Digital SAT Practice #27

These questions come from The Princeton Review DIGITAL SAT Premium Prep Book 2024.

The questions all come from the practice test of the 2nd math test (easier version). Remember that after taking test 1, you are directed to either the easier version or the harder version based on how you did on part 1

• I understand

• Don't click here

Tags

CCSS.7.NS.A.1D

Answer explanation

This is algebra. 35% of the test will be on these types of questions.

1. 1. Perpendicular lines have negative reciprocal slopes. Since f(x) has a slope of -1/5, g(x) will have a slope of 5

2. 2. Since g(0) = 0 the y intercept is zero.

3. 3. This make the equation for g(x)=5x+0

4. 4. They want to know g(2) so 5(2) + 0 = 10

Answer explanation

This is an Advanced Algebra question.

This is an problem you might want to tag and come back to, or use your LOTD.

1. 1. Solve 2nd equation for y (y = -10x)

2. 2. Set equations equal to each other (-10x=5kx^2+2x+3) or 0 = 5kx^2 + 12x +3

3. 3. Since there is only 1 solution the discriminant should be equal to 0

4. 4. D = b^2 - 4ac.

5. 5. 0 = (12^2) - 4(5k)(3)

6. 6 k = 2.4

33, 34, 38, 41, 43, 44, 47

Which of the following is the median of the data listed above?

• 38

• 40

• 41

• 42

Answer explanation

This is data analysis. About 15% of 3-4 questions of each module will be of this type.

Median is the middle number when listed in order. Note that they have already put them in order so you just need to find the middle or 4th number.

Tags

CCSS.7.EE.B.3

Answer explanation

This is an algebra question

Isolate the variable y by adding 10 to both sides of the equation so y = 22 + 10 or 32

Tags

CCSS.1.OA.D.8

A rectangle has a height of 23 inches and a width of 9 in. What is its perimeter, in inches?

• 32

• 64

• 207

• 1,024

Answer explanation

This is an algebra question

Perimeter is when we add all measurements around a figure. Since this is a rectangle we have 2 sides that are 23 inches and 2 sides that are 9 inches.

23+23+9+9= 64 inches

Tags

CCSS.7.EE.B.3

• 5a

• 7a

• 11a

• 23a

Answer explanation

1. 1. Simplify inside the parentheses first

2. 15a - (6a - 2a) becomes 15a - 4a

3. note that the parentheses are no longer needed

4. 2. add like terms 15a - 4a = 11a

Tags

CCSS.7.NS.A.3

Which equation represents the relationship between the numbers a and b if a is half of b?

Answer explanation

Translate from English to math in bite-sized pieces

1. 1. A is becomes a =

2. 2. half of b becomes 1/2(b)

2. so putting it together makes

3. a = 1/2 (b)

Tags

CCSS.7.RP.A.2C

• 3

• 6

• 8

• 150

Answer explanation

These 2 fractions are equal to each other

Comparing them it looks like the numerator of the first was multiplied by 5 to get the new numerator of 15. So we should do the same thing with the denominators

5(y+c) = 5y + 30

5y + 5c = 5y + 30

so 5c = 30 making c = 6

A total of 200 pets were adopted at an event. If 70% of the adopted pets were dogs, how many of the pets were dogs?

Answer explanation

Notice that there are more free - response type questions and that they are now embedded in the test. This is to encourage problem solving.

Translate the english to math in bite - sized pieces

percent means "out of 100" so 70% becomes 70/100

How many becomes the variable. I'll pick d for dogs

Of means times and the pets means 200

that means d = (70/100)*(200) or 140 dogs

Tags

CCSS.6.RP.A.3C