SAT/PSAT Math Review 2

If 2x + 3 = 9, what is the value of 6x - 1?

• 17

• 10

• 7

• 11

Answer explanation

To solve for x, subtract 3 from both sides: 2x = 6, then divide by 2: x = 3. Now, substitute x into 6x - 1: 6(3) - 1 = 18 - 1 = 17. Thus, the value of 6x - 1 is 17.

Tags

CCSS.7.EE.B.4A

Given the equations: y = 2x + 10 and y = 2x - 1 At how many points do the graphs of the given equations intersect in the xy-plane?

• Zero

• Exactly one

• Exactly two

• Infinitely many

Answer explanation

The equations y = 2x + 10 and y = 2x - 1 have the same slope (2) but different y-intercepts (10 and -1). This means they are parallel lines and do not intersect, resulting in zero points of intersection.

Tags

CCSS.8.EE.C.8B

Oxygen gas is placed inside a tank with a constant volume. The graph shows the estimated temperature y, in kelvins, of the oxygen gas when its pressure is x atmospheres. What is the estimated temperature, in kelvins, of the oxygen gas when its pressure is 6 atmospheres?

• 6

• 60

• 700

• 760

Answer explanation

The graph indicates a direct relationship between pressure and temperature for a gas at constant volume. At 6 atmospheres, the estimated temperature of the oxygen gas is 700 kelvins, making 700 the correct choice.

Tags

CCSS.8.EE.B.5

Last week, an interior designer earned a total of $1,258 from consulting for x hours and drawing up plans for y hours. The equation 68x + 85y = 1,258 represents this situation. Which of the following is the best interpretation of 68 in this context?

• A. The interior designer earned $68 per hour consulting last week.

• B. The interior designer worked 68 hours drawing up plans last week.

• C. The interior designer earned $68 per hour drawing up plans last week.

• D. The interior designer worked 68 hours consulting last week.

Answer explanation

In the equation 68x + 85y = 1,258, the coefficient 68 represents the hourly rate for consulting. Thus, 68 indicates the interior designer earned $68 per hour consulting last week, making choice A the correct interpretation.

Tags

CCSS.HSF.LE.B.5

The graph of the linear function f is shown, where y = f(x). What is the x-intercept of the graph of f?

• (−12, 0)

• (0, 0)

• (1/4, 0)

• (12, 0)

Answer explanation

The x-intercept occurs where the graph crosses the x-axis, meaning f(x) = 0. The correct choice, (−12, 0), indicates that the graph intersects the x-axis at x = -12.

In the xy-plane, the graph of y = x + 3 intersects the graph of y = 2x - 6 at the point (a, b). What is the value of a?

• 3

• 6

• 9

• 12

Answer explanation

To find the intersection, set x + 3 = 2x - 6. Solving gives x = 9. Thus, the value of a is 9.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Line k is defined by y = 7x + 1/8. Line j is perpendicular to line k in the xy-plane. What is the slope of line j?

• -8

• -1/7

• 1/8

• 7

Answer explanation

The slope of line k is 7. The slope of a line perpendicular to another is the negative reciprocal. Thus, the slope of line j is -1/7.

Tags

CCSS.8.EE.B.6

Hydrogen is placed inside a container and kept at a constant pressure. The graph shows the estimated volume y, in liters, of the hydrogen when its temperature is x kelvins. What is the estimated volume, in liters, of the hydrogen when its temperature is 500 kelvins?

• 0

• 7/500

• 7

• 500/7

Answer explanation

The graph indicates a direct relationship between temperature and volume at constant pressure. At 500 kelvins, the estimated volume of hydrogen is 7 liters, making the correct choice 7.

Tags

CCSS.8.EE.B.5

Julissa needs at least 100 hours of flight time to get her private pilot certification. If Julissa already has 86 hours of flight time, what is the minimum number of additional hours of flight time Julissa needs to get her private pilot certification?

• A. 14

• B. 76

• C. 86

• D. 186

Answer explanation

Julissa needs 100 hours for certification and has 86 hours. To find the additional hours needed, subtract 86 from 100: 100 - 86 = 14. Therefore, the minimum additional hours required is 14 (Choice A).

What value of p satisfies the equation 2p + 275 = 325?

• 5

• 25

• 48

• 300

Answer explanation

To solve for p, subtract 275 from both sides: 2p = 325 - 275, which simplifies to 2p = 50. Dividing both sides by 2 gives p = 25. Thus, the correct answer is 25.

Tags

CCSS.7.EE.B.4A