SAT Hard questions

FIVE FIRES ACADEMY

SAT Math Practice Worksheet

Sequences, Parabolas, Quadratics & Word Problems

Name: ____________________________

Date: ____________________________

Score: ______ / 14

Time: 30 minutes (suggested)

Instructions: Read each question carefully. Show your work in the space provided or on scratch paper. Choose the best answer from the choices given. Calculator permitted unless stated otherwise.

PART 1 — Geometric Sequences

Question 1

The first term of a sequence is 5. Each term after the first is 3 times the preceding term. If w represents the nth term of the sequence, which equation gives w in terms of n?

A)  w = 5(3ⁿ)

B)  w = 5(3ⁿ⁻¹)

C)  w = 3(5ⁿ)

D)  w = 3(5ⁿ⁻¹)

Question 2

The first term of a geometric sequence is 8, and each term after the first is one-half the preceding term. Which equation gives the nth term, aₙ, of the sequence?

A)  aₙ = 8(½)ⁿ

B)  aₙ = 8(½)ⁿ⁻¹

C)  aₙ = ½(8)ⁿ

D)  aₙ = ½(8)ⁿ⁻¹

Question 3

In a geometric sequence, the first term is 7 and the common ratio is 2. What is the value of the 6th term of the sequence?

A)  84

B)  112

C)  224

D)  448

Question 4

The 3rd term of a geometric sequence is 12, and the 6th term is 96. What is the value of the first term of the sequence?

A)  2

B)  3

C)  4

D)  6

Question 5

The first three terms of a geometric sequence are 6, 18, 54, …. What is the value of the 7th term of the sequence?

A)  1,458

B)  2,916

C)  4,374

D)  13,122

Question 6

The nth term of a geometric sequence is given by w = 2(5ⁿ⁻¹). What is the first term and the common ratio of the sequence?

A)  First term 2, common ratio 5

B)  First term 5, common ratio 2

C)  First term 10, common ratio 5

D)  First term 2, common ratio 10

PART 2 — Arithmetic Sequences

Question 7

The first term of an arithmetic sequence is 7. Each term after the first is 4 more than the preceding term. If w represents the nth term of the sequence, which equation gives w in terms of n?

A)  w = 7 + 4n

B)  w = 7 + 4(n − 1)

C)  w = 4 + 7(n − 1)

D)  w = 4n + 7

Question 8

The first term of an arithmetic sequence is −3, and the common difference is 5. What is the value of the 20th term?

A)  87

B)  92

C)  97

D)  100

Question 9

In an arithmetic sequence, the 4th term is 11 and the 9th term is 31. What is the value of the first term?

A)  −1

B)  1

C)  3

D)  5

Question 10

The first three terms of an arithmetic sequence are 3, 7, 11, …. What is the sum of the first 10 terms of the sequence?

A)  150

B)  190

C)  210

D)  230

Question 11

The nth term of an arithmetic sequence is given by w = 2n + 7. What is the first term of the sequence and the common difference?

A)  First term 7, common difference 2

B)  First term 9, common difference 2

C)  First term 2, common difference 7

D)  First term 9, common difference 7

PART 3 — Parabolas, Quadratics & Word Problems

Question 12

In the xy-plane, a parabola has vertex (4, −10) and intersects the x-axis at two points. If the equation of the parabola is written in the form y = ax² + bx + c, where a, b, and c are constants, which of the following could be the value of a + b + c?

A)  −15

B)  −12

C)  −10

D)  −8

Question 13

A sample of pine has a density of 750 kilograms per cubic meter. The sample is in the shape of a cube, where each edge has a length of 0.85 meters. To the nearest whole number, what is the mass, in kilograms, of this sample?

A)  384

B)  461

C)  543

D)  638

Question 14

x² − 28x + c = 0

In the given equation, c is a constant. The equation has no real solutions if c > n. What is the least possible value of n?

Answer: __________