SAT math review

What is the equivalent expression for (2x + 3)(x - 4) - (x - 4)?

(2x + 3)(x - 4) - (x - 4) simplifies to (2x + 2)(x - 4).

In the expression 5(a + b) - 2(a - b) = ka + mb, what are the values of k and m?

k = 3, m = 3.

How do you simplify the expression 3(x^2 − 2x) + 4(2x − x^2)?

The expression simplifies to x^2 + 6x.

What are the real solutions for the equation x^2 − 5x + 6 = 0?

x = 2 and x = 3.

If x^3 = 27, what is the value of x?

x = 3.

Find all real solutions to the equation 2x^2 + 3x - 2 = 0.

x = 1 and x = -2.

Solve the system of equations: 2x + y = 10 and x^2 + y = 13.

The solutions are (2, 6) and (3, 4).

What are all solutions to the equations x + y = 4 and x^2 + y^2 = 20?

The solutions are (2, 2) and (4, 0).

If y = 2x + 1 and x^2 + y = 10, what are all possible values of x and y?

The solutions are (2, 5) and (-3, -5).

What is f(−2) if f(x) = x^2 + 3x?

f(−2) = -2.

Find all x for which g(x) = 2x^2 − 5x + 1 equals 0.

The solutions are x = 1 and x = 0.5.

What is the minimum value of h(x) = x^2 − 4x + 7?

The minimum value is 3.

What is the solution for 4x − 7 = 9?

x = 4.

If 3(x + 2) = 2x − 5, what is the value of x?

x = -11.

What value of x satisfies 7x + 3 = 2x + 18?

x = 3.

What is y when x = 5 in the equation 2x + y = 14?

y = 4.

For which value of x does x + 3y = 12 and y = 2x?

x = 2.

If 4x − y = 8 and x = 3, what is y?

y = 4.

What is the slope of the line represented by y = −3x + 2?

The slope is -3.

If f(x) = 2x − 5, what is f(4)?

f(4) = 3.

What are the values of m and b in the function f(x) = mx + b if f(2) = 7 and f(5) = 16?

m = 3, b = 1.

Solve the system of equations: x + y = 8 and 3x − y = 4.

The solution is (4, 4).

What is the solution to the system: 2x + 5y = 19 and x − y = 1?

The solution is (3, 2).

If x + 2y = 10 and 3x − y = 5, find x and y.

x = 3, y = 2.

Solve the inequality 5x − 3 < 12.

x < 3.

If 2x + y ≥ 7 and x = 2, what is the smallest integer value of y?

y ≥ 3.

Graph the solution set for x − y ≤ 4.

The region above the line y = x - 4.

What is the ratio of girls to boys if there are 21 boys in a class with a ratio of 3:4?

28 girls.

If a car travels 180 miles in 3 hours, what is its average speed?

60 miles per hour.

If 5 pens cost $8, what is the cost of 12 pens at the same rate?

$19.20.

What is 30% of 250?

75

What is the percent increase when the price of a shirt goes from $40 to $50?

25%.

If a number is decreased by 15% and the result is 85, what was the original number?

100

Find the median of the data set: 12, 8, 15, 10, 20.

Median is 12.

What is the mean score of the test scores: 70, 80, 90, 100?

Mean score is 85.

What is the range of the data set: 5, 12, 7, 18, 9?

Range is 13.

What type of relationship does the points (1,2), (2,4), (3,6), (4,8) suggest?

A linear relationship.

If a scatterplot shows a downward trend, what kind of correlation is indicated?

Negative correlation.

Find the equation of the line of best fit for the data points (2,3), (4,7), (6,11).

y = 2x - 1.

What is the probability of rolling a sum of 7 on two fair dice?

1/6.

What is the probability of drawing a blue marble from a bag containing 3 red and 5 blue marbles?

5/8.

If the probability it rains on a given day is 0.3, what is the probability it does not rain?

0.7.

Estimate the percent that prefer online classes from a survey of 200 students where 60 prefer online classes.

30%.

If a poll has a margin of error of 4% and 52% favor a policy, what is the possible range for the population proportion?

48% to 56%.

What is the confidence interval if a sample mean is 75 with a margin of error of 3?

72 to 78.

Is a study where researchers assign treatments to participants an experiment or an observational study?

An experiment.

What kind of study would be needed to establish causation for the claim that eating chocolate causes better memory?

A randomized controlled trial.

Why might an observational study be less reliable than a randomized controlled trial?

It may have confounding variables.

What is the area of a circle with radius 5?

Area = 25π.

Find the volume of a rectangular prism with length 4, width 3, and height 6.

Volume = 72.

What is the area of a triangle with base 10 and height 8?

Area = 40.

In triangle ABC, if angle A = 50° and angle B = 60°, what is angle C?

Angle C = 70°.

What are the other angles formed when two lines intersect to form angles of 120° and 60°?

The other angles are 60° and 120°.

In a right triangle, if the legs are 6 and 8, what is the length of the hypotenuse?

Hypotenuse = 10.

If sin θ = 3/5, and θ is an acute angle, what is cos θ?

cos θ = 4/5.

In a right triangle, if the adjacent side to angle θ is 7 and the opposite side is 24, find tan θ.

tan θ = 24/7.

If a ladder leans against a wall making a 60° angle with the ground and is 10 feet long, how high up the wall does it reach?

Height = 5√3 feet.

What is the circumference of a circle with diameter 12?

Circumference = 12π.

A central angle of 90° in a circle cuts off an arc of what length if the radius is 8?

Arc length = 12.57.

If the area of a circle is 36π, what is its radius?

Radius = 6.