Digital SAT Practice #26

These questions are taken from the Princeton Review Digital SAT Premium Prep 2024 book. They are all from Module 1. Module 1 has a variety of of difficulty levels

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• 8

• 16

• 24

• 64

Answer explanation

This is a Geometry/problem solving question. 15% will be geometry and 70% will be problem solving

Perimeter means the length around the figure. So AB + BC + CD + AD = 64

Answer D would be too big for the short side since 2 of these is already 64 and that is what the total should be

Lets try 8 --- If the short sides are 8 the the long sides would be 24 ("AB is 1/3 of AD).

and 8 + 24+ 8 + 24 = 64 Yippee. 8 is the answer

Tags

CCSS.HSG.CO.C.11

• 4

• 9

• 13

• 36

Answer explanation

This is Geometry and problem solving

SAT gives a formula sheet that says for a triangle A = 1/2 (b)(h)

plugging in the info from the problem makes this

18 = (1/2)(m+5)(m)

Now I should plug in answer choices to find the one that works

Choice A = 4 so (1/2)(4+5)(4) = (1/2)(9)(4) = 18

Choice A works!

Tags

CCSS.6.G.A.1

The table shows the exponential growth of a type of yeast over time s, in seconds. There are c total yeast colonies on the count plate. What is the equation that represents this relationship, assuming that no yeast was added or removed after counting began?

Answer explanation

This is advanced algebra and problem solving. About 35% of the test will be advanced algebra and about 70% will be problem solving

This is best solved by trying each answer choice. In the table the first column is the variable s and the 2nd is the variable C

Raising something to 0 makes 1 so choices A and B don't make sense

Choice C using row 1: 5 = 3(1+5)^0 isnt true so it must be choice D

Tags

CCSS.HSF.LE.A.2

The equations 12x=y and 24x+7=2y intersect at how many points when graphed in the xy-plane?

• 0

• 1

• 2

• 7

Answer explanation

This is Algebra and problem solving. About 35% is Algebra.

Logic tells us that lines can either cross 1 time, be parallel and not cross at all (0) or be the same line and ALL points "cross"

So choices C and D can be ruled out

If the slopes are different the lines will cross 1 time.

BOth slopes here are 12 so the answer is either 0 or ALL points Must be A

Tags

CCSS.8.EE.C.8B

Several tiles labeled with either an A or a B are placed in a bag, the tiles are worth a different point value depending on the label. The equations 15a+10b = 100 represents the situation when a of the A tiles and b of the B tiles are drawn from the bag for a total of 100 points. How many points would be earned by drawing one A tile and 1 B tile?

(a)  

Answer explanation

This is problem solving

In the formula 15a + 10b = 100

15a is the points earn from all the a tiles. We have 1

10b is the points earned from all the b tiles. We have 1

So our points would be 15(1) + 10(1) =25 points

Tags

CCSS.8.EE.C.8C

The amount of money remaining in a scholarship fund is reduced by one-fourth every year. The amount of money in the fund is represented by d and the number of years by y. If the fund starts with $10,000, which equation represents this situation after y years

Answer explanation

Thinking in complements can be helpful here.

If the fund is 'reduced by 1/4 every year' then that means that 3/4 is kept each year. This narrows options to either B or D.

Choice B states that we are raising the initial amount of 10,000 to the number of years. That would get pretty big pretty quick (in year 3 it would be 10,000^3 or 1 TRILLION dollars. I don't think so

CHoice D is the only one that makes sense

Tags

CCSS.HSF.LE.A.2

• 6

• 9

• 12

• 36

Answer explanation

SAT gives us a reference sheet that shows the formula for Volume of a cylinder is:

V = pi(r^2)(h)

Plugging in options is the way to go but read carefully. The answers are in DIAMETER and the formula uses RADIUS so I will need to put in 1/2 of the answer when checking each choice

Choice A ----V = pi(3^2)(4) = 36pi too small

Choice B -----V = pi(4.5^2)(4)= 81 pi too small

Choice C ---V = pi(6^2)(4) = 144 pi. PERFECT

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

• -20

• -10

• 6

• 14

Answer explanation

The place where the lines cross will be the point that works in both equations. Plugging in each choice for x to find which gives the same result for both equations is the easiest choice.

Choice A == 4(-20) + 2y = 4 makes y = 42 but

19(-20)+10y = 14 makes y = 19.4 NO

Choice C ===4(6)+2y = 4 makes y = -10

19(6) + 10y = 14 makes y = -10 YEP

Tags

CCSS.8.EE.C.8B

The longest side of right triangle ABC is opposite angle B. If sin(A) = 9/41, what is the value of sin(C)

(a)  

Answer explanation

You are expected to know the 3 basic trigonometric Functions.

Sine = opposite/hypotenuse

Cosine = adjacent/hypotenuse

Tangent = opposite/adjacent.

Start by drawing the triangle. From the question you know to put 9 on the side across from A and 41 as the hypotenuse

Use the pythagorean thm to find the missing side.

9^2 + b^2 = 41^2. it should be 40

Now use the sine ratio again to figure out that Sine C = 40/41. You can put it in as a fraction or you can use the decimal equivalent.

Tags

CCSS.HSG.SRT.C.7