Problem sets by domain

A-1 · Linear equation (M1)

If 3(2x − 5) + 4 = 7x − 11, what is the value of x?

A) 0   B) 1   C) 2   D) 4

A-2 · System (M1)

If 2x + y = 7 and x − y = 2, what is x + y?

A) 3   B) 4   C) 5   D) 6

A-3 · Linear context (M2)

A tank starts with 240 L and drains at a constant rate. After 5 min it has 195 L. Which equation gives volume V after t minutes?

A) V = 240 + 9t   B) V = 240 − 9t   C) V = 240 − 5t   D) V = 195 − 9t

A-4 · Parallel lines (M2)

Line ℓ passes through (1, 4) and (3, 10). Line m is parallel and passes through (−2, 0). What is the y-intercept of m?

A-5 · No solution (M2)

The system 2x + 3y = 12, 4x + ky = 30 has no solution. Find k.

A-6 · Inequality (M1)

Solve for x: −3(x − 4) ≥ 9.

A-7 · Slope from two points (M1)

What is the slope of the line through (−2, 5) and (4, −7)?

A-8 · System with substitution (M1)

If y = 2x + 3 and 3x + y = 18, what is x?

A-9 · Perpendicular slope (M2)

Line k has slope −2/5. Line p is perpendicular to k. What is the slope of p?

A-10 · Word problem to equation (M2)

A taxi charges a base fare of $3.50 plus $0.45 per quarter-mile. Sasha pays $12.50. How many miles did she travel?

A-11 · Linear function value (M1)

f(x) = 4x − 7. What is f(3) − f(−2)?

A-12 · Absolute value (M2)

How many integer solutions satisfy |2x − 7| < 5?

A-13 · Solve for a variable (M1)

If 5(x + 2) − 3 = 2x + 19, what is the value of x?

A) 3   B) 4   C) 5   D) 6

A-14 · Literal equation (M2)

The formula P = 2(L + W) gives the perimeter of a rectangle. Which expression gives W in terms of P and L?

A) W = P − 2L   B) W = (P − 2L)/2   C) W = P/2 − L   D) Both B and C

A-15 · Linear context, find rate (M1)

A gym membership costs a $40 signup fee plus a monthly charge. After 6 months a member has paid $190 in total. What is the monthly charge?

A) $20   B) $25   C) $30   D) $35

A-16 · System, value of an expression (M2)

If 3x + 2y = 16 and 5x + 2y = 24, what is the value of x − y?

A-17 · Infinitely many solutions (M2)

The system 3x − y = 5, 9x − cy = 15 has infinitely many solutions. What is the value of c?

A-18 · Inequality word problem (M1)

A delivery van can carry at most 1,200 kg. It already holds 450 kg. If each box weighs 25 kg, what is the greatest number of boxes n it can still carry?

A-19 · Equation of a line from a point (M2)

A line has slope −4 and passes through (2, 3). What is its x-intercept?

A) 11/4   B) 11   C) 3/4   D) 4/11

A-20 · Mixture / linear combination (M2)

Adult tickets cost $9 and child tickets cost $5. A group buys 12 tickets for $84. How many adult tickets did they buy?

A-21 · Distribute and solve (M1)

If 4(x − 3) = 2x + 6, what is the value of x?

A) 3   B) 6   C) 9   D) 12

A-22 · Solve for a fraction variable (M1)

If (x/3) + 4 = 10, what is the value of x?

A-23 · Elimination system (M2)

If 4x + 3y = 27 and 2x − 3y = 3, what is the value of x?

A) 3   B) 5   C) 6   D) 9

A-24 · Linear cost model (M1)

A plumber charges a flat $60 visit fee plus $45 per hour. Which equation gives the total charge C for h hours of work?

A) C = 45h − 60   B) C = 60h + 45   C) C = 45h + 60   D) C = 105h

A-25 · Slope-intercept interpretation (M2)

A line is given by 2x + 5y = 20. What is the slope of the line?

A) −2/5   B) 2/5   C) −5/2   D) 4

A-26 · Compound inequality (M2)

If −2 ≤ 3x − 5 ≤ 7, what is the greatest possible value of x?

A-27 · Equivalent equations (M2)

The equation ax + 12 = 6x + b is true for all values of x. If a = 6, what is the value of b?

A-28 · Two-variable word problem (M1)

A vendor sells small drinks for $2 and large drinks for $3. On one day she sold 50 drinks for a total of $124. How many large drinks did she sell?

A) 12   B) 24   C) 26   D) 38

A-29 · Find the constant for parallel lines (M2)

Line ℓ is given by y = 3x − 4. Line m is parallel to ℓ and passes through (2, 5). What is the equation of line m?

A-30 · Solve a proportion equation (M1)

If x/4 = (x + 6)/10, what is the value of x?

A-31 · Linear function and intercept (M2)

The function f is linear with f(2) = 11 and f(5) = 23. What is the value of f(0)?

A) 1   B) 3   C) 5   D) 7

A-32 · Inequality from a budget (M1)

Tickets cost $8 each. With a $100 budget, what is the greatest whole number of tickets that can be bought?

A-33 · System, no solution constant (M2)

The system y = 5x + 2, y = 5x + k has no solution. Which statement about k must be true?

A) k = 2   B) k ≠ 2   C) k = 0   D) k = −2

A-34 · Solve for one variable in terms of another (M1)

If 3a − 2b = 12, what is a in terms of b?

A-35 · Rate and distance (M2)

A train travels at a constant speed. It covers 210 miles in 3 hours. How many miles will it cover in 5 hours at the same speed?

A-36 · Value of an expression from a system (M2)

If x + 2y = 9 and 2x + y = 12, what is the value of 3x + 3y?

A) 7   B) 18   C) 21   D) 24

A-37 · Solve a literal formula (M2)

The formula F = (9/5)C + 32 converts Celsius to Fahrenheit. Which expression gives C in terms of F?

A) C = (5/9)(F − 32)   B) C = (9/5)(F − 32)   C) C = (5/9)F − 32   D) C = F − 32

A-38 · Linear comparison (M2)

Plan A costs $30 plus $2 per visit. Plan B costs $10 plus $4 per visit. At how many visits do the two plans cost the same?

A-39 · Graph point on a line (M1)

The point (k, 7) lies on the line y = 2x − 1. What is the value of k?

A) 3   B) 4   C) 6   D) 13

A-40 · Mixture proportion (M2)

A 20-liter solution is 30% acid. How many liters of pure acid must be added to make the solution 50% acid?

AM-1 · Quadratic sum of roots (M1)

What is the sum of the solutions to x² − 7x + 10 = 0?

AM-2 · Vertex (M2)

For f(x) = 2x² − 12x + 7, what is the minimum value of f?

AM-3 · Exponential model (M2)

Bacteria double every 4 hours. 500 cells at t = 0. Which gives P(t)?

A) P = 500 · 2^(4t)   B) P = 500 · 2^(t/4)   C) P = 500 + 2t   D) P = 500 · 4^t

AM-4 · Rational equation (M2)

Solve (x + 6)/(x − 2) = 4.

AM-5 · Discriminant (M2)

For what value of k does x² + kx + 9 = 0 have exactly one real solution?

AM-6 · Factoring (M1)

Which is a factor of x³ − 4x?

A) x − 4   B) x + 2   C) x − 1   D) x² + 4

AM-7 · Function composition (M2)

If f(x) = 2x + 1 and g(x) = x², what is f(g(3))?

AM-8 · Exponent rules (M1)

Simplify (2x³)² · x⁻⁴.

AM-9 · Radical equation (M2)

Solve √(2x + 1) = x − 1 for x > 1.

AM-10 · Vertex form (M2)

Rewrite x² − 8x + 13 in vertex form.

AM-11 · Polynomial root (M2)

If P(x) = x³ − 6x² + 11x − 6 and P(1) = 0, factor P.

AM-12 · Inverse function (M2)

If f(x) = (x − 3)/2, what is f⁻¹(x)?

AM-13 · Logarithm value (M2)

If log₂(8x) = 5, find x.

AM-14 · Product of roots (M1)

What is the product of the solutions to x² − 2x − 15 = 0?

A) −15   B) −2   C) 2   D) 15

AM-15 · Quadratic in context (M2)

A ball's height is h(t) = −16t² + 48t feet after t seconds. How many seconds until it returns to the ground?

AM-16 · Exponential decay (M2)

A car worth $24,000 loses 15% of its value each year. Which expression gives its value after t years?

A) 24000(0.15)^t   B) 24000(0.85)^t   C) 24000(1.15)^t   D) 24000 − 0.15t

AM-17 · Equivalent expression (M2)

Which is equivalent to (x² − 9)/(x + 3) for x ≠ −3?

A) x − 3   B) x + 3   C) x − 9   D) x² − 6

AM-18 · Function from a table (M1)

A linear function f satisfies f(0) = 5 and f(4) = 17. What is f(10)?

AM-19 · Solving by substitution (M2)

If y = x² − 1 and y = 3x + 3, what is the sum of the possible values of x?

AM-20 · Rational exponent (M2)

If x > 0 and x^(3/2) = 27, what is the value of x?

AM-21 · Number of x-intercepts (M2)

How many distinct real x-intercepts does the graph of y = x² − 6x + 9 have?

A) 0   B) 1   C) 2   D) infinitely many

AM-22 · Quadratic by factoring (M1)

What are the solutions to x² + 3x − 10 = 0?

A) 2 and 5   B) −2 and 5   C) 2 and −5   D) −2 and −5

AM-23 · Evaluate a function (M1)

If g(x) = x² − 3x, what is the value of g(−2)?

AM-24 · Vertex of a parabola (M2)

The parabola y = (x − 4)² + 3 has its vertex at which point?

A) (4, 3)   B) (−4, 3)   C) (4, −3)   D) (3, 4)

AM-25 · Exponential growth model (M2)

A population of 800 increases by 5% each year. Which expression gives the population after t years?

A) 800(0.05)^t   B) 800(1.05)^t   C) 800 + 0.05t   D) 800(5)^t

AM-26 · Simplify a polynomial product (M1)

Expand (x + 4)(x − 4).

AM-27 · Quadratic formula (M2)

What is the sum of the solutions to 2x² − 8x + 3 = 0?

AM-28 · System with a parabola (M2)

How many points do the graphs of y = x² and y = 2x + 3 share?

A) 0   B) 1   C) 2   D) 3

AM-29 · Negative exponent (M1)

What is the value of 3⁻²?

AM-30 · Solve a rational equation (M2)

Solve 6/(x + 1) = 2.

AM-31 · Completing the square (M2)

Write x² + 6x + 5 in the form (x + a)² + b. What is the value of b?

AM-32 · Function composition (M2)

If f(x) = x − 5 and g(x) = 3x, what is g(f(8))?

A) 9   B) 19   C) 24   D) 29

AM-33 · Equivalent radical expression (M2)

Which is equivalent to √(50)?

A) 5√2   B) 2√5   C) 25√2   D) 10√5

AM-34 · Zeros of a cubic (M2)

The polynomial p(x) = x(x − 3)(x + 2) has how many distinct real zeros?

AM-35 · Maximum of a quadratic (M2)

The height of a projectile is h(t) = −5t² + 20t. What is its maximum height?

A) 15   B) 20   C) 25   D) 40

AM-36 · Rational exponent equation (M2)

If x^(1/3) = 4, what is the value of x?

AM-37 · Exponent product rule (M1)

Simplify x⁵ · x³ / x².

AM-38 · Coefficient from a known root (M2)

If x = 3 is a solution of x² − 5x + c = 0, what is the value of c?

AM-39 · Interpreting an exponential (M2)

A sample of a substance decays according to A = 200(1/2)^(t/6), where t is in hours. What is the half-life of the substance?

A) 2 hours   B) 6 hours   C) 12 hours   D) 100 hours

AM-40 · Difference of function values (M2)

If f(x) = x² + 1, what is f(5) − f(3)?

AM-41 · Nonlinear system substitution (M2)

If y = x² − 4x and y = −3, what is the sum of the possible values of x?

D-1 · Percent + tax (M1)

A laptop priced at $800 is discounted by 25%, then a 10% sales tax is added. Final price?

D-2 · Mean shift (M2)

20 students have mean 78. Add 4 bonus points to every score. New mean?

D-3 · Two-way table (M2)

200 students: 60 play a sport, 80 play an instrument, 30 do both. Of those who play an instrument, what fraction also play a sport?

D-4 · Rate (M1)

A printer prints 90 pages in 6 minutes. At this rate, how many pages in 15 minutes?

D-5 · Median vs mean (M2)

Data set: 4, 7, 7, 9, 10, 12, 80. Which is greater, mean or median, and by how much?

D-6 · Ratio (M1)

A recipe calls for 3 cups flour to 2 cups sugar. To make a batch using 9 cups flour, how much sugar?

D-7 · Probability (M2)

A bag has 4 red, 3 blue, 5 green marbles. Two are drawn without replacement. Probability both red?

D-8 · Sampling inference (M2)

A poll of 500 randomly selected residents found 320 favor a measure. With a margin of error of ±4 percentage points at 95% confidence, which conclusion is best supported?

A) Exactly 64% favor the measure.   B) Between 60% and 68% favor the measure.   C) Less than half favor the measure.   D) The measure will pass.

D-9 · Standard deviation intuition (M2)

Two data sets have the same mean. Set A: 50, 50, 50, 50. Set B: 30, 50, 50, 70. Which has the larger SD?

D-10 · Unit conversion (M1)

A car uses 8 liters of fuel per 100 km. How many liters does it use over 250 km?

D-11 · Scatterplot reasoning (M2)

A scatterplot shows hours studied (x) vs test score (y). A best-fit line is y = 5x + 60. Interpret the slope.

D-12 · Compound percent (M2)

A stock rises 20% in year 1 and falls 20% in year 2. What is the net change after 2 years?

D-13 · Percent change (M1)

A town's population grew from 4,500 to 5,400 in one decade. What was the percent increase?

A) 9%   B) 18%   C) 20%   D) 25%

D-14 · Unit rate / best value (M2)

Brand A sells 750 g for $4.50; Brand B sells 1.2 kg for $6.60. Which is cheaper per gram, and by how much per kilogram?

D-15 · Reading a frequency table (M2)

A table records the number of pets owned by 50 households: 0 pets → 12 households, 1 pet → 20, 2 pets → 13, 3 pets → 5. What is the median number of pets per household?

D-16 · Two-way table probability (M2)

A survey of 300 people is split by age and whether they bike to work. A two-way table shows: under 30 → 90 bike, 60 do not; 30 or older → 36 bike, 114 do not. If one respondent is chosen at random from those who bike, what is the probability the person is under 30?

A) 90/300   B) 90/126   C) 90/150   D) 126/300

D-17 · Interpreting a bar graph (M2)

A bar graph shows monthly revenue (in $1,000s) for a shop: Jan 40, Feb 50, Mar 45, Apr 65. Which statement is best supported?

A) Revenue increased every month.   B) April revenue was the highest of the four months.   C) Revenue doubled from January to April.   D) The mean monthly revenue was $65,000.

D-18 · Density / proportion (M1)

A 12 m by 8 m garden has 240 plants spread evenly. At the same density, how many plants would a 15 m by 8 m garden hold?

D-19 · Expected value of a sample (M2)

In a random sample of 80 light bulbs, 6 were defective. If a shipment contains 2,000 bulbs, what is the best estimate of the number of defective bulbs?

D-20 · Linear model interpretation (M2)

A phone plan's monthly cost is modeled by C = 0.10g + 25, where g is gigabytes used. What does the value 25 represent?

A) The cost per gigabyte.   B) The fixed monthly fee when no data is used.   C) The maximum monthly cost.   D) The number of free gigabytes.

D-21 · Percent of a number (M1)

What is 35% of 140?

D-22 · Unit rate (M1)

A factory produces 540 widgets in 9 hours. At this rate, how many widgets are produced per hour?

A) 45   B) 54   C) 60   D) 90

D-23 · Mean from a total (M1)

Five test scores have a mean of 84. What is the sum of the five scores?

D-24 · Finding a missing value from a mean (M2)

Four numbers have a mean of 20. Three of them are 15, 22, and 19. What is the fourth number?

D-25 · Reading a two-way table (M2)

A two-way table classifies 250 survey respondents by region and preference. North: 70 prefer A, 30 prefer B. South: 90 prefer A, 60 prefer B. What fraction of all respondents prefer A?

A) 70/250   B) 90/250   C) 160/250   D) 100/250

D-26 · Probability from a table (M2)

From the table in D-25 (250 respondents; North 70 A / 30 B, South 90 A / 60 B), if one respondent who prefers B is chosen at random, what is the probability the person is from the South?

D-27 · Percent increase (M1)

A subscription price rose from $40 to $50. What was the percent increase?

A) 10%   B) 20%   C) 25%   D) 50%

D-28 · Scaling a recipe (M1)

A recipe for 4 servings uses 6 eggs. How many eggs are needed for 10 servings?

D-29 · Best-fit line prediction (M2)

A line of best fit relating advertising spend x (in $1,000s) to sales y (in $1,000s) is y = 3x + 12. What is the predicted sales when $5,000 is spent on advertising?

A) $12,000   B) $15,000   C) $27,000   D) $60,000

D-30 · Interpreting a slope in context (M2)

A line of best fit for distance d (km) versus time t (hours) is d = 65t + 5. What does the slope 65 represent?

A) The starting distance.   B) The total distance traveled.   C) The average speed in km per hour.   D) The travel time.

D-31 · Median of a data set (M1)

What is the median of the set 3, 8, 5, 12, 7?

D-32 · Effect of an outlier (M2)

A data set is 10, 12, 11, 13, 90. Removing the value 90 would most affect which measure the least?

A) Mean   B) Range   C) Median   D) Standard deviation

D-33 · Density of a population (M2)

A region of 250 km² has a population of 60,000. What is the population density in people per km²?

D-34 · Compound discount (M2)

A jacket is marked down 30%, and a member then gets an additional 10% off the reduced price. What single percent discount is equivalent?

A) 37%   B) 40%   C) 33%   D) 27%

D-35 · Estimating from a sample (M2)

In a random sample of 120 voters, 78 support a proposal. If the town has 5,000 voters, what is the best estimate of the number who support the proposal?

D-36 · Reading a line graph (M2)

A line graph shows a company's quarterly profit (in $1,000s): Q1 20, Q2 35, Q3 30, Q4 50. By what percent did profit increase from Q1 to Q4?

A) 30%   B) 60%   C) 100%   D) 150%

D-37 · Conditional probability grid-in (M2)

Of 80 students, 50 take Spanish and 30 take French; 12 take both. If a student who takes Spanish is chosen at random, what is the probability the student also takes French? Give your answer as a fraction.

D-38 · Proportional reasoning (M1)

A map uses a scale of 1 cm = 25 km. Two cities are 7 cm apart on the map. What is the actual distance between them?

D-39 · Percent of a percent (M2)

In a school, 60% of students play a sport, and of those, 25% play soccer. What percent of all students play soccer?

A) 15%   B) 25%   C) 35%   D) 85%

D-40 · Frequency table mean (M2)

A frequency table of quiz scores: score 2 → 3 students, score 3 → 5 students, score 4 → 2 students. What is the mean score?

G-1 · Pythagorean (M1)

Right triangle: one leg 9, hypotenuse 15. Other leg?

G-2 · Circle equation (M2)

x² + y² − 6x + 4y − 12 = 0. Radius?

G-3 · sin of acute angle (M2)

Right triangle, right angle at C, AC = 5, BC = 12. Find sin A.

G-4 · Similar triangles (M1)

Two similar triangles. The smaller has perimeter 12; the larger has perimeter 30. If the smaller's area is 6, what is the larger's area?

G-5 · Arc length (M2)

A circle has radius 6. A central angle measures π/3 radians. Arc length?

G-6 · Volume of cylinder (M1)

Cylinder, radius 4, height 10. Volume?

G-7 · Complementary trig (M2)

If sin θ = 3/5 for an acute angle θ, find cos(90° − θ).

G-8 · Angle sum (M1)

In a triangle, two angles are 35° and 85°. What is the third?

G-9 · Parallel lines & transversal (M1)

Two parallel lines are cut by a transversal. One of the alternate interior angles is 110°. What is the other?

G-10 · Coordinate distance (M2)

Distance between (1, 2) and (7, 10)?

G-11 · Area of a triangle (M1)

A triangle has base 14 and height 9. What is its area?

A) 63   B) 96   C) 126   D) 252

G-12 · 30-60-90 triangle (M2)

In a 30-60-90 right triangle, the side opposite the 30° angle is 7. What is the length of the hypotenuse?

G-13 · Circle area and circumference (M1)

A circle has circumference 10π. What is its area?

G-14 · Volume of a cone (M2)

A cone has radius 3 and height 8. What is its volume?

A) 24π   B) 48π   C) 72π   D) 8π

G-15 · Tangent ratio (M2)

In a right triangle with the right angle at C, the leg opposite angle A is 8 and the leg adjacent to A is 6. What is tan A?

G-16 · Inscribed angle (M2)

A central angle in a circle intercepts an arc of 80°. What is the measure of an inscribed angle that intercepts the same arc?

A) 40°   B) 80°   C) 100°   D) 160°

G-17 · Radians to degrees (M1)

Convert 3π/4 radians to degrees.

G-18 · Surface area of a cube (M1)

A cube has a volume of 64 cm³. What is its total surface area?

G-19 · Pythagorean theorem (M1)

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

A) 10   B) 12   C) 14   D) 48

G-20 · Sum of interior angles (M1)

What is the sum of the interior angles of a pentagon?

G-21 · Volume of a rectangular prism (M1)

A box measures 5 cm by 4 cm by 3 cm. What is its volume?

G-22 · Cosine ratio (M2)

In a right triangle, the angle θ has an adjacent side of 9 and a hypotenuse of 15. What is cos θ?

A) 3/5   B) 4/5   C) 9/15 only when reduced to 5/3   D) 12/15

G-23 · Circle equation center (M2)

What is the center of the circle (x − 2)² + (y + 5)² = 16?

A) (2, 5)   B) (−2, 5)   C) (2, −5)   D) (−2, −5)

G-24 · Area of a sector (M2)

A circle has radius 6. What is the area of a sector with a central angle of 60°?

G-25 · Isosceles triangle angles (M1)

An isosceles triangle has a vertex angle of 40°. What is the measure of each base angle?

G-26 · Similar triangle side (M2)

Two triangles are similar. The smaller has sides 3, 4, 5; the largest side of the larger triangle is 15. What is the shortest side of the larger triangle?

A) 6   B) 9   C) 12   D) 15

G-27 · 45-45-90 triangle (M2)

In a 45-45-90 right triangle, each leg has length 5. What is the length of the hypotenuse?

G-28 · Volume of a sphere (M2)

A sphere has radius 3. What is its volume?

A) 9π   B) 12π   C) 36π   D) 108π

G-29 · Coordinate midpoint (M1)

What is the midpoint of the segment joining (2, 6) and (8, 2)?

G-30 · Exterior angle (M2)

What is the measure of each exterior angle of a regular hexagon?

A) 45°   B) 60°   C) 72°   D) 120°

G-31 · Trig complementary angles (M2)

If cos θ = 4/5 for an acute angle θ, what is sin(90° − θ)?

G-32 · Surface area of a rectangular prism (M2)

A box measures 4 by 3 by 2. What is its total surface area?

G-33 · Radius from area (M1)

A circle has area 49π. What is its radius?

G-34 · Arc measure to length (M2)

A circle has radius 10. An arc subtends a central angle of 90°. What is the length of the arc?

A) 5π   B) 10π   C) 20π   D) 2.5π

G-35 · Angle in a triangle with parallel lines (M2)

Two parallel lines are cut by a transversal. A pair of co-interior (same-side interior) angles is given, one measuring 65°. What is the measure of the other?

G-36 · Diameter and inscribed right angle (M2)

A triangle is inscribed in a circle so that one side is a diameter. What is the measure of the angle opposite that diameter?

A) 45°   B) 60°   C) 90°   D) 120°

G-37 · Degrees to radians (M1)

Convert 120° to radians.

G-38 · Volume comparison (M2)

A cone and a cylinder have the same radius and the same height. The cylinder's volume is 90 cm³. What is the cone's volume?

I-1 · Central idea

"Octopuses possess the ability to change the color and texture of their skin within milliseconds. This camouflage capability, controlled by specialized pigment cells called chromatophores, is unmatched by any other invertebrate. Recent studies suggest that even blind octopuses can match background colors, hinting at a light-sensing capability distributed across the skin itself."

Which choice best states the central claim?

A) Octopuses are the most intelligent invertebrates.   B) Octopus camouflage is exceptionally fast, fine-grained, and possibly skin-mediated.   C) Blind octopuses cannot fully camouflage.   D) Chromatophores evolved for predator avoidance.

I-2 · Logical completion

"Although solar panel costs have fallen ninety percent since 2010, deployment in many regions has lagged. Permits, grid connections, and labor remain comparatively expensive and slow. ____."

A) Therefore, the price of solar panels is the main barrier to deployment.   B) Therefore, non-panel costs may now dominate the total system cost.   C) Therefore, governments should subsidize panel manufacturing.   D) Therefore, solar deployment will reach grid parity within a decade.

I-3 · Textual command of evidence

"A researcher hypothesizes that crows learn to recognize individual human faces. Which finding, if true, would most directly support this hypothesis?"

A) Crows in urban areas are more numerous than in rural areas.   B) Crows that previously interacted with a specific masked researcher gave alarm calls when that mask reappeared, but not when a new mask appeared.   C) Crows produce a wide range of vocalizations.   D) Crows can use simple tools.

I-4 · Quantitative evidence

"A table reports rainfall totals for City X across four years: 2019: 78 cm, 2020: 90 cm, 2021: 85 cm, 2022: 102 cm. Which choice most accurately uses these data to support the claim that rainfall in City X has trended upward over this period?"

A) Rainfall in 2020 exceeded rainfall in 2019.   B) The 2022 value is the highest of the four years.   C) Rainfall increased each year.   D) The four-year mean rainfall is approximately 89 cm.

I-5 · Inference from passage

"Migratory birds rely on a combination of celestial cues, magnetic fields, and landmarks to navigate. When researchers shifted magnetic fields in a controlled environment, even captive-raised birds reoriented in the direction predicted by the new field, suggesting that ____."

A) magnetic orientation can be learned only through prior migration experience   B) magnetic orientation may be present without prior migration experience   C) celestial cues are not used in real migration   D) landmarks are the most important navigational input

I-6 · Detail question

"In the 19th century, the chemist Marcellin Berthelot synthesized organic compounds from inorganic precursors, challenging the long-held belief that organic molecules required a vital force. His syntheses of methanol and acetylene from carbon, hydrogen, and water marked turning points in chemistry."

According to the passage, what was the significance of Berthelot's syntheses?

A) They produced the first commercial fuels.   B) They disproved the idea that organic molecules require a vital force.   C) They led to the discovery of carbon.   D) They were rejected by his contemporaries.

I-7 · Central idea

"Coral reefs occupy less than one percent of the ocean floor, yet they shelter roughly a quarter of all marine species. This disproportion arises from the reef's three-dimensional structure, which multiplies the number of microhabitats available to fish, invertebrates, and algae."

Which choice best states the main idea?

A) Coral reefs are shrinking worldwide.   B) Reefs support outsized biodiversity because their structure creates many microhabitats.   C) Most marine species live in deep water.   D) Algae compete with fish for space on reefs.

I-8 · Logical completion

"Electric vehicles produce no tailpipe emissions, but the electricity that charges them is often generated by burning fossil fuels. In regions whose grids rely heavily on coal, the lifetime emissions of an electric car can approach those of an efficient gasoline car. ____."

A) Therefore, electric vehicles are always cleaner than gasoline vehicles.   B) Therefore, the climate benefit of an electric vehicle depends partly on how its electricity is generated.   C) Therefore, coal is the cleanest source of electricity.   D) Therefore, gasoline cars should be banned.

I-9 · Command of evidence

"A geologist claims that a particular valley was carved by a glacier rather than a river. Which finding, if true, would most directly support this claim?"

A) The valley contains a small modern stream.   B) The valley has a U-shaped cross section and contains scattered boulders far larger than any nearby stream could move.   C) The valley is located in a mountainous region.   D) Sediment at the valley floor is fine-grained.

I-10 · Quantitative evidence

"A table lists the average daily screen time (hours) of students in four grades: 6th 2.1, 7th 2.8, 8th 3.0, 9th 3.6. Which choice most accurately uses the data to support the claim that screen time rises with grade level?"

A) Ninth graders average the most screen time of the four grades.   B) Average screen time increases from each grade to the next.   C) Sixth graders average more than two hours.   D) The difference between 6th and 9th grade exceeds one hour.

I-11 · Central idea

"Tardigrades, often called water bears, can survive conditions that would kill nearly any other animal: boiling heat, the vacuum of space, and doses of radiation hundreds of times the lethal human level. They achieve this by entering a dehydrated, dormant state in which their metabolism nearly stops, then reviving once water returns."

Which choice best states the main idea?

A) Tardigrades are the smallest known animals.   B) Tardigrades endure extreme conditions by entering a dormant, dehydrated state.   C) Tardigrades live only in water.   D) Radiation has no effect on tardigrades.

I-12 · Logical completion

"Many cities have installed sensors that adjust traffic-light timing in real time based on vehicle flow. Early data show shorter average wait times at intersections equipped with the system. ____."

A) Therefore, traffic lights should be removed entirely.   B) Therefore, adaptive timing may reduce delays compared with fixed schedules.   C) Therefore, sensors increase the number of vehicles.   D) Therefore, drivers prefer longer waits.

I-13 · Command of evidence

"A biologist hypothesizes that a certain frog species uses skin toxins acquired from its diet rather than produced internally. Which finding, if true, would most directly support this hypothesis?"

A) The frogs are brightly colored.   B) Frogs raised in captivity on a toxin-free diet produced no skin toxins.   C) The frogs live in tropical forests.   D) The frogs are preyed upon by snakes.

I-14 · Quantitative evidence

"A table lists the recycling rate (percent of waste recycled) for a city across four years: 2018: 22%, 2019: 28%, 2020: 26%, 2021: 34%. Which choice most accurately uses the data to support the claim that the recycling rate generally improved over the period?"

A) The rate increased every year.   B) The 2021 rate was the highest of the four years and exceeded the 2018 rate by 12 percentage points.   C) The rate never exceeded 30%.   D) The 2020 rate was higher than the 2019 rate.

I-15 · Inference

"Researchers found that a species of desert ant counts its steps to find its way home: when they lengthened the ants' legs with tiny stilts, the ants overshot their nest, and when they shortened the legs, the ants stopped short. This suggests that ____."

A) the ants navigate primarily by counting steps rather than by visual landmarks   B) the ants cannot see their nest   C) leg length has no effect on navigation   D) the ants rely entirely on scent trails

I-16 · Detail question

"In the early 1800s, the inventor Sophie Germain submitted her work on the mathematics of vibrating surfaces under a male pseudonym, fearing her ideas would be dismissed because she was a woman. Her analysis later earned a prize from the French Academy of Sciences, though she was barred from attending its sessions."

According to the passage, why did Germain initially use a pseudonym?

A) She had not finished the work.   B) She feared her ideas would be dismissed because she was a woman.   C) She wanted to win a larger prize.   D) The Academy required pseudonyms.

I-17 · Central idea

"Mangrove forests grow where land meets sea, their tangled roots trapping sediment and dissipating wave energy. Coastlines fringed with mangroves suffer markedly less erosion and storm-surge damage than bare shorelines, making the forests a natural form of coastal defense."

Which choice best states the central claim?

A) Mangroves grow only in tropical regions.   B) Mangrove forests protect coastlines by reducing erosion and storm damage.   C) Mangrove roots are difficult to walk through.   D) Storms are becoming more frequent.

I-18 · Logical completion

"Streaming services recommend content using algorithms trained on each user's past viewing. Because these systems favor titles similar to what a user already watched, viewers may rarely encounter genres outside their established habits. ____."

A) Therefore, recommendation algorithms expose users to the widest possible range of content.   B) Therefore, such systems may tend to narrow rather than broaden a viewer's exposure.   C) Therefore, users dislike all recommendations.   D) Therefore, streaming services should stop collecting data.

CR-1 · Vocabulary in context

"The committee's report was praised for its candid assessment of the program's shortcomings."

As used here, "candid" most nearly means:

A) honest   B) photographic   C) brief   D) hostile

CR-2 · Vocabulary in context

"The author's prose is spare, relying on short sentences and concrete nouns."

As used, "spare" most nearly means:

A) extra   B) lean   C) reserved   D) decorative

CR-3 · Purpose of underlined sentence

(Passage describes the Mariana Trench; an underlined sentence reads: "Despite its depth and darkness, the trench teems with life forms uniquely adapted to high pressure.")

The main purpose of the underlined sentence is to:

A) introduce a counterintuitive finding   B) summarize the geological history of the trench   C) describe specific species   D) argue for further exploration

CR-4 · Text structure

"Some economists argue that minimum wage increases raise unemployment among low-skill workers. Others find no such effect in their empirical studies. A recent meta-analysis suggests the estimated effect depends heavily on whether neighboring counties are used as controls."

How does the third sentence function?

A) Provides a definitive resolution to the debate.   B) Suggests a methodological reason for the disagreement.   C) Refutes both prior positions.   D) Introduces a third unrelated position.

CR-5 · Cross-text

"Author A argues that universal basic income (UBI) would reduce poverty without significantly affecting labor supply. Author B, citing experimental data from Finland, argues that while UBI did not measurably reduce work, it also did not produce the dramatic well-being gains UBI advocates predict."

Which best describes Author B's stance toward Author A's claim?

A) Agrees with the labor-supply portion but is skeptical of UBI's broader benefits.   B) Rejects the labor-supply portion entirely.   C) Argues UBI worsens poverty.   D) Asserts Finland's experiment failed.

CR-6 · Vocabulary in context

"The professor's lecture was so dense that students struggled to extract its main argument."

As used, "dense" most nearly means:

A) heavy   B) packed with ideas   C) unclear   D) stubborn

CR-7 · Vocabulary in context

"Early critics dismissed the painter's work, but later generations came to esteem it as a turning point in modern art."

As used here, "esteem" most nearly means:

A) measure   B) regard highly   C) tolerate   D) restore

CR-8 · Purpose of a sentence

(A passage on bee colonies includes the underlined sentence: "It is worth pausing here to note that a single foraging bee may visit several thousand flowers in one day.")

The main purpose of the underlined sentence is to:

A) cast doubt on a prior claim   B) emphasize the scale of an individual bee's activity   C) define a technical term   D) propose a new experiment

CR-9 · Text structure

"For decades, paleontologists assumed that the largest dinosaurs were sluggish. Newer biomechanical models, however, indicate that some could move at a brisk trot. The reversal stems less from new fossils than from improved methods of estimating muscle force."

How does the final sentence function?

A) It introduces an unrelated topic.   B) It explains why the earlier view changed.   C) It restates the opening assumption.   D) It questions the newer models.

CR-10 · Cross-text comparison

"Author A contends that remote work permanently raises productivity by eliminating commutes and interruptions. Author B, drawing on surveys of new employees, argues that remote work weakens the informal mentoring that helps newcomers ramp up, so its productivity effects may be uneven across experience levels."

Which best describes how Author B would most likely respond to Author A?

A) By fully agreeing that remote work raises productivity for everyone.   B) By noting that the benefit may not extend to less-experienced workers.   C) By denying that commuting affects productivity.   D) By arguing remote work has no effect at all.

CR-11 · Vocabulary in context

"The treaty's language was deliberately ambiguous, allowing each side to claim it had won the concessions it sought."

As used here, "ambiguous" most nearly means:

A) hostile   B) open to more than one interpretation   C) lengthy   D) outdated

CR-12 · Vocabulary in context

"Far from being static, the dune field shifts shape with every season's winds."

As used, "static" most nearly means:

A) electric   B) unchanging   C) noisy   D) crowded

CR-13 · Purpose of a sentence

(A passage on urban gardens includes the underlined sentence: "Consider that a single rooftop plot in the study yielded more vegetables per square meter than a conventional rural farm.")

The main purpose of the underlined sentence is to:

A) introduce an unrelated comparison   B) provide a striking example that supports the passage's point about urban yield   C) define a farming term   D) cast doubt on the study

CR-14 · Text structure

"For years, conservationists assumed that reintroducing wolves would simply reduce deer numbers. Subsequent studies revealed a broader effect: by changing where deer grazed, the wolves allowed riverbank vegetation to recover, which in turn stabilized the riverbanks themselves."

How does the second sentence function in relation to the first?

A) It restates the first sentence.   B) It replaces a narrow expectation with a more far-reaching finding.   C) It contradicts the existence of wolves.   D) It introduces an unrelated topic.

CR-15 · Cross-text comparison

"Author A argues that standardized testing provides an objective benchmark that lets colleges compare students from very different schools. Author B counters that test scores correlate strongly with family income, so the 'objective' benchmark partly measures advantage rather than ability."

Which best describes Author B's response to Author A?

A) B agrees the tests are fully objective.   B) B challenges the claim of objectivity by pointing to a confounding factor.   C) B argues testing should be expanded.   D) B denies that schools differ.

CR-16 · Vocabulary in context

"The young composer's style was openly derivative, echoing the masters she had studied before she found her own voice."

As used here, "derivative" most nearly means:

A) original   B) imitative   C) mathematical   D) profitable

CR-17 · Purpose of a phrase

(A passage on glaciers reads: "The ice, it turns out, is anything but still.")

The main rhetorical purpose of this sentence is to:

A) introduce a surprising correction to a common assumption   B) summarize measurement methods   C) define the word "glacier"   D) concede an opposing argument

CR-18 · Text structure

"Most histories credit a single inventor with the light bulb. In reality, dozens of researchers across several countries developed competing versions over decades; the famous patent represents the endpoint of that collective effort, not its origin."

How does the passage primarily develop its point?

A) By offering a step-by-step set of instructions.   B) By correcting a popular oversimplification with a fuller account.   C) By comparing two unrelated inventions.   D) By predicting future technology.

T-1 · Cause-effect

"The exhibit drew record crowds in its first week. ____, the museum extended its hours through the end of the month."

A) However   B) For example   C) As a result   D) In contrast

T-2 · Contrast

"Most reviews emphasized the novel's plot. ____, several critics argued the book's real achievement lay in its prose style."

A) Therefore   B) Specifically   C) However   D) Similarly

T-3 · Example

"Many crystalline minerals exhibit remarkable structural symmetry. ____, halite forms perfect cubes whose faces meet at right angles."

A) However   B) For example   C) Nevertheless   D) In addition

T-4 · Concession

"The proposed bridge would shorten travel time considerably. ____, environmental groups have raised concerns about its impact on the river ecosystem."

A) Therefore   B) Nonetheless   C) For instance   D) Likewise

T-5 · Restatement / specification

"The new policy prioritizes prevention over treatment. ____, hospitals will be funded based on community health metrics rather than admissions."

A) However   B) Specifically   C) On the contrary   D) Earlier

T-6 · Conclusion

"The data show consistent gains across all three pilot regions. The trend held even after controlling for income. ____, the intervention appears effective regardless of local economic conditions."

A) Nevertheless   B) For example   C) Thus   D) Meanwhile

T-7 · Addition

"The new alloy is far lighter than steel. ____, it resists corrosion better than most metals currently used in shipbuilding."

A) However   B) In addition   C) For example   D) In contrast

T-8 · Contrast

"Surveys suggested the candidate would win easily. ____, the final vote was nearly tied."

A) Likewise   B) Therefore   C) However   D) For instance

T-9 · Cause-effect

"Heavy rains saturated the soil for three straight weeks. ____, the hillside gave way in a sudden landslide."

A) Nevertheless   B) Consequently   C) For example   D) Similarly

T-10 · Sequence

"First the dough is kneaded and left to rise. ____, it is shaped into loaves and baked at high heat."

A) However   B) In contrast   C) Next   D) Nevertheless

T-11 · Concession

"The medication relieved symptoms within hours. ____, some patients reported mild side effects that lingered for days."

A) Therefore   B) Still   C) For example   D) Likewise

T-12 · Example

"Several everyday materials change properties dramatically when cooled. ____, rubber becomes brittle enough to shatter when dipped in liquid nitrogen."

A) However   B) For instance   C) Therefore   D) In contrast

S-1 · Goal-driven sentence

Notes:

• The Antikythera mechanism is an ancient Greek analog computer.
• It was discovered in 1901 in a shipwreck off Antikythera.
• It was used to predict astronomical positions and eclipses.
• It dates to approximately the late 2nd century BCE.

Goal: Introduce the Antikythera mechanism to an audience unfamiliar with it.

A) Discovered in 1901, the Antikythera mechanism dates to the late 2nd century BCE.
B) The Antikythera mechanism, discovered in 1901, was used to predict astronomical positions.
C) The Antikythera mechanism is an ancient Greek analog computer used to predict astronomical positions and eclipses.
D) The Antikythera mechanism was discovered off the island of Antikythera in 1901.

S-2 · Emphasize a comparison

Notes:

• Quokkas live on Rottnest Island, Australia.
• They weigh 2.5–5 kg.
• Tree kangaroos live in New Guinea rainforests.
• They weigh 7–14 kg.

Goal: Emphasize a key difference between quokkas and tree kangaroos.

A) Quokkas live on Rottnest Island in Australia, while tree kangaroos live in the rainforests of New Guinea.
B) Quokkas weigh 2.5 to 5 kg, considerably less than tree kangaroos, which weigh 7 to 14 kg.
C) Both quokkas and tree kangaroos are marsupials.
D) Tree kangaroos and quokkas inhabit very different ecosystems.

S-3 · Concluding sentence

Notes:

• A team studied 240 retired professional musicians.
• Average age was 68.
• Musicians scored higher than non-musicians on tests of auditory working memory.
• No significant difference appeared on visual working memory.

Goal: Summarize the study's primary finding for a general audience.

A) The study's design was robust.   B) Musicians outperformed non-musicians on tests of auditory, but not visual, working memory.   C) Musicians age more slowly than non-musicians.   D) The study examined 240 retired musicians.

S-4 · Goal-driven sentence

Notes:

• The kakapo is a flightless parrot native to New Zealand.
• It is nocturnal and one of the world's heaviest parrots.
• It was once nearly extinct, with fewer than 60 birds in the 1990s.
• Conservation efforts have since increased the population.

Goal: Introduce the kakapo to an audience unfamiliar with it.

A) The kakapo numbered fewer than 60 birds in the 1990s.
B) The kakapo is a nocturnal, flightless parrot native to New Zealand and one of the heaviest parrots in the world.
C) Conservation efforts have increased the kakapo population.
D) The kakapo is nocturnal.

S-5 · Emphasize a contrast

Notes:

• The first design used 1,200 parts.
• It took 14 hours to assemble.
• The redesigned version used 300 parts.
• It took 3 hours to assemble.

Goal: Emphasize how much simpler the redesign is.

A) The first design used 1,200 parts, while the redesign used only 300 and assembled in a quarter of the time.
B) Both designs were eventually assembled.
C) The redesign used 300 parts.
D) The first design took 14 hours to assemble.

S-6 · Concluding sentence

Notes:

• A study tracked 500 commuters who switched from driving to cycling.
• Average resting heart rate dropped over six months.
• Self-reported stress levels also declined.
• Commute times were largely unchanged.

Goal: Summarize the study's main health-related findings.

A) The study tracked 500 commuters.   B) Switching to cycling was associated with a lower resting heart rate and reduced stress, without lengthening commute times.   C) Commute times were unchanged.   D) Cycling is faster than driving.

S-7 · Emphasize a similarity

Notes:

• The Atacama Desert receives almost no rainfall.
• Parts of Antarctica's Dry Valleys also receive almost no rainfall.
• Both are studied as analogs for the surface of Mars.

Goal: Emphasize a key similarity between the two regions relevant to Mars research.

A) The Atacama Desert is in South America.   B) Like Antarctica's Dry Valleys, the Atacama Desert is so dry that scientists study both as analogs for the Martian surface.   C) Antarctica is cold.   D) The Atacama Desert receives almost no rainfall.

S-8 · Goal-driven sentence

Notes:

• Bioluminescent waves are caused by tiny organisms called dinoflagellates.
• The organisms emit light when disturbed by motion.
• The glow appears blue.
• It can be seen along certain coastlines at night.

Goal: Explain what causes the glowing waves.

A) The glow appears blue and can be seen at night.   B) Glowing waves occur along certain coastlines.   C) The blue glow of certain waves is produced by dinoflagellates, microorganisms that emit light when disturbed by motion.   D) Dinoflagellates are microorganisms.

S-9 · Emphasize a result

Notes:

• A library replaced late fees with automatic renewals in 2021.
• Before the change, 18% of borrowers had overdue items.
• After the change, 4% had overdue items.
• Total checkouts rose by 30%.

Goal: Emphasize the effect of the policy change.

A) The library made a policy change in 2021.   B) After the library replaced late fees with automatic renewals, overdue items fell from 18% to 4% and total checkouts rose 30%.   C) The library used to charge late fees.   D) Automatic renewals were introduced.

C-1 · Joining clauses

"The committee reviewed the proposal carefully ____ they delivered their verdict the following week."

A) carefully,   B) carefully;   C) carefully and   D) carefully, and

C-2 · Subject-verb agreement

"The list of approved candidates ____ posted on the bulletin board."

A) is   B) are   C) were   D) have been

C-3 · Dangling modifier

"Walking through the gallery, ____."

A) the paintings impressed her   B) it was an impressive experience   C) she was impressed by the paintings   D) the experience impressed her

C-4 · Colon usage

"The kit included three essential items ____ a flashlight, a notebook, and a compass."

A) —   B) :   C) ;   D) ,

C-5 · Possessive apostrophe

"The ____ favorite exhibit closed last week."

A) childrens   B) children's   C) childrens'   D) childrens's

C-6 · Pronoun agreement

"Each of the volunteers brought ____ own tools to the site."

A) their   B) his or her   C) its   D) there

C-7 · Verb tense consistency

"By the time the conference started, the keynote speaker ____ already arrived."

A) has   B) had   C) was   D) will have

C-8 · Comma splice

"The data are surprising, the researchers plan to replicate the study next year."

Which best corrects this sentence?

A) (no change)   B) surprising; the   C) surprising the   D) surprising, the researchers, plan

C-9 · Non-essential modifier

"The novel ____ was published in 1924 ____ remains widely read today."

Which choice uses paired commas to set off a non-essential modifier?

A) , which,   B) which   C) , which   D) — which

C-10 · Misplaced modifier

"Running across the meadow, the photographer caught the deer in mid-leap."

What is the issue and how to fix?

C-11 · Subject-verb agreement (intervening phrase)

"The collection of rare manuscripts ____ stored in a climate-controlled vault."

A) are   B) were   C) is   D) have been

C-12 · Semicolon vs comma

"The river had risen overnight ____ the bridge remained passable by morning."

A) overnight,   B) overnight;   C) overnight   D) overnight, but,

C-13 · Apostrophe: plural possessive

"The three ____ schedules were finally aligned for the project."

A) managers   B) manager's   C) managers'   D) managers's

C-14 · Dangling/misplaced modifier

"Having studied all night, ____."

A) the exam felt easy to Maria   B) Maria found the exam easy   C) it was an easy exam for Maria   D) the questions seemed easy

C-15 · Colon to introduce an explanation

"The recipe failed for one reason ____ the oven had never reached the required temperature."

A) ,   B) ;   C) :   D) and

C-16 · Pronoun-antecedent agreement

"Neither of the two proposals included ____ projected budget in the appendix."

A) their   B) its   C) they're   D) there

C-17 · Subject-verb agreement

"The team of engineers ____ meeting to finalize the blueprint."

A) are   B) is   C) were   D) have been

C-18 · Verb tense

"Last summer, the museum ____ a major exhibit on ancient navigation."

A) hosts   B) will host   C) hosted   D) has hosted

C-19 · Possessive vs. plural

"The ____ wings shimmered in the morning light as it left the cocoon."

A) butterflys   B) butterflies   C) butterfly's   D) butterflies'

C-20 · Joining two independent clauses

"The trail was steep and rocky ____ the hikers reached the summit before noon."

A) , so   B) ,   C) so   D) ; so

C-21 · Pronoun-antecedent agreement

"Every member of the orchestra tuned ____ instrument before the performance."

A) their   B) his or her   C) its   D) they're

C-22 · Colon to introduce a list

"The lab restocked three supplies ____ beakers, gloves, and pipettes."

A) ,   B) ;   C) :   D) and

C-23 · Non-essential modifier punctuation

"The author's first novel ____ which she wrote at nineteen ____ won a national award."

Which pair correctly sets off the non-essential clause?

A) , … ,   B) , … (no punctuation)   C) (no punctuation) … ,   D) ; … ;

C-24 · Comma splice correction

"The shipment arrived early, the warehouse staff had not finished clearing space."

Which best corrects the sentence?

A) (no change)   B) early; the   C) early the   D) early, the warehouse, staff

C-25 · Subject-verb agreement with "or"

"Either the manager or the assistants ____ responsible for closing the store."

A) is   B) are   C) was   D) has been

C-26 · Modifier placement

"Covered in fresh snow, ____."

A) the hikers admired the peaks   B) the peaks looked majestic to the hikers   C) it was a majestic view   D) the view was admired

C-27 · Apostrophe in a contraction vs. possessive

"____ clear from the data that the new method reduces waste."

A) Its   B) It's   C) Its'   D) Their

C-28 · Parallel structure

"The internship taught her to analyze data, to write reports, and ____ presentations to clients."

A) delivering   B) to deliver   C) delivered   D) she delivered