by 3 to get x + 2 = 7. Then subtract 2 from both sides to find x = 5; check: 3(5 + 2) = 21.

4^2 = 16, and -4 is also a solution but is not listed.

Average speed equals total distance divided by total time. The train covers 120 miles in 2 hours, so speed = 120 / 2 = 60 miles per hour.

A negative slope means the y-value decreases as the x-value increases. On a coordinate graph, that line falls from left to right, which is the correct description.

To evaluate f(x) = x + 1 at x = 3, substitute 3 for x: f(3) = 3 + 1 = 4. Function notation simply names the rule applied to the input.

This is the Fibonacci sequence; each term is the sum of the previous two, so 5 + 8 = 13.

Many SAT Reading questions ask you to support an answer with passage evidence.

A horizontal line has slope 0; a vertical line has undefined slope.

An odd plus an odd always produces an even number.

A prime number is divisible by exactly two distinct positive integers: 1 and itself. Numbers with additional divisors are composite, so the statement is true.

The mode is the most frequent value, not necessarily the largest.

Vocabulary-in-context questions ask how a word is used in the passage.

The median is the middle value when the data are ordered.

A negative slope means the line falls from left to right.

Start with 2x + 6 = 14 and subtract 6 from both sides to get 2x = 8. Then divide both sides by 2 to find x = 4.

The area of a square is side length squared. For side length 9, area = 9 × 9 = 81 square units.

To find 40% of 90, convert 40% to 0.4 and multiply: 90 × 0.4 = 36. Another approach is 40/100 × 90 = 36.

Each term in 5, 10, 20, 40 is twice the previous term. Multiplying the last term 40 by 2 gives the next number, 80.

The median is the middle value when the numbers are ordered. For 4, 8, and 12, the middle value is 8, so the median is 8.

The exponent 4 means multiply the base 3 by itself four times: 3 × 3 × 3 × 3. Working step by step, 3 × 3 = 9, 9 × 3 = 27, and 27 × 3 = 81.

Slope measures steepness, median is the middle value, mode is the most frequent value, and mean is the average.

Perimeter is distance around, area is 2D space, volume is 3D space, and radius goes from center to edge.

A prime has exactly two divisors, an even number is divisible by 2, an odd number is not, and a square equals n^2.

The x-intercept crosses the x-axis, the y-intercept crosses the y-axis, slope is the rate of change, and a constant is a fixed value.

Integers are whole numbers, fractions show parts of a whole, decimals use base-10 place value, and percents mean parts per hundred.

An inference is a conclusion from evidence, evidence is supporting facts, a paraphrase restates an idea, and a summary gives main points.