Reading & Writing + Math Practice Modules

Focus areas based on your self‑reported weaknesses: Punctuation with describing phrases and Geometry/Trigonometry. Each module has 5 multiple‑choice questions and a compact answer key.

English — Module 1: Commas with Nonessential Describing Phrases

Reading & Writing

Rule focus: set off nonessential info (appositives, which-clauses, participial phrases) with commas.

1) Which sentence punctuates a nonessential appositive correctly?

A. My sister Lena who lives in Chicago is visiting this weekend.

B. My sister, Lena, who lives in Chicago is visiting this weekend.

C. My sister Lena, who lives in Chicago, is visiting this weekend.

D. My sister, Lena who lives in Chicago is visiting this weekend.

2) Choose the best punctuation for the nonessential participial phrase.

Many owls _____ hunt silently in dense forests.

A. which having fringed feathers,

B. having fringed feathers

C. having fringed feathers,

D. , having fringed feathers,

3) Identify the correctly punctuated sentence with an introductory participial phrase.

A. Walking across the quad the professor waved.

B. Walking across the quad, the professor waved.

C. Walking across, the quad the professor waved.

D. Walking, across the quad the professor waved.

4) Choose the sentence that correctly distinguishes restrictive vs. nonrestrictive information.

A. The novel which won the prize is inspiring.

B. The novel, that won the prize, is inspiring.

C. The novel that won the prize is inspiring.

D. The novel, which won the prize is inspiring.

5) Pick the best punctuation for the nonessential, emphatic remark.

Our coach — always calm under pressure — called timeout.

A. Our coach always calm under pressure called timeout.

B. Our coach, always calm under pressure, called timeout.

C. Our coach — always calm under pressure — called timeout.

D. Our coach (always calm under pressure) called timeout.

Answer Key: 1) C · 2) C · 3) B · 4) C · 5) C (B is also acceptable, dashes add emphasis)

English — Module 2: Colons, Semicolons, & Descriptive Phrases

Reading & Writing

Rule focus: fix comma splices; use colons to introduce explanations/lists; set off mid‑sentence descriptions.

1) Choose the sentence that correctly fixes the comma splice.

A. The data were limited, we drew careful conclusions.

B. The data were limited; we drew careful conclusions.

C. The data were limited: we drew careful conclusions.

D. The data were limited we drew careful conclusions.

2) Select the correct colon usage.

The toolkit includes the following _____ wrenches, hex keys, and a torque driver.

A.;

B.:

C.,

D.—

3) Choose the sentence that best sets off a mid‑sentence descriptive phrase.

A. The museum which recently expanded its galleries welcomed more visitors.

B. The museum—recently expanded—welcomed more visitors.

C. The museum, recently expanded, welcomed more visitors.

D. The museum recently expanded welcomed more visitors.

4) Pick the correct punctuation for a nonessential participial phrase.

The hikers _____ reached the lake at noon.

A. , moving steadily through the pines,

B. moving steadily through the pines

C. moving steadily through the pines,

D. which moving steadily through the pines,

5) Choose the sentence that punctuates examples correctly.

A. Many endurance sports such as, cycling and rowing, demand pacing.

B. Many endurance sports, such as cycling and rowing, demand pacing.

C. Many endurance sports such as cycling, and rowing demand pacing.

D. Many endurance sports—such as cycling, and rowing—demand pacing.

Answer Key: 1) B · 2) B · 3) C (B acceptable for stronger emphasis) · 4) C · 5) B

Math — Module 1: Geometry Essentials

Math

Focus: triangle angle sums, area, right triangles, circles, and similarity.

1) In △ABC, m∠A = 47° and m∠B = 61°. What is m∠C?

A. 58°

B. 62°

C. 72°

D. 74°

2) A rectangle is 12 units long and 7 units wide. What is its area?

A. 19

B. 42

C. 84

D. 96

3) In a right triangle, the legs measure 5 and 12. What is the hypotenuse?

A. 11

B. 12

C. 13

D. 17

4) A circle has radius 6. What is its circumference?

A. 6π

B. 12π

C. 36π

D. 72π

5) △PQR is similar to △STU. If PQ = 8 corresponds to ST = 12, what length corresponds to PR = 10?

A. 12

B. 14

C. 15

D. 16

Answer Key: 1) C · 2) C · 3) C · 4) B · 5) C (scale factor 12/8 = 1.5; 10×1.5 = 15)

Math — Module 2: Trigonometry Basics (Right Triangles)

Math

Focus: SOH‑CAH‑TOA, special angles, degree↔radian, and triangle side relations.

1) In a right triangle, for angle θ, the opposite side is 9 and the hypotenuse is 15. What is sin θ?

A. 3/4

B. 4/5

C. 3/5

D. 5/3

2) If tan θ = 3/4 (θ acute), what is cos θ?

A. 3/5

B. 4/5

C. 5/4

D. 7/25

3) A 10‑ft ladder leans against a wall and reaches 8 ft high. What is sin θ, where θ is the angle between the ladder and the ground?

A. 3/5

B. 4/5

C. 5/4

D. 2/5

4) Convert 60° to radians.

A. π/6

B. π/3

C. 2π/3

D. π/2

5) In a right triangle, cos θ = 12/13 and the hypotenuse is 13. What is the length of the adjacent side to θ?

A. 5

B. 12

C. 13

D. 156

Answer Key: 1) C · 2) B · 3) B · 4) B · 5) B

PSAT Practice Modules — With Concept Reviews

Enhanced modules include built-in concept reviews that explain the rules and formulas behind each question set.

English — Module 1: Commas with Descriptive Phrases

Reading & Writing

Five practice questions focus on using commas around nonessential information (appositives and participial phrases).

Answer Key: 1) C · 2) C · 3) B · 4) C · 5) C

Concept Review — “Spot the Extra Info”

Use commas around information you can remove without changing the core meaning.
Words like which, who, and having... often start nonessential phrases.
✅ My brother, a firefighter, lives in Austin.
❌ People who work hard succeed.

English — Module 2: Colons, Semicolons & Dashes

Reading & Writing

Five questions test how to connect ideas correctly and avoid comma splices.

Answer Key: 1) B · 2) B · 3) C · 4) C · 5) B

Concept Review — “Connect Ideas Cleanly”

Semicolon (;) links two related complete sentences.
The rain stopped; the sun came out.
Colon (:) introduces a list or explanation.
He brought three things: a map, food, and water.
Dash (—) adds emphasis or surprise.
She knew the truth—finally!

Math — Module 1: Geometry Essentials

Math

Five geometry problems reviewing triangles, circles, and similarity.

Answer Key: 1) C · 2) C · 3) C · 4) B · 5) C

Concept Review — “Remember Your Shapes”

Triangle Rule: All angles = 180°.
Pythagorean Theorem: a² + b² = c² (right triangles only).
Circle: Circumference = 2πr · Area = πr².
Similarity: Shapes keep same ratio of sides.

Math — Module 2: Trigonometry Basics (SOH-CAH-TOA)

Math

Five trig questions covering sine, cosine, tangent, and special triangles.

Answer Key: 1) C · 2) B · 3) B · 4) B · 5) B

Concept Review — “SOH-CAH-TOA Explained”

Use this mnemonic to remember trigonometric ratios in right triangles:

Function	Formula	Meaning
Sine (sin)	Opposite / Hypotenuse	How steep the rise is
Cosine (cos)	Adjacent / Hypotenuse	How far across it goes
Tangent (tan)	Opposite / Adjacent	Steepness or slope

Example: In a 3–4–5 triangle → sin θ = 3/5, cos θ = 4/5, tan θ = 3/4.
Pick an angle θ, then label its sides: opposite, adjacent, hypotenuse.